text:
Do professors like answering questions from non-students/private citizens?
I am a non-student/private citizen and I am eager to meet with professors at universities in my area so I can ask these professors a particular question about a particular subject matter.  I want to ask them the same question to see if they all will give me the same answer.  Based on their answers, I will then decide whether or not to pursue writing an article to be published which relates to this particular subject matter.
I have sent emails to six local universities requesting a meeting with a professor in this particular area of study and so far I have only received one e-mail reply. In that one email reply, the professor suggested that I meet instead with one of their graduate students because his consultation fee is very high. I am still waiting for the professor to provide me with the names of these grad students.
I have decided to wait at least a week before sending follow-up e-mails, or perhaps calling them directly to ask for an appointment, because I realize that professors are busy people.
This experience with trying to communicate with college professors makes me wonder if professors, in general, like answering questions from non-students/private citizens. Is it safe to say that professors, in general, would prefer that non-students/private citizens seek answers from subject matter experts in the private sector?

Seems heavily linked to https://academia.stackexchange.com/q/133956/72855

@SolarMike, it is related to that question.

Yes, I thought it was...

"because his consultation fee is very high" --- Clearly this isn't pure mathematics!

@DaveLRenfro or, the professor really does not want to meet with the OP. I have known Professors who vase consultation fee based upon their desire to work with the client.

Who are people who are not private citizens?

@user2705196, good point. I guess I could have said '...those who are non-academia'.

@Richard Erickson : So does that mean it would be wrong to pay the fee if one had the requisite pile of money?

@The_Sympathizer If someone wants to spend a "pile of money" to buy a professor's time, there is nothing inherently wrong with the transaction (unless the transactions violates university policies or other laws). However, as the conman's saying goes There's a sucker born every minute and I suspect the person's money would be better spent on other endeavors.

@Richard Erickson : So then how can they best get the trustworthy information they seek in this context?

As in general, people are typically happy to be asked to exercise/express their expertise on the things they've worked their whole lives to understand.
But/and the most expert people are very busy, working on moving forward in that.
So their time is very valuable.
So an email response is much preferred, typically. The email back-and-forth, to arrange a physical meeting, is not preferred...
And if I, for one, found out that my opinion as a professional whatever was just supposed to be one vote out of some larger number... for the potentially misguided project of an amateur... I'd most likely not agree to spend the time. It's disrespectful, whatever you feel about that, for non-experts to think that the time of experts is at their disposal in this way, for free, etc. Be serious.
Many academics are kind and generous, but like to have just a token of respect and appreciation (rather than big bucks).

+1, particularly for the penultimate paragraph

@paul garrett, in each of the e-mails that I sent to these professors I told them that I would pay them a consultation fee and I did not request for a meeting on a particular date or time, I was leaving that decision up to them. I also told them that I would only need about 15 minutes of their time.  I have the upmost respect for those in academia and its unfortunate that you think that I am being disrespectful.

@HRIATEXP I actually work as a consultant (free-lancer) on the side to pay the bills as I start academia. Its not "you" are disrespectful its those types of emails are disrespectful (even the ones that offer to pay, I get these too and the numbers are low compared to my standard rates).

@HRIATEXP, re "I also told them that I would only need about 15 minutes of their time." Experience quickly teaches that other people's estimates of how long it will take you to answer a question are rarely accurate.

First, you do not request meetings. You should kindly ask for a moment of their valuable time. Second, be prepared to share your research design upfront including a description of what questions you are trying to answer, how are you going to analyze the data and how you handle participants privacy. If your research idea is interesting and design solid, there is a good chance to get access to actual peope.

What do you mean by "one vote"? Do you mean that it is wrong for amateurs to seek guidance from them?

@JGreenwell : then what is respectful? How do you get the guidance you need in the genuinely right way?

Moreover, given the fact that he was willing to pay them fees suggests he understands already that the "time is valuable", but he doesn't know how to properly put that understanding into proper action, and what is needed is a post that will not only answer the question given here, but  also to detail the proper action here meaning the proper way to show respect that will be understood as such.

Most researchers I know - including myself - are happy to discuss honest questions from the public. What most researchers do not particularly like, is to be part of a session where the asker either has a hidden agenda (why don't you just ask your question in an email?) or does not put any value to the time put into doing such sessions (do you really need to ask multiple professors? To me, that approach would put you directly in the spam category).
I would suggest that you simply write the question directly to the professor suggesting you to meet up with the grad student, and possibly ask him/her to forward it.

that is good advice. I think I will wait about a week and then send emails requesting a meeting with a grad student at each of these universities.

@HRIATEXP Even that seems pretty rude to me. You can maybe ask one person. Don't turn this into a test or survey. Don't waste the time of 4 different people.

@BryanKrause, this is an eye opener for me. I had no idea that it is considered to be disrespectful to seek an answer/opinion to a particular inquiry from more than one professor. At this point, I have decided to give up on the whole matter and will instead only seek answers from subject matter experts working in the private sector.

@HRIATEXP again, I still work in industry and I can assure you private emails offering to pay me for my opinion on subject X are all deleted as spam because they tend to be spam. All my consulting contracts started with an email from an official business address versus the hundreds of "head-hunter" or "research needed on subject 83728 for $xxxxx.xx dollars an hour" a week from gmail or other private accts which never even make it past my spam filter. In academia, we like our research and are not only in it for the money so might answer - in industry: consult only after agreement is signed.

There is really no need to try and play clever tricks here. Write down the question the best you can, and send it as a polite request to the person you've had the best interaction with previously. Don't mention consulting fees. Don't solicit the opinion of several. Don't mention private sector or other grievances. Just this.

@nabla : Don't accuse him of something ulterior when it seems and I empathize with that he likely genuinely does not know. This issue touches very closely on something I have been going through personally right now, to much grief, and I take this thread and everything said in it EXTREMELY seriously as a result. Heck, even, wanting to "spam" things could very well be the result of a long, LONG build-up process of frustration with not really knowing what the GENUINELY "right" way is.

@JGreenwell : I suspect though that people who put down "$xxxxx.xx per hour" are trying simplistically to humour the idea that the "time is valuable", yet don't know of a better way. Detailing those better ways, on a public forum, in explicit, algorithmic and non-assumptive terms, can benefit a great, great many people (regardless of the specific one that precipitated it - my thought process is always on "someone can/will benefit from this".).

@nabla : (by "accuse of something ulterior" I mean when you said "try and play clever tricks". By saying "tricks" it suggests you're assuming he's just trying to make mischief, which is just that, an assumption. You have no clue [unless you evidence that you have closer contacts] as to how this person you just met [unless you can evidence same] actually feels and/or thinks internally.

Some people are not good communicators, and also, very often the most logical way to state something seems to end up carrying some kind of "load" due to various prejudices on the part of the listener and it may not be at all clear then, esp. to such non-good communicators, how to get that across if one really means what one is saying.)

@The_Sympathizer no, I meant that literally: I looked at my spam folder (the amount on the last one was "$100.00 per hour"). I looked at it more carefully, it was a phishing email. Hence, most job offers that are not from official sources or one of the few agencies I've used over the years - are filtered out due to safety concerns (viruses, phishing, etc).

STOP.  If you have an agenda (such as asking and comparing answers) this will be rapidly known, especially if you limit yourself to a single university.
Please read a lot of relevant literature before contacting anyone: if you are not current with the literature chances are your meetings will be very short and you will be ignored as yet another crackpot amateur.  Bear in mind that your chances of successfully publishing as a non-student/private citizen are extremely small.
Note: Unfortunately every so often I meet someone with an alternate method to solve a question for which the current paradigm works perfectly well.  There’s no harm in this of course, but the method fails at any other problem except the original.  In all cases I can remember the author had not done proper prior research and did not realize how much the current paradigm explained, and how little this new approach did beyond the initial problem.  Often non-specialist fail to appreciate the level of professionalism required to perform at the research level in any field.
As a result, most non-specialists are dismissed simply because of poor background preparation.  All crackpots fall in this category but not all in this category are crackpots so it is incumbent on the non-specialist to be well prepared.

if you only knew the particular question that I was planning to ask these professors I think you would agree that it was wise for me to try to get multiple opinions before putting my question and the answer to it out on the public domain, which I plan to do in the near future. Time will tell.

@HRIATEXP With due respect your comment does not inspire confidence and is in like with what crackpots say; please be more forthcoming with people you contact.

@HRIATEXP: I agree with ZeroTheHero's comment on your comment, and given what you said (in your comment), I think it would be helpful for you to read over the many internet postings/lists about how to identify cranks (these have been posted since at least the late 1990s), if for no other reason than to assist you in getting past people's hardened "mental crank filters".

@ZeroTheHero and Dave L Renfro, I am not a crackpot or a crank. I have never been into conspiracy theories, nor do I wear a tin foil hat, and I've never made an argument for the existence of UFOs/aliens, etc., etc.  I have also watched many Youtube videos about people considered by the scientific community to be crackpots/cranks. I consider myself to be a very sound-minded, rational, and analytical individual who has experienced an 'scientific epiphany' and I am struggling with finding the best way to share it with the scientific community.

@HRIATEXP We've never met and it's not for me to decide on the merit of your idea without having additional details so please take my comment to be friendly and simply meant to lower your expectations: from the information available here, you are likely to be ignored as a crackpot simply on the basis of probabilities.  Overcoming this perception will be a serious challenge unless you can display some mastery of the topic by understanding relevant recent papers and reviews on the topic.  Unfortunately simply having a "scientific epiphany" is not enough.

@HRIATEXP Cranks are not necessarily conspiracy theorists; they almost certainly don't self identify as one. "I consider myself to be a very sound-minded, rational, and analytical individual who has experienced an 'scientific epiphany'" - this is the sort of sentence a crank utters and is exactly what you would find if you followed Dave's advice. https://en.wikipedia.org/wiki/Crank_(person)

@ZeroTheHero, fair enough. I will try to find recent papers to support my theory and bring those to an interview with a professor if/when I get one.

@BryanKrause, so I guess it is safe to say that the academic/scientific community considers all amateur scientists to be cranks until they can prove that they are not cranks, yes?

@HRIATEXP No, they consider amateurs who claim they have solved an open problem without any background to be cranks until they demonstrate otherwise. I think people that fall into that category don't recognize how common they are. Here's an example of the effort it takes: https://www.cnn.com/2019/07/27/health/doug-lindsay-invented-surgery-trnd/index.html Most amateur scientists want to learn to be professional scientists: academics deal with them all the time, they are called students, and they only have to prove they are interested, capable, and willing to learn.

@HRIATEXP : Could you email to me what the question you have is? I am curious.

@The_Sympathizer, I'm sorry but I cannot do this at this time, but perhaps in a couple of weeks from now I will.

@HRIATEXP : thx :)

Call them and ask the question. It is much easier to get 5-10 minutes informally with someone on the phone than expecting them to write a well worded e-mail. If your question takes more than 10 minutes to answer you really should compensate them in one way or another.

Do not under any circumstances call them uninvited.

@d-b, my question cannot be convened only verbally. It's necessary that I show the professor a drawing that I have made as I explain what it is all about and what I believe the end result will be.

@Maeher I have called several professors and similar and asked them politely if they have time for a question. Most of the time they have been very helpful. Never have they been hostile. Sometimes they have said "I only have a couple of minutes".

@d-b, actually a few minutes may be all that I would need.

@d-b Obviously most people are polite. That doesn't in any way imply that they were happy about you calling them.

@Maeher : How then is he supposed to know what their actual feelings are?

@Maeher I reckon this is adults and they are capable of denying a request they don't have time for. This is no different than calling a neighbour or acquaintance and ask them for a quick favour.


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How to structure presentation to avoid getting questions that will be answered later in the presentation?
In the past when I've given presentations at my lab and conferences, I've not had to deal with this problem. But at my new institution I'm constantly dealing with the following phenomena.
I'm constantly being asked questions that will be answered later in the slides.
First try, I tried top down approach. So I started with the overall problem. I work in AI, so in my particular situation, I start off by saying this is the problem we're trying to solve, here's the overall architecture and now let's analyze the individual components. But then, I'm constantly bombarded with, well what about this component, what about this metric, can you go deeper into just that one component - I don't understand the mechanics behind it, etc. And all these questions will be answered later on. But no one seems to wait to see what the next slides are going to be.
Second try, I tried bottom up approach. "Here are all the individual tools you'll need to understand the overall architecture. Here are the metrics, here are individual mathematical concepts, etc. Now, let's see how these are incorporated into a larger framework." But before I can explain what the larger frameworks are, at every slide, they're constantly asking, wait, why is this being used, why are you talking about this, etc etc.
I understand questions arise and I can simply say I'll cover it in the next few slides. But there are sooo many questions being constantly asked and it completely throws off the presentation because constant tangents are being drawn and one person's question confuses another person. This isn't a classroom setting, it's more of a lab setting.
How can I get around this? The only solution I can think of is to have a little box on each slide, right about the page number that has the title of the next page.
Any advice on dealing with this would be very helpful!
Update: After listening to everyone's suggestion, the following tips really helped solve this problem.

Preparing slides to control the conversation. Focusing on only what I prepared instead of making all encompassing slides. For example, if I want to convey the training procedure of a neural network, then only have details regarding input, output, architecture(not every detail, just overview), and the loss functions. Stating "I used equation 'x' because it does will in situations 'a' and 'b'," instead of pasting the actual equations and inciting more questions for understanding every detail of the equation (as was happening previously). But I keep more detailed notes in the appendix slides in case anyone has a very specific question.
If someone does have a very specific question, then I can refer them to the appendix of these slides and say "Thank you, that's a great question. I have lots of information regarding that in the appendix of these slides. But due to time constraints, let's take that conversation offline."
Sending the audience the slides and notes before your talk so that people can review the slides before hand and better prepare their thoughts before asking random left-field questions during the actual presentation. This doesn't work in conferences, but definitely helps in lab settings.
When stating a key concept in a slide that hasn't been addressed previously, I have a small textbox that says "will be covered in upcoming slides" in red lettering. This seemed to curtail a lot of questions as the audience no longer feels anxiety over not understanding something on the slide.
Right after the title slide, I had a "goals of today's talk" slide in which I stated "goal is not to explain every detail of a particular technique. Rather present overview and my adaptation of it."

Disclaimer: the above suggestions work great if you're presenting at an internal team conference amongst peers. For example, an R&D lab at a tech company (my situation) or in an academic lab setting. Doesn't go great in a conference, but the audience are generally kinder in such public avenues.

If it happens in a scenario like weekly group meeting isn't tgat dramatic. If it is otherwise, I agree with Solar Mike.

You could hand out a detailed outline.

Well, if it is a presentation, and this particular problem crops up all the time, perhaps a short intro (with possibly slides showing a bit more detailed table of contents of the points you're going to talk about) would help?

I wonder if you are phrasing your points in a way that implies that you will not be covering a particular topic. For example, if you introduce a particular term before you define it, you are guaranteed to be asked what it means, even if you plan to define it on the next slide.  Minor word choice makes a difference - instead of saying "The conditions guarantee that..." you should say "There are certain conditions that guarantee that...". The first wording makes the audience think that they should already know the conditions while the second implies further explanation is coming.

A good talk should unfold like a thriller, with appropriate foreshadowing. The obvious questions are anticipated with hints of possible answers, and the audience knows just enough of the intrigue to keep them turning the pages.

Only take questions at the end?

I'm constantly being asked questions that will be answered later in the slides.

You have to understand that this is a great problem to have. There is nothing worse than giving a presentation and facing a bunch of blank stares. Questions mean that

People actually understand what you're talking about.
They care enough about your idea to actually ask.
The problem you're explaining is not trivial.
You actually have an answer to the question - later in the slides!

You mention both conference talks and lab talks. In the first case you need to be a bit more prompt (always respect the time assigned to you in a conference, you're not alone and you'll put everyone in an awkward position if you go over time): just say "this is a great question, can we wait for the next slides?" or "can we take it offline?". I have yet to have seen anyone respond to this by insisting that you answer them right now.

But there are sooo many questions being constantly asked and it completely throws off the presentation because constant tangents are being drawn and one person's question confuses another person.

This is less a problem of structure than a problem of you not controlling the discussion. If there are many questions and people start discussing amongst themselves you need to take command of the room - say, "it's great that we're having this discussion, but I'd really like to move forward!", or something to that effect.
I believe that neither of your approaches (if I understand them correctly) is as effective as it can be. In conference presentations you need to focus on one big idea and explain it well - the objective of the presentation is to get people to read (and cite) your amazing new paper. Avoid giving broad overviews, and getting into every little detail. The audience needs to know why they should spend time reading your paper, and that's it.
In lab presentations make sure that the group knows what the big plan for today is. If there is a constructive discussion that's great. Tell them in the beginning the big points and then try to cover everything else. Give references to stuff you didn't cover so that the group knows where to look for things that weren't covered in the presentation.
Good luck!

Such a good answer, wish I could give more than one upvote.

To provide a counterpoint to your 4 (positive) justifications for getting questions, there could be a 5th reason for the questions - the OP is not good at giving presentations.

Usually I hear comments like "I believe your question will be answered soon in the presentation, let me get through it and if you still have a question at the end please ask then"

A frequent method I have seen and used (granted mostly in military and business) for a topic that tends to get a lot of questions, is you start the briefing with a statement to the effect of "Please hold all questions until the end", or setting aside a slide between sections or logical breaks to answer questions on the section/topic just covered.  The first one works great for generally short briefings where you don't have to worry much about attention falloff.  The second one refreshes and re-engages the audience.  Both help you keep within your time limits.

This is not a great problem to have. While questioners who take you off on tangents may have good intentions, this detracts from your ability to share your presentation effectively with those who patiently wait for it to unfurl in the manner you intended it to. Don't take the attention from a handful of people to be an indication that your presentation is well received. It can actually prevent otherwise interested listeners from having the opportunity to benefit in the way you intended them to.

There’s a point to be made about being a good audience member as well! Hint: it’s not your personal show...

My experience is that when people don’t understand, they completely zone out (at least in conferences)

+1 from me. I think the only thing that I would add is that it can be very effective if the speaker thanks the questioner for their question, acknowledges that it's a great question, and says something like 'thanks very much, we're coming to that in a few slides time/hold that thought, we'll come back to it'

Thank you for all these great suggestions!

For some people, the second something enters their brain it comes out their mouth, leading to a constant stream of questions and comments until you shut them down somehow. It may may for a nice contribution if they are smart, but can be quite the opposite if they are not smart.

@Spark Please see updated OP. Thanks for your help!

Glad to hear it. I draw a lot of inspiration from Simon Peyton Jones’ talks on giving good talks. Look him up!

Make it clear at the start that you will take questions at the end.
Then, when someone interrupts with a question, don't answer, but say: "please keep that question for the end" and continue.
If you stick to it then it will work, if you answer just one question you have failed...

Many supervisors would not appreciate this response from a student.

@AnonymousPhysicist Many supervisors would not appreciate being interrupted in their own presentations and ask for questions at the end...

It's all about managing expectations. If someone interrupts and you know it's going to be answered later, you can also say, "I'll get to that in just a little bit." Adding in a "You're one step ahead of me" will make you ignoring their question a little easier to take.

@Solar Mike Many supervisors are, well, supervisors, so as a student you would likely depend on their good will way way more than they would on yours...

@Headcrab Most conference attendees won't be your supervisor...

I would consider "when someone interupts with a question don’t answer, but say 'please keep that question for the end' and continue" to be a rather arrogant way to put it, especially if it's coming from a colleague

@posdef I had a colleague that would interrupt anybody in meetings to "take over" their point to steal the glory. So after a while most of us noticed... The way I dealt with it was to wait for a clear moment where I would say "anyone have a point here? because I would like to make the following"... The manager talked to me afterwards to say that they had seen that colleague's behavior and it was not doing them any favors...

@SolarMike I understand where you are coming from, I'd just initially not consider malicious or at least self-promoting intent. Also it's a bit unclear from the OP if the many questions come from the same individual consistently or rather many people chime in here and there.

@posdef I think the OP is having the problem in some type of "internal meeting" not at conferences... If that is time limited, and they usually are, then keeping questions to the end is effective as it maximizes the presentation time.

Use a more defensive wording and most supervisors will understand. A "I will come to this in minute" should usually work. After you got to the slide, you can ask back "is your question from 3 slides ago answered? Otherwise we can discuss it now".

I disagree with this.  Sometimes there is a crucial point that the speaker doesn't address - if this happens, much of the audience will be lost if they don't have a chance to interject in the moment, and the value of the talk after that point is diminished.  Furthermore, audience members may feel embarrassed to ask such a basic question at the end, for fear of revealing that they didn't understand most of the talk.

@JairTaylor Given the statement by the OP that they have made several presentations, then I don't think he will be likely to leave out something crucial, unlike a presenter doing their first one...

@SolarMike Whether a point is crucial or not depends on the audience more than the speaker.  For one group it might be taken as obvious, for another group not so much.  I've seen many experienced speakers wrongly assume that the audience would easily understand a given detail.  In any case, presenters are human, and sometimes mistakes are made - even one typo can seriously derail a math talk.

@JairTaylor I just love the stunning silence when a person asks a question and the whole audience looks at them..... then they realize they have just asked something so.... blindingly obvious...

"No questions till the end" is too rigid for almost all types of presentations.  As @JairTaylor said, there are questions that occur during a presentation that are really important to answer during the presentation.  This doesn't have to be about "crucial information" either.  A person very familiar with some topic may leave something out (or fail to clarify a point) that seems obvious to them but non-obvious to the members of the audience less familiar with the subject material.  A good example would be a general clarification or defining a jargon term or acronym.

@eps then you should post your own answer...

I completely agree with the answer given by Spark. It is as much of a luxury problem as it ever gets in academia (maybe with the exception of having too much grant money and too few projects/staff).
To add on to that answer, I would like to give a couple of tips/insights on presentation techniques which may help you see this from a different angle.
First off, remember it all makes sense for you and for you alone. Often enough, connections and relations that may seem obvious to you will not be as obvious to someone else who has been thinking about other problems up until (and possibly even during your talk). So you need to take your audience by the hand and guide them through what you want to say. (Also related, but slightly off-topic, there is a saying in literature "The author is dead" meaning when you are reading something you cannot ask questions since the author is not there. However, during a talk you can very much ask questions about bits and pieces that do not make sense for you. Some people do that, and at time over zealously)
So, what can you do? I for one appreciate the introspection you seem to show and that you have tried different approaches. Either approach is fine, I'd say, but as you have commented neither is a solution alone.
I would suggest having some "meta-talk" within your talk. Overview/Agenda slides are particularly good for this purpose. You can tell people what you intend to go through/cover in your talk, how the concepts relate to each other, without going into any detail, in the beginning of your talk. That way you can prepare them for what is to come. This is also a good time to point out that some details will be revealed later, perhaps after you introduce the concepts but not their relationships to each other. This is a highly effective way to keep people interested, actually.
If questions arise, then as Spark also pointed out, you can quickly swat them away by saying something like "I am glad you caught that, let me come back to that in a minute". That way you acknowledge the wisdom and relevance of the question, without getting derailed. It takes some practice to keep your composure and stay confident, when your flow is interrupted, especially it happens multiple times.
I am not sure if this is an issue for you, but by getting frustrated or confused you might leave the impression that you are not actually sure about what you are saying and some people (especially on a conference setting) might see that as a sign of weakness and keep prying into it.
Finally, if despite your best efforts people keep interrupting you in your own lab meetings, you can bring it up with whoever is chairing these meetings and tell them that maybe questions should be kept for the end, or wherever the belong, in order to not hurt the flow of the talk. I cannot imagine an environment where people don't care about the fact that they are hurting a colleague's flow.
After all what is the point of going to a talk if you don't allow the speaker to speak?

Thank you for your answer. For the first few questions I maintain composure, but after constantly having to go on tangents, it throws me off my main point and I do less some amount of coherence. So I'll keep your advice in mind.

+1 for overview/agenda slides. If screen estate allows, you can even place it (possibly with abbreviated section headings) on every slide. The LaTeX Beamer package has an option to put a TOC on every page, highlighting the current section and optionally folding the others.

Letting other spoil your flow disrupts your train of thought as well as those who may be very interested in what you have to say - you should remember them...

Structure is everything!
The first rule to managing a presentation effectively is to provide an overview before going into details. This follows the classic 3 step process of

Tell them what your going to tell them in the presentation,
Provide the main presentation,
Tell them what you told them.

You can spend a short amount of time verbalizing step 1 while providing a succinct written agenda. The agenda will provide everyone with anchor points that you can refer to when questions come up during step 2. (It's often helpful if the agenda is always visible to the audience, either in their own copy or as a sidebar on the slides. You can get creative with this.)
If you're at a conference and time is an issue, you can safely skip step 3.
The point to doing this is that when a question of the type you describe comes up, you can plausibly tell the questioner that you will get to the subject of that question at a specific point later in the presentation (tell them where that lies in the agenda) and ask them if they wouldn't mind waiting until then. This is usually sufficient to get them to hold their questions without objection, and avoids the unwanted tangents that you refer to in your question.

Regarding structure, you can find more ideas in Barbara Minto, The Pyramid Principle.

Latex Beamer has templates that display the structure in various ways on every slide, by the way. And big upvote, scrolled down looking for just this answer.

Building on @user24582 and Jim's answers: "start with answer first"! A presentation is not a "live version" of a paper. It has a different purpose, and thus, can/should have a different structure. So starting with "This is my research question" and "This is my contribution" in the first 2 slides is not a bad things and won't spoil the suspense, but rather raise interest.

When do you want to answer questions? If you want to answer questions at the end then say this at the beginning and stick to it. If you want questions asked throughout at specific moments, then perhaps have a question slide after each section and inform the audience that you will be doing this. The audience is along for the ride here and you can fill them in on the plan so they get the optimal experience.

One more approach you could try is a chronological presentation: describe your actual process of solving the problem. Presumably you did not work on entirely separated components and combine them only at the end (bottom-up), nor did you have such a good overview at the beginning that you could break it up (top-down).
Stepping through your progress should limit the number of "why don't you do it this way" questions, because you can easily give design rationale. Because you are building up the system as you speak, the components are directly connected to each other (unlike bottom-up), so it's clear how they relate to each other. And because the audience has an understanding of how far you are with solving the problem, they should understand that some things will only come later.
Of course, a top-down overview at the beginning and/or the end can still be very helpful.

If you have the opportunity during preparation, one technique that helps with this is to present a draft of your talk to a test audience and get feedback about what things are confusing or seem ungrounded at the time you mention them. As mentioned in other answers, the context of each piece of information makes sense to you, since you already have the full picture, but by getting the perspective of someone who isn't already familiar with the topic, you can get a better sense of how to sequentially build on the information you're presenting.

I have a love-hate relationship with agendas in presentations, for that exact reason.

I do not like to describe what I will be talking about because, well, I will be talking  about these things anyway.
On the other hand your question is exactly why I use them: so that people do not wonder whether I will mention wazii and wazaa. A well built agenda (not like the example above) can help them to cool down the excitement and wait for slide 54 where it is discussed.

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Difference between Statistics and Machine Learning?
What would I learn as a Ph.D Student in Statistics that I wouldn't learn and vise-versa in Machine Learning Ph.D program?

Note it is vice versa...

From a purely business perspective, statistics is what you do. Machine Learning is what you tell your client you're doing

What is called "machine learning" is essentially just statistical prediction, but coming at it from more of a computer-science background, with a greater focus on non-parametric algorithms, divergence measures, and big data problems where computation issues become a concern.  The field includes many standard statistical techniques, but many of the algorithms in use are complex non-parametric algorithms where the full statistical properties of the algorithms are not yet known.  The field seems to have arisen as a consequence of computer scientists entering into the field of statistical prediction, and approaching that field in a different way to the traditional statistical field.  There is less emphasis on foundational theory (though that is changing) and more emphasis on algorithm development and computational issues.  There is a greater emphasis on non-parametric models and simulation, with theoretical underpinnings framed in terms of properties of divergence measures.
Since machine learning is essentially replicating one subject within statistical analysis, there is a huge cross-over in material between these fields, and anything in either field can be regarded as also useful to the other.  Indeed, arguably machine learning is not even a new field at all; just a new approach to an old field, with slightly different points of emphasis.  In any case, machine learning is likely to focus less on foundational issues in probability theory and statistics, and more on computation and programming of a particular 'toolkit' of predictive methods (e.g., sparse models, neural networks, classification algorithms, random forests, etc.).  Theoretical underpinnings of machine learning are presently in development, and tend to focus on the mathematics of divergence measures, with convergence often framed in terms of 'order' arguments framed in classical computational terms.
In terms of what you are likely to learn in each PhD program, that is largely self-driven, so there is no reason you cannot learn material from one field while formally enrolled in the other.  Indeed, regardless of which you pick, I would strongly recommend that you try to learn as much as possible about both.  If you become a statistician (like me) then it is useful to have familiarity with the material in machine learning, and if you go into formal computer science and machine learning, it is useful to have familiarity with probability theory and statistical science.  The mathematical foundations in a statistics PhD will focus more on measure theory and probability theory, and the applied work will focus more on traditional parametric and nonparametric models, whereas in machine learning the mathematical foundations focus more on broader divergence measures (e.g., Bregman divergence), and the applied work focuses on certain types of nonparametric methods that are on the fringes of traditional statistics.

Machine learning is a quickly developing branch of technology, based on some basic statistics but also including elements of computer science, high performance computing, etc.
Unfortunately, ML/AI is currently a buzzword and many departments want to have a course on it assuming it will attract students and bring money. This means that when it comes to taught courses, there is no consensus yet what should definitely be included and how the course can be structured. There are examples of ML courses drawing significantly from the classical foundations of Statistics, courses more focused on use of software, more vocal courses with significant discussion of ethics / legal issues around artificial intelligence. Similarly, a PhD project in ML can be either highly theoretical (e.g. proving a convergence or stability of training), or highly practical (e.g. building 100s of NNs until one of them does better than others for some reason), or whatever else.
Statistics is a more established science, which has many applications. Depending on the area of applications, there may be some variations (e.g. Medical Stats may be slightly different from Statistical Physics), but the core methods are still the same, largely based on probability theory, calculus and linear algebra. I would not expect a PhD thesis in Stats to avoid maths completely  (something which I can not say about ML).

Statistics is a tool with many uses. It is, at its core, unrelated to machine learning, so, in a statistics degree you might never hear anything about machine learning.
On the other hand, many techniques of machine learning depend on a fairly deep knowledge of statistics, so you'd better come to such a degree program in machine learning already knowing at least the basics of statistics. In fact, the basics may not be enough, depending on the faculty of the program and their preferred toolset.

Both are about getting answers from data, both can lead to good jobs (if you are good at them), and makes a lot of sense to take courses from both fields.
Statistics is more about theoretic foundation (in Probability theory), and methods that are consistent with that theory. Expect math-heavy coursework and dissertation. Likely branched out from Math department, more suited to academic types.
Machine Learning is more of a bag of tools, without much theory as to why some of them work. Expect homeworks and dissertation that focus on programming. Probably branched out from Computer Science; more suited to industry types.
If you are considering specific programs, look at their "placements" page, i.e. what kind of jobs their recently graduated Ph.D's get.

what is math? proofs all day?

I'd push back on ML being a bag of tools, especially at PhD level. You'd certainly need an understanding beyond just using high-level apis with little thought about what's going on. Recreational/enterprise use of ML is very different to a PhD.

yes, statistics will involve more proofs, like consistency of your estimation method. ML will involve more programming.

Doesn't it rather depend on what is the precise topic of your research? I am currently researching a subject as a member of my university's school of mathematics and statistics, but, for my subject, I need to know quite a bit about ML, and, as it happens, fluid dynamics.
Surely it is a bad idea to tie yourself into a narrow discipline prematurely.
I am in the UK, so coursework generally is not a feature of a PhD programme.

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Applying to more selective programs after having been diagnosed with a long-term mental condition
I have discovered recently that I had ADHD, and possibly some other mental condition, which explain some past academic difficulties. This gave me hope that with treatment (which I will start soon) and newfound motivation, I can improve my academic results dramatically and aim for a PhD.
My opinion for now is that the plan that gives me the best chances would be to get a second master's degree containing more theory compared to my current one (computer engineering). I'm aiming for some universities I have visited, which are quite highly regarded compared to my current one.
My results have had ups and downs over the years, and would be clearly insufficient without a very good justification, which I believe my mental health problems to be. I have documentation of the mental health problems I suffered from during part of my studies. I don't plan to use these as an argument for admission, but providing that I get better results in the next semester after getting medical help, I am hoping that the admission committee won't disqualify me instantly based on my past results, and give more importance to the next semester.
One additional difficulty is that I'm nearing the end of my current degree, so I won't have another occasion to get good results. I worry that getting good grades in the last months could be insufficient to offset my less-than-stellar record.
Is a very late mental disorder diagnosis followed by a significant improvement in results likely to save my applications to selective programs? Should I lower my ambitions for the moment?

Why do you want to get a second masters degree?

@AnonymousPhysicist the one I’m doing is just software development with a few data science courses, like basic application of machine learning and some principles. I would like to do research in a field related to AI. I can’t imagine doing anything like that when my only experience is coding and applying some ML algorithms from libraries. I talked a bit more about my reasons in the question I linked to.

Is a very late mental disorder diagnosis followed by a significant
  improvement in results likely to save my applications to selective
  programs?

I do not think one semester of grades can make a huge difference.  Only your doctors can predict the effectiveness of your treatment.

Should I lower my ambitions for the moment?

No, you should apply.  After you have submitted your applications is a good time to start working on your backup plan.

It's certainly a huge relief to finally know, after years or decades of struggling, what the underlying problem is. But people with ADHD tend to assume that a diagnosis and treatment is a magic bullet that will suddenly make them like everyone else. I think part of this is ADHD tendencies and part is internalizing the erroneous belief that if you just tried harder you'd stop screwing up. I don't have any first-hand experience with ASD, but the issues seem to be similar.
So here's my first observation: A diagnosis does not "fix" ADHD. A diagnosis together with medication and therapy or coaching does not "fix" ADHD. Right now you're at the starting point and you've been pointed in the right direction, but it's probably going to take some time and experimentation to find out exactly what you need to successfully manage advanced academic work. Expect that what you need might be really different than what is ordinarily offered in an academic setting. Don't beat yourself up trying to be like the neurotypicals the work is designed for.
My second observation: As you can see from the answers already given, many professors and programs take the attitude that learning disorders/differences are the student's problem and it's not their job to deal with them (except maybe in a very superficial legally-mandated way). This attitude might vary by country--my own experiences in the US have been pretty dismal. So even once you know what you need, and even though the law is on your side, you might find yourself fighting a losing battle against these attitudes to get it. So it's also important to be sure that you're entering an environment that sets you up for success.
I honestly don't know the answer to this second problem. I might post a related question here later to see what the ASE community thinks. I don't mean to sound pessimistic, but the fact is that the academic community is on the whole not particularly welcoming to people with learning differences, and ADHD is particularly misunderstood. The trick here is to find the exceptions who will provide the conditions you need to flourish.

You make some good points, but this does not answer the question.

I think that, given you are seeking help, and probably learning to compensate for your condition, that you can otherwise ignore it as far as seeking future degrees. I think that you will find that many people in academia are at various points on the autism spectrum. Communication difficulties are pretty common, even if no cause has been diagnosed.
But, I think you are probably learning that some compensation is possible. If you can manage that, then the question of your suitability for a degree lies elsewhere, grades and other accomplishments as for any other person.
Follow the advice of your doctor/therapist, of course.

I'm not sure that my question was clear enough. I was mainly interested in the point of view of the admission committee. If they received my current record was sent to them without mentioning my problems, it would be dismissed in less than a minute, and I'm asking whether these conditions can be enough to give me a chance. I don't see how I can "ignore it", it would just transform my application into a regular one with okay grades, which is not enough. As for my doctor's advice, I follow it for my treatment, but I don't think they can be of much help in university applications.

There are two problems: 1) I have to justify my past insufficient results, and the reason is my mental health. 2) I only have one semester left to get good grades, which I worry may not be enough to make my record acceptable. Ignoring my condition in my applications would make them reject me for sure.

Can you get a supporting statement from a recommender? "Elzo has struggled mightily with a communication disorder, and ... " (I don't mean to characterize it, your words will do.) If it comes from a recommender who also attests to your likelihood of success it will mitigate any issues, I think.

I can try next semester, but no one at my university is familiar with my problems, from their perspective I'm just an average student. All I could do would be to bring proof to the professors I ask for recommendation letters, and ask them to mention it. I'm not sure how effective that would be, since I have no experience with recommendation letters.

Try to find a mentor - a trusted professor.

While your condition can explain some of your past poor academic performance, you still need to convince an admissions committee that (1) your condition is under control and won't interfere with your future performance and (2) you have the ability do well in their program.  The fact that you now have a diagnosis and have started treatment doesn't really answer either of these questions.
One strategy would be to establish these things by taking some courses on a part-time basis in a less competitive program and doing very well in those courses.

Go ahead and apply. Say in (the middle of) your research statement that you had an issue affecting your performance in earlier years, but now you have identified it  and found a way to deal with it, as evidenced by your  improved performance in the recent semesters.
If possible have your recommendation letter writers confirm your story, briefly. Something like "X had a bumpy start, but recently developed the right attitude to succeed in an advanced program"
You do not have to name the issue or provide medical evidence. Instead, focus on what the new you can and will do.
PS I suggest not using the word "mental". It reminds people of stuff like schizophrenia. ADHD is not nearly as severe as that (at least in your case, I hope).
In response to your comment: I feel that talking too much about your condition signals that you focus too much on it, and will continue using it as an excuse for poor performance in the future. And generally, most people do not like hearing about problems of others (b/c they have plenty of their own). Instead, I suggest you focus on how much you accomplished since the issue was resolved.

This seems like a good method; what bothers me is that I won't be able to provide supporting documentation if I choose to keep the details for myself. I imagine that "I had issues and fixed them" has less strength than "I was officially diagnosed with X and Y, from which I suffered since I was born, started treating Y, and got better grades as a result". To be clear, I don't have a problem with disclosing the details, I just wonder what the best strategy is and how much it could help my chances.

As for the last sentence from your edit, I don't know if you meant "don't say 'mental in your application'" or "don't say 'mental' ever because it's wrong". If you meant the latter, ADHD is not just a behavioral issue, it's seen as a neurological disorder and I have often seen it described as a mental disorder. I just have the Wikipedia page at the moment. If you meant the former, I agree, thank you for the advice.

This is nothing wrong with using the term "mental health". And it's not our place to judge how severe somebody else's illness is.

There is a stigma around mental-health issues. I think Bald Bear's point was that if you state that you have mental issues some people assume the worst and think you are a crazy person or something like that.  As stupid as that is, I think it does happen. Being more specific and mentioning the ADHD would prevent this from happening (somewhat at least). Your attitude is the right one @Flyto, but in my experience people who think like you are in the minority.

"but recently developed the right attitude to succeed" This is terrible advice and potentially offensive.  ADHD and Asperger's syndrome are not attitudes.  Anyone on an admissions committee in the USA would read this comment as code for "this student has a bad attitude most of the time."

I flagged as "rude or abusive," but I would like to clarify that I think the answer is inadvertently offensive because it implies that a medical condition is an attitude.

@AnonymousPhysicist: Given the rest of the post, I would give Bald Bear the benefit of doubt and interpret this as: “They developed the right attitude towards their mental issues.” I agree that the phrasing has several issues and is easy to misinterpret though.

@Wrzlprmft I don't care one bit what Bald Bear's intent was.  I suggest the answer be edited or deleted.  I'm just not sure how it should be edited.


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No GRE offered in my country and I cannot really afford traveling elsewhere
Would there be any hope in applying to a doctoral STEM program (geared toward EE) in the US without the GRE?
Simply put, there are no test centers offering the GRE in my country, for this year and the upcoming one. In other words, my potential applications for fall 2021 are essentially ruined. And I can unfortunately not afford going elsewhere to take it.
Should I apply without it and take the risk of having my application rejected right from the outset?
I sincerely hope the GRE will be abolished once and for all, for it serves  only
private interests. It is such a financial hurdle for those living in low-income countries.
Any advice or suggestion is more than welcomed.

See this recent question: https://academia.stackexchange.com/q/91800/17254

If you country has a Fulbright exchange program with the US, it might be worth contacting the center administering it. If no GREs are offered in your country, they will have encoutered this problem before, and may know a solution.

The GRE actually helps us admit students from developing countries since it's one thing we can trust. Otherwise we  need to know your school well (which tends to be unlikely except for the top few schools in your country). It is actually less important for students from developed countries since we can trust the grades from accredited universities.

You might want to explain GRE?

First, not all universities require the GRE for graduate admissions, but you will need to explore that yourself. Second, under the conditions you cite, you can ask for an exception and it is possible, but not guaranteed, that it will be granted.
The GRE is only one measure of likely success. Its only real advantage is that it is standardized. Any university wants assurance that admitted students are likely to succeed, hence they ask for such standard things. But, it is possible, in some places anyway, to provide that assurance through other means, such as an exceptional record or exceptional letters of recommendation. A prior research record can also help in some fields.


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My class bunked lectures!
My class decided to bunk today's lectures. Because there is so much chaos in my city due to heavy rain and blockage. Many student can not come and some of them are not coming due to their parents not allowing them to go. So we executed our plan.
Now, our class teacher want us to meet HOD and take permission from him and then only we are allowed to sit in next lectures.
So, my question is how should we handle this situation?
How should we put ourselves in front of him?

This is what happens when you think you know the rules of the game. You made a plan and executed it, now the consequence is a meeting with the HoD... Better make sure you all get your story straight... So, don't forget that the teacher and HoD may already have been told or given (social media) the story...

I suggest humility and remorse. Your "plan" was flawed.

Did you at least let the teacher/the HoD/anyone know that "sorry, due to the severe wheather conditions, many of us can't come in today"? Or did you just decide among yourself that you will skip, so that the teacher fought his way through the storm to be a good teacher to his students, just to see that they decided to bail on him? In the latter case, I could fully understand why he isn't entirely happy right now.

Is it mandatory for you to attend lectures?

Please explain HOD.

"parents not allowing them to go" -- How old are you and your classmates?

@user111388 I assume "HOD" means "head of department" here (though to me it normally means "hereditarily ordinal definable")

@shoover we are 19 year old, but condition in some part of city is really bad, so..

Preparation for meeting the HoD will depend on the individual student's situation.
Students who attempted to warn the teacher of their non-attendance should document their efforts to do so.
Students who really could not attend should document the road closures and transit cancellations that prevented them from attending.
Minors who were told to stay home by their parents should get a note from the parents taking responsibility and explaining their reasons for keeping the student home.
Anyone who did not attend without a good reason needs to think about the wording of an appropriate apology.
Students who could not attend and made at least some effort to notify the teacher are in the strongest position. Even those should be apologetic about the group non-attendance if they encouraged it.
At the other extreme, I don't see anything other than an apology for a student who could have attended, chose not to, and made no attempt to notify the teacher.

What about the students who organized the mutiny? Flogged? Or an extra assignment?

@SolarMike I think their best strategy is an apology, with promise of no repeat.

Years ago, I did the reverse, snow blocked all the students coming in except me as I walked. Reason was if I did not attend college I would loose a day’s wages... The lecturer was not pleased to see me... marked me present and told me to go home..  10 miles there and back :)

our class teacher want that we should meet HOD and take permission from him and then only we are allowed to sit in next lectures.

Your teacher wants* you to meet the HOD, so meet the HOD.
*Given the context it seems the teacher has demanded, rather than merely wants.

This is not really an answer to the question.

@user111388 Perhaps you can elaborate on why.


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Email address etiquette - Which address should I use to contact professors?
I am currently a master's student outside the U.S., and I plan to contact professors in U.S. universities for PhD applications. I have a bunch of email addresses available, and I don't know which one is the most appropriate for communication.
My main objective is to make sure my email doesn't get lost in the spam folder, and a decent first impression would not hurt.
My options:
(1) surname@university.edu.xx: Email given from the current institution where I attend.
(2) surname@alumni.university.edu.xx: Alumni email from the university where I got my undergrad degree.
(3) f.surname@university.edu: Email from a well known U.S. university where I spent a year as an exchange student.
(4) firstname.surname@gmail.com : Private email address
My question is, do you think the possibility of getting a response depends on the email domain? What email domain should I use?
A friend of mine who ended up at a top-5 grad program suggested me to use (3), saying that it could increase my chances of getting a response. However I am cautious that it may look pretentious or delusional, considering I had been there some time ago.
Am I overthinking this?

I cannot believe you still have access to an email account at a US university from eight years ago. If you still have a forwarder from that address (strange enough), I wouldn't use it because your outgoing mail server and email address won't fit, which is guaranteed to give you a high spam-rating.

@Karl I still have email access to an account at a US uni that I graduated from in 1994. They use lastname.#. It's not unheard of.

@Karl Why is that so hard to believe? Many universities provide more or less permanent e-mail accounts for students. I still have mine from the IT University where I studied for two years between 2007 and 2009.

@JanusBahsJacquet I'll believe you, but all my universities disabled your account eight weeks after the end of your last semester, and switched of the forwarder after one year. There are legal problems, email accounts cost money (all mailboxes with a, say, 1GB per account must be on a fast and failsafe storage system, 4000 new students per year, since 25 years, thats 100 TB), and last but not least Joe Smith, freshman 2020, doesn't want to end up with the address joe.smith1472@uxyz.edu

@Karl Wow, that’s rather harsh! Eight weeks is very quickly. To be fair, both the universities which have let me keep accounts use generic usernames (e.g., abc123@xyz.edu), which are ridiculous and annoying, but at least they’re equally ridiculous and annoying for all, not only for the newer users. I do think they cap the email accounts after you graduate, but in both places the email is tied up with the ability to log on and create exam result printouts, which is something they’re legally required around here to provide former students with these days.

There's no escaping insane University spam filters. My (Russell Group UK) Uni's spam filter regularly marks my colleagues' Uni domains from around the world as spam. There's no pattern to it. I've also had communications from the US state department, etc marked as spam...sigh

Personal email is OK, as long as it doesn't look too unserious (mickeymouse666@gmail.com is bad). Gmail looks more professional than other providers, but not by much.
Avoid email addresses that will expire soon. Unfortunately, many university addresses are like that. An expired address means you won't get late followup answers (and trust me, there are emails threads in research that span decades).
Avoid anything with alumni in it. Many people have a delete reflex when they see the word "alumnus", as it mostly appears in the context of panhandling by alumni orgs.
There is nothing pretentious about .edu addresses.

I think the pretentiousness comes from the fact they were only an exchange student at that university and are putting it because it's more prestigious than the one they attended full-time.

I suggest you use your current email address, i.e. option 1 with name@university.edu.xx.
The reasoning is that this is the email address that reflects your position. Writing with another email address from a different university does not really tell the person who you are. Especially if you are listed on the homepage of your current institution.
The second best option is to use your private address, but as darij grinberg stated in his answer, it should look serious.
Finally, to answer your question: As long as you use either of the two options (current institutional address, "serious" private address) your mail domain will not matter. You are probably overthinking.

You are overthinking and your professor will probably not even read your address when your mail programm adds a real name to the from field, but there are two things you should consider:
Spam rating: When your e-mail ends up in the spam folder, you probably won't be noticed. GMail should not have a problem with this.
It should be a permanent address: This is the address, that the will be used forever.
It is rather common, that someone will start typing your name and use the first address that is suggested by the mail program, disregarding that you changed institutions and have a new primary mail address. So you probably should have a forward when you use an address that will change, or it really needs to bounce. When the e-mail is delivered to a mailbox that you do not read anymore, you will miss out on important mails, even when you told him the new address.
In addition, you may want to use an address that can guarantee to conform to data protection regulations. For your personal e-mail it is your personal risk, but when you start working for the professor and you exchange details about students, it may be a problem to use services like GMail. A university usually provides better data protection in their e-mail terms of service.

You may be overthinking it, but everyone who wishes to communicate by email needs to find a way of avoiding spam filters.
Having been in your position a few years ago, namely wishing to engage the attention of professors who would never had heard of me, my strategy was to use an obviously personal email address, a very clear but brief subject, and a very brief email message (in impeccably grammatical language) with a clearly stated question, such as "Would you be willing to consider me as a possible graduate student?".
Brevity is crucial, but for a counter-example consider Ramanujan's unsolicited letter to GH Hardy. Ramanujan stated theorems that were very exciting but not so exciting as to suggest that he was a crank. Unless you are offering material of that quality, I advise a short clear statement of what you want from an honest personal email address.

I don't see how Ramanujan is relevant; maths professors in 1913 surely weren't receiving barrages of snail mails asking for internships and all the other junk that we get by email today.

@Richerby the relevance is that famous maths professors in 1913 were indeed receiving unsolicited mail claiming eg that the circle had been squared, that Fermat's last theorem had been solved etc etc. Read Hardy's book ' A Mathematician's Apology'. The point is that something Ramaujan said lifted his unsolicited letter into the class of letters to be thought about, and away from the class of letters to be binned.

I don't disupute that they received some unsolicited mail; the question is how much.


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How did Milton Babitt teach math at Princeton and research math, without an undergraduate degree in math?

Even if Babbitt taught merely elementary calculus, don't universities hire someone with at least an undergraduate degree in math to teach it?
I quote Schoenblog.com:

Babbitt came to teach at Princeton in 1938—before there was even a music department. We did not have offices. We lived under very Spartan conditions.” When the U.S. entered World War II in 1941, Babbitt was working toward one of the first graduate degrees offered in music at Princeton. During the second semester of that year, he taught music and math (mostly elementary calculus [I bolded.]). “Everybody suddenly began taking math courses that semester after Pearl Harbor. I was teaching on Saturdays.” The music section disappeared as everyone was either drafted or preparing for technical jobs in the army. Babbitt was sent by the Army to Washington, but soon was sent back to teach, because mathematicians were considered top priority. Babbitt stayed with the math department until the end of the war, when he made the not-so-difficult decision to return to music.

In avouching his 'mathematical research in Washington, D.C', Wikipedia hints that Babbitt was skilled at more than elementary calculus.

Babbitt's father was a mathematician, and it was mathematics that Babbitt intended to study when he entered the University of Pennsylvania in 1931. However, he soon left and went to New York University instead, where he studied music with Philip James and Marion Bauer. There he became interested in the music of the composers of the Second Viennese School and went on to write a number of articles on twelve tone music, including the first description of combinatoriality and a serial "time-point" technique. After receiving his bachelor of arts degree from New York University College of Arts & Science in 1935 with Phi Beta Kappa honors, he studied under Roger Sessions, first privately and then later at Princeton University. At the university, he joined the music faculty in 1938 and received one of Princeton's first Master of Fine Arts degrees in 1942 (Barkin & Brody 2001). During the Second World War, Babbitt divided his time between mathematical research in Washington, D.C., and Princeton, where he became a member of the mathematics faculty from 1943 to 1945 (Barkin & Brody 2001).

I taught in a psychology department without ever having taken a class formally offered by a psychology department.

Even in 1970 I got a programming job with a mathematics degree and no for-credit computer courses.

Universities set their own hiring standards, and even if they create a requirement to have a degree, they can also waive that requirement as they see fit.  I don't think we really have much way of knowing what criteria Princeton used to decide to hire Babbitt in 1938, what rules they might have had, whether any of them were waived, nor why.

You may be interested in: https://en.m.wikipedia.org/wiki/Credentialism_and_educational_inflation During the time you could be a doctor or a lawyer with no college degree at all. The "ivy league" also meant close to nothing in the US at the time, it was not synonymous with exclusive, prestigious, or elite - that came later, much more recently. Labor, professions, and higher education has changed tremendously in the last 60-100 years, at least in some ways.

Duplicate of History of Science and Math question.

The theoretical work that Babbitt did in music was highly mathematical.  He essentially worked out all of the additive combinatorics of actions of the dihedral group of 24 elements (and its direct sum with itself) on finite sets.  (That's what "musical set theory" means in mathematical terms.)

Even today, there are people in physics departments who have math PhDs; there are people in math departments who have computer science PhDs; there are people in computer science departments who have physics PhDs.  Having the same degree as the department you are in is not a requirement. Music and mathematics are farther away than usual in these situations, but if somebody has the necessary knowledge to teach mathematics, there is no regulatory obstacle to letting them do it.

The first part of the answer is that in the 1940s, requirements for hiring at American universities were clearly different than they are now. American universities at the time had not developed the world-leading position they have now, and hiring decisions may have had something to do with it -- though it also goes the other way around: If you're not at the level of Harvard today, you need not shoot so high in your hiring; you may also not be able to attract the same level of talent.
Secondly, the early 1940s were particularly difficult, with a large number of talented people needed elsewhere in the nation and not available to hire at universities. In addition, many others needed to get an education and so the demand for teachers was particularly high -- formal qualifications be damned.
Thirdly, in reality, universities have always (and continue) hired people who are qualified, but degrees do not equal qualification. It is generally true that qualified math professor applicants will have a PhD today, but that is not universally true and universities can and do hire people who don't have one if a candidate has demonstrated exceptional qualification in other ways. Babbitt may have been able to show that he knows what he was talking about in ways that convinced those who hired him that insisting on some kind of degree or title was pointless.


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Writing thesis with corrected data after being published
Lack of a systematic strict supervision has lead to inaccuracies in data evaluation. This data was published. While writing thesis I realize that and I don't know what to do. Should I write my "reanalysis" of published data in PhD chapters and explain, what was done incorrect and limitations of the interpretation? Or should I issue errata on the published materials (which is a red flag for thesis and following defense)?
I have learned my lesson for future and will be more accurate and precise. I do realize that it is the main stone of a good scientific practice. But now I just failed.
I feel that I need an advice of what to do with an actual situation to reach defense and be able to complete PhD studies?

Inaccuracy like error in normalization of measured quantity (around 15%) and inappropriate background subtract (introduced correction factor on undefined contribution).
The conclusion of the paper still valid. These results were complementary to the main findings.
I feel like erratum shows incompetence in data evaluation and I don't know how to decently answer when Committee would ask about it. Because I cannot say neither "sorry, did a mistake', nor "I was told to do it this way". I need to end up with sufficient answer to show that I now have realized it was wrong and will not do it again.

Thank you. Several of them answered in a way "don't change anything, it is bad that you did it, but now move forward". I just don't think that's the right approach.
From another perspective, the data presented should be correct to the best to your knowledge not to confuse anyone in scientific community. And if I will present corrected one in thesis, but without emphasis that there is a mistake in a paper, I hope that will be enough for committee as well.
If someone is truly interested in this research, than it will not be a problem to find my thesis after readinfg the paper.

Talk to your advisor.
write the thesis with the most up-to-date data. Analyse the data as a progression if necessary ie including the historical data if applicable - see 1...
contact the journal / editor (may or may not be the same editor you used when publishing originally and decide whether a follow-up paper or an erratum should be the way forward.

Thank you for your advice.
Will my thesis still be "defendable" if I correct my mistakes there?
For the paper published corrected result will not change conclusions, although it is so embarassing for me, because I have tried to do things the best way I could that time.
Additional point was impatient supervisor, who wanted results which are in line with what he wants to observe. It lead to misunderstanding and wrong data evaluation..


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Reuse of published data in PhD thesis
if it is the same data, but you put it in another style for your PhD thesis and created a new figure - does it still counts like "figure from publication "***" ?

Are you asking about copyright/reproduction of figures or is your question directed at scientific citing?

Better safe than sorry. "Redrawn from publication Spongebob et al, [2018]", "based on data from Squidward and Squirell [1878]", etc. Why should this be a problem?

The question if I need to ask permission of the publisher to reuse data in "another" way and style without using the exact same Figure from the paper.

The publisher does not own the data, only (perhaps) the copyright to the representation (aka the figure in and of itself).

The copyright attaches to the "presentation" of the data, not the data itself. If you want to replace (say) barplots from your first publication with the violin plots you used in the rest of your projects, go for it! The publisher doesn't need to be involved.
However, you should still cite the original paper by including something like "data from XYZ et al. (2015)" or "redrawn from [1]" in the caption. This ensures that the reader knows where the original data comes from and avoids implying that those results were somehow confirmed--exactly--by a second set of experiments. More practically, it also means your examiners won't ask for as many changes since the data have already been vetted by the papers' reviewers.

There might be two parts to this question here, so I will answer them separately.
Is it plagiarism if I do not cite my own published results?
Answer: Yes, that's called self-plagiarism. It does not matter if the results you want to cite where published by yourself or another person. It must be cited. Even if you have the same data and plot it differently, it is essentially not a new source. Since you usually have more data accessible from your own publications, you might come into temptation to use an altered figure from a previous publication. These must also be cited as part of the published paper. Better safe than sorry, just cite it if it can be attributed to a previous piece of research.
Do I have the right to reprint figures from a publication in my thesis?
Answer: Well, that depends on which licensing agreement your published paper falls under. For example, the very popular open access CC-BY license allows you to retain the rights to your images and to reprint them. However, attribution (i.e. via citation) must still be specified.
If you do not own the rights to reprint the pictures as they are, you can always redraw a figure (as suggested by Oleg Lobachev in the comments) and correctly cite the source as "Redrawn from Author et al. [54]" or similar.
TL;DR Yes, if you rearrange data from an old publication in a new form you still have to cite the old publication.

An interesting variation on this is if you put the same data in your thesis and a paper and submit them essentially at the same time. Which should cite which?

@IanSudbery Interesting, indeed. I think this is a bit of an XY problem, because you should not cite unpublished data in your thesis. I think the most common solution would be to cite the paper as submitted to Journal of Blah in the thesis.


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Protecting yourself when leaving PhD which involves misrepresentation of results and potentially unsafe bio-containment procedures?
I am in the process of leaving a PhD program after less than one year. I have spoken with my advisers and am slated to leave by the end of the summer.
I have various reasons for leaving, including general disinterest in lab work and that is the official story that my advisers are giving.
During the course of my PhD, I have had to write some reports and an abstract for a talk that involve seriously stretching the truth. In short, I am misrepresenting the promise of the molecule that I am studying. I am misrepresenting this to the grant people. I am also omitting data that doesn't support the conclusions my advisers want, but not producing any false data.
The other thing that I have been doing is growing transgenic plants that express a drug for oral delivery in a food crop. Our lab does not have the proper approval from the university to do this, and we are growing it in a greenhouse without proper containment. I am not a plant scientist so I do not know the potential danger, but I do know the species I am studying has the potential to cross pollinate and produces many tinny seeds that get everywhere. I am concerned about the safety and another lab member has voiced his concerns to my advisers but no action has been taken. We are in the process of trying to get a permit to grow it, but it hasn't been issued yet.
By leaving my PhD, I have already lost all potential to enter my field of study so I am currently switching to statistics and happy about it. My concern is that I might be implicated in something if all this sloppiness catches up to my advisers.
What steps can I do to protect myself so that my work here doesn't come back to haunt me?

I have nothing useful to say, except that you are right to worry about the situation, both for general dangers to the public and for danger to your own reputation. You can obviously hope that "nothing comes of it", but the chances are that something will. Maybe you have to be a whistle-blower... but be careful.

I would strongly consider whistle-blowing (internal, within your organization) in this particular situation.
There are many reasons (good, bad, and hybrid) that lead people to the decision of becoming whistle-blowers: plain vanilla ethics, the desire for power & attention, willingness to protect others, legal requirements, etc. However, protecting yourself by whistle-blowing is a totally legitimate reason.
Whistle-blowing comes with some potential consequences, but here are the reasons why you might incline towards doing it:

you already made a decision to quit your program: thus, the situation influenced you (and other group members) heavily;
you already decided to switch the field of study;
this story can have direct consequences as bio-material is involved. There are very good reasons why special regulations exist for working with such materials;
the fact that the wrong-doing is happening has documental evidence: lack of the permit that is required.

If you decide to proceed, be careful in terms of the facts you present. Try to be as objective as possible without adding unnecessary emotions. Make sure that you present the facts with as little interpretation of your own as possible. Let the knife do the work facts speak for themselves.

@dantonio totally understand, it is a tough decision. You would have to weigh the probability and consequences for the whistle-blowing in comparison to even worse consequences of you not whistle-blowing. Nothing prevents turning the fact upside-down to make you be (at lest partially) responsible for the mess - if you had not blown the whistle.


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Where can/should I, as a high schooler, publish a paper regarding the derivation of a formula?
For a high school engineering project, a friend and I have found ourselves deriving an equation for how to most efficiently configure a system.
We found an equation that, given a few parameters about the system, equates the amount of material added (and thus weight), to the amount of energy this system will gain. Along the way, we needed to find an equation that, given an amount of material, would describe how to most efficiently use the material.
We were thinking we'd write this up in a nice paper, and publish it somewhere. (For resume building, college applications, etc.).
Where/how could we do this (if anywhere), and how long would it take?

I posted this on Physics StackExchange and it was recommended that I post it here as well.

Has an answer on Physics, worth checking if you are about to answer: https://physics.stackexchange.com/q/498498

Coming from somebody with very little knowledge of academia and the field of physics: What speaks against publishing it on your website? I would assume your target audience is students who google their problems, not researchers who regularly read papers (Of course, I could be wrong)

@lucidbrot: why do you assume they have a homepage?

In all likelyhood, this is already published in some obscure paper in german/russian 60 years ago. Go find a professor, and they will help you decide if there is enough novelty to warrant trying to publish it (Probably not, but go for it).

The big question here is whether what you've done is new to the world - whether it's a genuine new advance that nobody in the world has done before, or whether it's something known to the world that you, and perhaps your teacher, have not seen before. Without meaning any disrespect to you and your friend, the second option here is more likely - but the first is of course possible.
If it's genuinely new, you can look to publish in a scientific journal. If it's not new (but perhaps still unusually advanced for a high school student), you should perhaps look for other types of publication, which could still be good for your resume. The difficult question is how to tell which category your work falls into.
My suggestion is to speak to your high school teacher about this. They have seen a lot of different students' work. If they think that it may be a novel development, then either write, or get your teacher to write, to a professor in a relevant subject at a local university. See if they will look it over and advise you.

And another factor making this aggravatingly worse is that it is extremely difficult to, say, electronically search databases of papers specifically for mathematical formulas.

Check out the American Journal of Undergraduate Research. You need a faculty mentor. Make contact with your state university.
Do plenty of online searches to see if your work is already published. This will take some time. Use various keywords.
Even if your formula or equation is not new, if the derivation is new, you can still publish. This is especially true if your derivation yields new insights into the result, or if the derivation serves as a model to solve harder problems. So take a look at the derivation to see if it yields any insights to harder problems.
If you have something publishable, don't give up. Be persistent. This may not happen for a while, but keep at it.

Do you both have any contacts in the engineering field? They may be able to situate your issue and have contacts that might be able to help.
It is a big ask for high school students I know but try to spend the time to do the research if you can? Paywalls to journals are a big problem. What else has been done around your issue and question. What other available equations can be used? What do people do now to sort out this problem? This would give you a clue to who and what sort of people/researchers are tackling the problem and would be interested in your equation if it is indeed unique. Even if it is not unique, the contacts may also become a useful resource for your future.
Physics SE have not addressed your question and I suspect that your equation addresses a pragmatic issue rather than a theoretical problem so maybe the  Engineering StackExchange might be a better fit. However, spend the time going through the various tags and branches in the SE rather than just jumping from one StackExchange to another. Write a couple of paragraphs about the current approaches available, quote other relevant questions or sites that explain the issue in better detail and explain how your equation is unique. This skill of "situating" the problem and being to respectful to others trying to solve the same problem while discussing the background in an engaging way is an important and underappreciated part of "doing research".

I agree with @lucidbrot's comment.
Even if you are not the first to derive the formula, successfully doing it on your own shows you have a fairly good understanding of it. This puts you in a good position to help others understand it or learn of its existence. Write it up, post it online, give a talk, whatever. There are many opportunities created for young people to practice their communication skills or get recognised for impressive work. And you can create your own opportunities.
I'm sure you have read useful online tutorials about technical things; hardly any of them are actually written by the first person to publish that concept!
A journal is not the right avenue unless there is something new and of significant value in your work. But there is nothing stopping you from writing things up on your website, or making some YouTube videos. There are online communities of various sorts (hobbyist communities may be a good bet). Also you should see if there are student awards that may be applicable to what you've done, and look at the criteria.
Do try to find an existing publication about the formula (or a more sophisticated version of your formula.) It's great to give a simple, practical explanation and then say, "by the way, you can check out xyz."


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Formulate an answer on PhD defense about mistakes you've made
Imagine, you did data evaluation, published. When preparing your data for the thesis, you've realized that your approach was wrong. It does not change the main course of the paper and do not damage main conclusions, although it does affect the quantitative part of research. It is more than 1 year back published, so instead of erratum you decided that you put your updated data in your thesis and will do your best to address your mistakes in the next publication.
Question is how to formulate decent answers during the PhD defense if the committee asks why didn't you publish erratum/correction if you've made a mistake in your data evaluation?
Could I answer in a way "I've realized I've made a mistake and it will not happen again. The correction will not change main conclusions of the publication. I will make sure to address these points in the next publication concerning this topic to avoid any misunderstanding"
Maybe some other ideas?
Thanks in advance!

I'm not clear how it can be meaningful and at the same time not matter to the result. If you did not prove the result then you need to do so before your thesis will be accepted. If you have done so within the thesis, but not published it yet (as you seem to be saying), you may or may not be allowed to graduate depending on how demanding your department is regarding publication requirements for graduation.

If I were on your committee, the key take-away I would look for is that the mistake will be corrected in the literature.  Either an erratum or an explicit correction in a future publication would satisfy me, though in the latter case I would ask, "What additional steps need to be completed before this future publication will be available, and how long do you anticipate that may take?"
If the future publication is still quite far away (by the standards of your field), then I would recommend an erratum in the meantime, which should do no harm.  I would not consider a long period of time since publication a very strong argument against providing an erratum.  Here is one famous paper in my field that received an erratum after 3.5 years.
A promise that no mistakes will happen in the future would strike me as naive and unrealistic.

There is a world of difference between publishing correct data with correct results that are in an incorrect direction compared to data and results that are incorrect.
The former may well save someone else lots of time when choosing the direction they need to go, in fact, it may well be the correct direction for them.
So, in your defense, it's not a "mistake" , just a "blind alley" which meant you had to change direction to the method you subsequently used. All the people at your defense have had the same...

From the question I got the impression that the latter case had happened: The mistake (as LongWay describes it) affects the quantitative data/results without changing the general direction ("the main course") of the research.  Of course, all the people at the defense probably will have had this happen to them as well.


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Can a (stapler) PhD thesis comprise multiple unrelated papers?
Traditionally, a thesis is assimilated to a monograph and comprises a unified body of work. However, with "stapler" theses becoming more common, I'd like to know if a thesis is allowed to comprise multiple unrelated projects.

To make the question more regional, assume that the country is Germany and that the subject is mathematics.
Indeed for the first few years, I have been working on several projects that had as outputs papers that are completely unrelated (except for the fact that they fall within the same broad subarea of mathematics -- really, one of those listed in the arxiv math section: https://arxiv.org/).

I think only your advisor or university can answer such a question. If you don't have an advisor, perhaps there is a "graduate council" or similar. Or a dean.

But at some point the advisor will have to approve the thesis. If s/he is happy you should be fine, but if not you are stuck. Really stuck. Better to ask now than learn the worst later. My opinion holds no sway at your university.

"My advisor can't be bothered by administrative questions of this kind" - this is not an administrative question, it is an advisor question: "Will you, my advisor (and by extension my committee), approve a thesis with this structure?"

As others have pointed out, this is really a question that only your advisor can answer. Nevertheless, stapler theses in which all of the papers are unrelated (except for falling under the same broad area, i.e., number theory) are not so uncommon. A lot of the time they have titles like "Topics in X" or "On A, B and C."

This is dependent on your supervisor, the comittee and the referees (in the systems I know, almost exclusively the supervisor). Moreover, I would expect from any sane supervisor that they know the projects you are working on and at least warn you if you work too much on topics which can not be put into your thesis.
Most of the time (if your supervisor agrees) and you write an introduction outlining connections between the topics, you are fine. I have seen theses where the introduction was "We present some.papers in the area X, here is an introduction to X" and everything was great. It's just a formality.