text:
Should I seek professional help because I have a lot of math books?
I’m a graduate student in mathematics. One day, there was a discussion between graduate students about how many books a working mathematician has. Then each student would talk about their personal math library and then they would name their preferred book in each area of math.
All the students had a relatively small library. When it was my turn, I simply said the truth that I have around 1,000 ebooks and 100 physical books and that I have bought all of them and have not downloaded any of them illegally. I also explained that I like to learn a lot of math and I’m passionate and enthusiastic about math. I also explained that I have not studied all of these books thoroughly.
Then suddenly a professor stated (when others were also present) that I have more books than the university library. He then said that I should immediately seek professional help.
I was very offended by what this professor said but I never discussed it with him because I thought that I was in an emotional state and I did not want to speak to him when I was not calm. After a while, I thought that it was my own mistake and I should not be so honest about my math library.
So I have now two questions:

Is the number of my books unreasonable compared to how many books a graduate student or working mathematician own?
If I need professional help because I buy math books regularly?

You are in good company: “When I have a little money, I buy books; and if I have any left, I buy food and clothes.” - Erasmus

Maybe he meant professional help from a librarian.

Is there any chance that the professor was simply joking? Some mathematicians have deadpan humor.

Why do you care what the professor things about your book collection?

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Do you have autism per coincidence? This is not meant as an insult, but is a genuine question. Because it sounds like your professor was simply making a joke. But jokes of this kind are often missed by autistics. Als your extreme passion about math (which is not a bad thing!) sounds like a hint?

you might enjoy https://www.orwellfoundation.com/the-orwell-foundation/orwell/essays-and-other-works/books-vs-cigarettes/

Is English your native language?  It sounds like you're just misinterpreting what was said.

"I have not studied all of these books thoroughly." What rough percentage have you studied thoroughly?

I think most mathematicians need professional help ;)

Personally, it seems to me that he was just making a joke. Awkwardly, perhaps, but still, just a joke. Your personal library seemed to him (and me) to be so "over the top" that it was hard to fathom. Had he said something like "Wow, are you ever intense?" it would have had about the same meaning.
It is possible that he had a negative feeling about it, but I really doubt it.
Or maybe a meaning like "Wow, you need to learn to relax a bit."
But if you are so intense that you are ending up hurting your health, then professional help is actually advisable.

Thanks for your answer. I think my main issue is that I’m a very sensitive person. My mind was occupied by what this professor said and I could not concentrate for one whole week.

@Alexandria in all seriousness, it might be worth talking to a therapist about how you can better handle comments like that so they don't preoccupy you for an entire week. That sounds really tough to deal with and a therapist might give you some techniques to deal more easily. That's not to say something is wrong with you because you're sensitive (there isn't!), just that you might be a happier person with some more tools in your toolbox. A lot of schools offer free counseling to students so might be something to take advantage of while you're in school

Agree that it's likely a joke, but disagree that it's awkward. Obviously the textual description is missing all the social cues that would help determine the situation, but I've seen or been part of exactly this kind of conversation multiple times -- the general format is Person A describes doing/having something in excess, Person B laughs and jokingly says "Man, you need to get [professional] help!", Person A (understanding that it's a joke) laughs back and says "yeah, I know..."

I agree, and- let's face it- mathematicians tend not to be very good at making jokes. @Alexandria: the thing that matters is that you've got some idea what's in each of them, rather than just buying them as a compulsion.

This, in my opinion, is why people in positions of authority should think thrice before making jokes with people over whom they have authority.

This is the correct answer, but it's probably worth pointing out that given Alexandria's reaction I think saying  "Wow, are you ever intense?" instead would have been a nicer thing to say and equally funny. Ambiguous jokes like this one can be stressful for some people

@Alexandria Sometimes people try to make jokes and the jokes are actually unfunny, or even offensive. It happens to the best of us. Unless it seems like he was trying to be hurtful, just move on.

Evidence that it's a joke includes the fact that you definitely do not have more books than the university library (unless you go to an utterly terrible university). I have far more than 100 physical books, and know plenty of people with 1000. They don't need 'professional help' (at least not for that).

@MarkMorgan I believe the stereotype about the humor taste of mathematicians similarly to the mental state of mathematicians is created by movies, where math people are mad, or laughing to the problem on the blackboard, and so on. Any profession has its own type of jokes based on the special knowledge, but none of the professionals are restricted to them.

Dear @Alexandria as someone who has benefited a lot from talk therapy allow me to highly recommend it. Everyone can benefit from it. What gives me pause is these statements: "I’m a very sensitive person. My mind was occupied by what this professor said and I could not concentrate for one whole week." I'm sorry you were so affected by what he said. Good for you to be so dedicated and capable at Math. I would ask myself two questions, in this situation, however: 1. Was that reaction helpful or not-helpful? 2. Is it really such a big deal to talk with someone? Might I benefit?

I believe the professor might need a professional help, in the form of sensitivity training. @Alexandria I'm sorry this person's words disturbed you so much. Your feelings matter and anyone telling you "it's just a joke, get over it" is gaslighting you.

@user253751 One time I made a joke that it was too bad someone was allergic to shellfish and they were missing out because shellfish was delicious. Everyone looked at me in disgust as if I had just been super rude and the thought that ran through my mind was "Now how on Earth is that considered rude when multiple times prior everyone in the room would laugh when people literally made the same joke about my peanut allergy?"

@vaultah It was obviously a joke and people make that kind of joke all the time. You can decide to live it as an aggression but you will be far happier if you learn to recognize a joke and laugh with the others. And nobody here denied her feelings nor gaslighted her, recognizing that she was hurt and blaming the teacher for being rude are simply two different things.

@DKNguyen: A huge part of jokes like this is the delivery. I’m terrible at it, even when I mean it as a joke and in no way intend it as a rebuke/insult. Other people can say “you asshole!” (for example when they lose to someone) with a voice and smile which makes everyone understand it as a joke.

@Benjamin R: Are you going to say "bad for you" to those who are NOT so "dedicated" because of money issues?

@The_Sympathizer Not at all, my dear fellow. Please don't look for things to take offence to, and recognise my comment was purely directed at Alexandria and not meant as a general comment on everybody and everything.

I own at least 4,000 physical books... True, some of my faculty colleagues own nearly none, and some treated me as a lending library. :)
Prior to the existence of any sort of electronic books, at active math departments it was essentially necessary to have one's own copy of a high-demand book, otherwise the endless cycles of recall requests would prevent useful access. In those days, in the Princeton Univ math library, most of the most significant books were eternally checked out.
Nowadays, yes, many things are available on-line without violation of rules. Still, not everything.
Also, the process of access with physical books adds a random element that is occasionally very lucky, in the sense of accidentally finding something you didn't know you wanted to find... in the course of looking for what you thought you wanted. In contrast, with a too-controlled search (especially if one is missing some keywords) one rarely finds anything one wasn't already aware of to some degree.
It's true that technical books are expensive. I did pay for all my books myself, rationalizing that what I saved on clothes was spent on books...? :)
It is also true that some people pretend that they "know enough" to do whatever their research is. Maybe so, but my own approach seems to require that I learn more and more things. Surely a matter of taste.

Thanks for your answer. I truly envy you for your math library.

I know it's tangential, but I completely agree about the wonders of wandering through shelves of physical books, finding random, fascinating things one wouldn't have thought to look for. I haven't been able to do this for six months now, at either the campus or public libraries, which is sad.

I just did a rough estimate/count and came up with about 1500 physical math books here, and probably that many or more others (physics, chemistry, biology, other science, semi-popular science, science fiction, philosophy, and all sorts of others that have caught my attention over the years -- for instance, I'm currently reading this book for the 2nd time). For me, I'm always looking up something in my math books, whether for my own interests, answering someone's email request, or (as I'm sure you know) my many online essays and reference citations.

(returning to this about half a day later) I strongly suspect the OP's professor is joking, as surely he/she knows virtually any university library (in a developed country, in which a math Ph.D. program exists) is going to have at least two or three thousand math books. In fact, the University of Illinois library has about 10,000 books (this excludes bound journal volumes), although to be fair, it's one of the largest in the U.S. Also, I have over digital 1000 math books, these being 1800s books freely available.

@Alexandria : Hmm. His book collection is 4x bigger than yours. Yours is anywhere from 150 to 500 times bigger than mine, depending on whether you count only "pure" mathematics books or whether books from heavily mathematical applied fields (e.g. have 2 volumes of Knuth's The Art of Computer Programming ) can also count. Sounds to me like you're unjustifiedly hating yourself by ignoring those who have justifiable hatreds.

@Alexandria : And I've flirted with stealing (piracy). Then I'd get guilty and delete it soon after. Just a couple of times. So I ended with nothing. Heck, even if I were to get a job, I might have to lie to do it.

Now that you've encountered your true bane, you see you don't have to hate yourself any more or any longer. Instead, you should be honest with others about how bad they are as people.

you probably have bought many more books than most mathematics grad students because 1100 books is prohibitively expensive. I didn't have an extra $1100 lying around when I was a grad student. All the physics grad students I know with substantial collections did download the PDFs illegally, and used their collection more for reference and particular sections of books rather than reading all of them.

you definitely don't need professional help just because you own a lot of books.

If you are looking for advice on your mental or emotional state, I think your reaction is a little off. The professor was either wrong or joking, but very likely you shouldn't take his advice so seriously. The fact that you took it to heart enough to write in about it might show that you're a little insecure about your habits (or you're fixated on other people agreeing you're correct or proving the professor wrong or something). If you lived with less of that stress you might be happier. Being stressed about these things is well within the range of normal behavior (though you may see more success if you watch out for overreacting in professional situations). Just something to think about.

Thanks for your answer. I started buying books when I finished high school so My math library was not created when I became a graduate student. I have been working and I spent most of my income on buying books. I also think your analysis about my reaction is not accurate. I’m a very sensitive person and that is why I got offended. I believe saying something like you should seek professional help should be done privately and not doing it when there are other people.

@Alexandria Which suggests it was a joke (maybe in poor taste) and not a serious appeal to you to get help.

When I was a student, I got a non-negligible number of physical books from the university library used book sales. And I buy second-last editions, used or slightly damaged books. I own <<1000 "professional" ebooks, but > 100 physical ones.

@Alexandria Sensitive is just a euphemism for that Well's analysis of your reaction was. They both mean the same thing.

@Alexandria you might be happier if you worked on being less sensitive. And the fact that this reaction can be interpreted as a strong need to be proven right or to prove someone else wrong is a flag that it might hurt you professionally. People could misread your sensitivity as always needing to be right, a common flaw in academia and a very bad trait in a collaborator or teacher. It could be a professional liability, depending on the frequency or intensity.

@cbeleitesunhappywithSX no matter how thrifty you were, surely you didn't purchase all your books for a rate of <$1/book though. 1100 is a lot of books to be able to afford (though it seems that Alexandria started their collection under different financial circumstances than most of the grad students I knew). Still, they asked if it was a common amount, and my answer is most cannot afford it.

@Well...: maybe I should have been more precise, the book counts are current, I guess I did not have > 100 physical "professional" books at the end of my studies. But: the university library used books were IIRC typcially at 1 DM (would be maybe 50 US-ct back then; I think this price is an accounting custom), some were also given away. Also, there's a whole bunch of old GDR textbooks in that lot. I.e., we're not talking about 500+ page bricks but shorter ≈100 page books. They were good, but had been heavily subsidized and were discontinued after the wall fell. So I guess the library couldn't

... go on having them as class sets of textbooks because they couldn't replace destroyed/missing books. So I may have been studying at a time and place where unusually many books were available this way. OTOH, nowadays there are much better possibilities to get used professional books or slightly older editions via internet. To put this in context, I had a quite good job at 20 DM/h (≈10 €/h ≈ 10 US$/h) and spent < 200 DM/month for housing (shared flat to be heated by wood/coal fire, in a house where the ownership was still uncertain 10 years after the wall fell) and ≈100 DM/month for food.

I wanted to post as a separate answer, but I don't have the needed reputation: I agree with some other posters that your reaction is the strangest and most "worrisome" part of this story. Having that many books does seem a little "obsessive", but many people have lots of "obsessive" collections and hobbies. Your book collection in and of itself is not necessarily indicative of a problem. However, the fact that you took the professor's criticism so harshly and seriously that you felt you had to post about here, does possibly point to deeper issues (e.g. your admitted insecurities).

Now, combining the book collecting issue with the sensitivity issue, it paints a slightly bigger picture of possible mental "problems" which are characteristic of certain personality types (usually personality disorders come with a range of common and recognizable traits). In that light, it becomes more plausible that the professor was telling you to seek mental help in the context of him knowing your other personality "quirks", which we as anonymous strangers on the Internet cannot possibly know.  Presumably your professor might know things about you that you haven't revealed to us.

All that said, there's no way for us to make a diagnosis like this over the Internet.  The situation here could range from something as simple and innocent as a passionate hobby, a lot of insecurity, and a joking professor, to something more dire like a serious mental problem, or it could be anything in the middle like a specific part of your personality with a minor problem that could use counsel and improvement.

In short, don't let your sensitivity issues make you paranoid about my comments, but have the maturity to self-analyze yourself honestly, and don't be afraid to consult a mental health professional just in case.  There's no shame in going to a doctor for stomach pains and there shouldn't be any shame in going to a doctor for brain problems either.  The brain is just another hunk of flesh that sometimes needs help and attention just like any other body part.  You'll either leave the experience more confident that you're "normal", or with a plan to make yourself "better".

@Alexandria That's the thing - you understood how and were able to get jobs. I wasn't, and didn't, mostly because of not being able to see the opportunities for it and again, being conditioned to cry poor. I'd have to pirate, but it didn't feel right, so I didn't. So I ended up with few books. You aren't the one who's the bad person here. You need more points of comparison.

(And also not having the social competency, either.)

tl;dr  I  think your professor was rude (and your library is underfunded).
I probably accumulated that many serious physical books over a long career, most of which I gave away when I retired. I have a friend with many more.
I still maintain a substantial collection of recreational mathematics, and some classics.
I don't collect ebooks.
I suspect that nowadays you're at the high end of the distribution for the number of physical math books mathematicians own. But that's no reason to need or seek therapy. Some people just like books.

Thanks for your answer. I mainly prefer ebooks because I have a very limited space for physical books so I try to buy the ebook of a title whenever possible. I’m a very sensitive person. My mind was occupied by what this professor said and I could not concentrate for one whole week.

I see no reason to conclude that the professor was rude, rather than making a joke or light conversation. I suppose a lot depends on the tone, which isn't known to the rest of us. The rest of the answer is good, though.

@RaghuParthasarathy Fair point. Perhaps "rude" should be "thoughtless". I think professors should be particularly careful attempting jokes like this with students.

I disagree with the prevailing sentiment. You could probably benefit from speaking to a professional.

"I spent most of my income on buying books." This is not a smart thing to do with your money. Unless you have a fully funded retirement, you are frittering away your money on something with extremely limited value. Books have almost no resale value, as I discovered when I sold my own academic collection.
"My mind was occupied by what this professor said and I could not concentrate for one whole week." This is not a healthy reaction to any kind of social interaction. Learning some coping strategies to escape these obsessive thoughts would certainly help you.
A thousand books is not necessary or useful. There are very many working mathematicians who do not accrue this number of books. What would you even do with them? Did you index them so that you can quickly search for information? What fraction of them have you read? Are these really useful tools to you or just tokens to accrue and hoard?

I am not a professional psychologist, but based on your unhealthy response to an offhand remark about what appears to be an obsessive (and certainly financially unsound) habit, I think you could probably benefit from talking to a professional. That's what they exist for: to help people. Think about it.

"I spent most of my income on buying books." This is not a smart thing to do with your money., wow, and some people would say the opposite. Who said what is smart to do with your time and money? After 100 years you will be dead. Smart is to spend money on what makes you happy, not what others think you should do. On the other hand point 2 is very valid. Most people will definitely benefit from some psychological education.

@akostadinov I'd be one thing if the OP actually read all the books, but they haven't. Furthermore, the OP is buying ebooks, or just licenses to read certain material. It's hard to argue that buying hundreds of license to read things, and then not actually reading those things is healthy behavior. It's certainly not financially healthy, and it could genuinely be indicative of a mental disorder, for example compulsive buying disorder—just as an example, I'm not a psychiatrist. Also note that spending related to a mental disorder rarely leads to happiness. Treatment is more effective for that.

@Vaelus, with science books it doesn't mean you buy to immediately read. But you can also check things in them when you need.btw going that line all people making collections of whatever are for psychiatrist.

@akostadinov: People who say the opposite are probably not really thinking about the implications. A love of books is one thing, but spending most of your income on books is objectively not a smart thing to do and not conductive to your happiness in the long run (except in exceptional cases like children whose income consists of pocket money and summer jobs, and very affluent collectors of rare books). The only way for a normal person to do that is by living in squalor and neglecting retirement savings.

@akostadinov: and yes, collecting things can and does have pathological dimensions in many people. They're called "hoarders".

@MichaelBorgwardt, if you ask a yogi, he will tell you that retirement savings, buying a house or having a family are "objectively not a smart thing to do". The only objective way to measure what is smart is whether you feel happy with your life or not. Which ironically is very subjective. This often requires trying different things and being open minded about advise, even professional help :)

For myself, I find the very idea of paying for a large number of ebooks, at the ridiculous prices publishers-which have no real reason to even continue to exist-charge for academic books, and knowing that the author will see essentially none of the money, to be incomprehensible. Erasmus had no other choice but to buy books if he wanted to get information...

Assuming that the OP meant to say they spend most of their disposable income on books, I don't see anything wrong with that. Entertainment and professional growth are both important. If they overlap, then so much the better. There's nothing wrong with entertaining yourself by buying and consuming books of any kind. Now, if you're buying books instead of necessities like food and clothes... well, that's an issue. But you probably wouldn't be posting here on Stack Exchange if you were in that situation.

One thing that you might want to pay attention to is that this interaction touched on the topic of money, which is a sensitive subject for a lot of people and can trigger a wide range of emotions. The fact that you could afford to buy over 1000 math books, in a place where your library may be underfunded and maybe your professor also cannot afford to buy as many books as he would like to, might have aroused negative emotions of jealousy, resentment based on economic or social status, and similar things. The professor’s remark might have been driven by such emotions. When people are upset they are more inclined to say hurtful things that reflect their own personal frustrations.
Moreover, it’s not just that you owned up to having (relatively speaking) a lot of money, but you are making a use of that money that the professor might consider frivolous or inefficient. The truth is, as much as all of us mathematicians love reading math books, it’s not realistically possible for someone to read that many books at a level of depth and over a time duration that makes it sensible to buy them when you are in graduate school. So one may get the feeling that you may be a person who likes owning books just for the sake of owning them even beyond the point where it might actually help you learn more mathematics (disclosure: I also went through a period where I also bought more math books than I’m able to read; eventually I realized there wasn’t any point to it so I stopped doing it). The professor’s negative reaction might reflect such a sentiment.

Is the number of my books unreasonable compared to how many books a graduate student or working mathematician own?

This question doesn’t make any sense to me. Different people have different preferences, and one should not decide what or how many books to buy by comparing oneself to other people.

If I need professional help because I buy math books regularly?

First of all, “professional help” is a very silly euphemism. If I were a psychologist I’d take offense that people refuse to name the service I offer but instead resort to such coded language. But if you mean to ask if you need therapy, I’d say you don’t need it any more than the professor you told us about, or any other random, healthy person.

As one of my colleagues likes to say: the point of buying a book is so that you don't need to read it---you always have it for when you need it.

@Kimball perhaps this makes a bit of sense for a small number of books, less so for 1000 books, especially considering that most of them are ebooks, which are available for purchase instantly if you ever do have need for them.

Thank you for pointing out the weirdness of "professional help" language both in the original joke and in how OP posed the question.

@DanRomik That comment is mostly tongue-in-cheek, as an excuse for not having read most of the books on your bookshelf, but it does have a hint of truth.  I personally have a large number of math books mostly for the purpose of occasional/potential future reference rather than careful study.  However, I also didn't buy most of them with personal funds (grants, hand-me-downs, e-access through libraries, ...), which I agree is probably not a practical approach for 1000 books unless you are rather well off.

@TheoreticalMinimum after you have lived a certain amount of time, a lot of things that once seemed to you very far-fetched start looking less far-fetched than they once did.

It might be a money comment, and perhaps it's true being that ebooks don't tend to be free (although I've heard of differential pricing based on country) ... but I have 1000+ cookbooks, and the majority of them were hand-me downs when people died, gifts, and from used book stores.  (I actually have a policy of not spending more than $10/book ... after a day when I bought 100+ books).  I've also been collecting for a couple of decades ... and have a library degree.  (professional help in my case would be a carpenter to make more book cases).

@TheoreticalMinimum Considering that these are university level books, at a conservative estimate of $50 a book, a thousand books is as much money as a decent car or a down payment on a house.

As someone who is Poor, I relate to this very much. That said, a professor, shouldn't have this excuse, ideally. Depending on what books we're talking, and that e-books tend to cost less my guess is it'd cost like $350 a month to get all those books. $4200 per year. Professor is quite far from a minimum wage job.

@The_Sympathizer 1. There are countries where professors are paid very little. 2. Even in rich countries, there are poor and low-ranked universities where professors are not paid well and may struggle financially. 3. Finally, there are people who are financially very well off but for various reasons (for example, because they grew up poor) still associate very strong emotions with the subject of money.

@Dan Romik thanks yeah I didn't think about foreign countries and yeah I understand that last point in #3 as that's me to a large extent. I wonder what their opinion is of poor people who pirate.

When I was a grad student (that was a very long time ago - we had no e-books), I loved to buy (mostly graduate-level) math paper books. There used to be more book store in NYC than there are now - we used to raid Book Scientific, Mir books at Viktor Kamkin, Warren Books, the math section at the Strand (still open), barnes & Nobles on 18th st, McGraw Hill, and the Dover books section in the Coliseum. I definitely had over 100 math books when I was a student, and I have even more of them now, as well as file cabinets full of copies of journal articles. I don't think this number of math books is unreasonable, especially if you're working on something obscure.
I further suspect that these days an average math graduate student has even more ebooks and articles than you because they download them for free from sites I don't want to mention. (Your insistence on paying for your ebooks may be a little unusual.)
Unless this causes you problems (like, you spend all your money on books and can't afford food, or you have no place to keep your paper books, or you feel obligated to read all the books that you have and have no time for anything else, etc) - I don't think you need to seek professional help or change anything, except:
Two pieces of advice that I want to give - avoid ostentatious displays of wealth in U.S. academia (it may be OK in other contexts) and avoid judging other people.

I have bought all of them and have not downloaded any of them illegally.

I'm sure some of the people who heard you, resented that you have the money to buy all these books, while others don't; and also resented your unprovoked dig at people who download books.
A better answer would have been to say that you have hundreds of books (without elaborating how you got them) and which ones are you favorites.

+1 for not mentioning Sci-Hub.

@lighthousekeeper Indeed. It's also important not to mention the Library Genesis (libgen) in answers.

Resented that I did NOT have the money, yes. Resented them for having it, no. I usually go and attack myself, not other people.

Movers!
The most probable professional help you are going to need is when you are moving. 100 physical books look manageable and fit even in a small car along with other items. Well, you probably have other (non-math) books as well.
I have a first-hand experience of moving ~4000 books family library and a ~1000 books personal one, both of them few times. Man, these things are HEAVY ! The last time I just called movers - money well spent, including the tip, I am sure.
Your professor probably did some medicore joke, related to how less-educated people traditionally see the owning any ammount of books.

A piece of advice for the OP. Stop buying physical books until you are settled (when you have a permanent residence.) When I moved from US to Taiwan, the moving company did an estimate. They said the charge would be about USD$10,000.00 I asked her why so expensive, she said the estimate is based on weight and I had too many books. I got rid of a lot books that I didn't really want to throw away. But, you know, for money's sake. The final bill was USD$8,000.00. I saved 2k. What a pity! Those were the books took me years to collect. Yes, I do know what kind of headache it is.

And use small boxes for books!  Ones about the size of a carton of printer paper (10 reams) are perfect.  Any larger and it's just awful moving them around.  (I helped a friend move last year, and his son had put all of the books in the largest box he had ... I had to repack it all into 4 or 5 smaller boxes to manage it)

Personal libraries and books in general are less important than they once were. Before moving across country, I filled an entire pickup truck with boxes of books from my personal library, and sold them at the second-hand book store to help pay for gas. I hated letting the books go, but most were rendered redundant by the digital age. My collection of math and science books are particularly cherished, so I held on to those. I went from six stuffed bookcases down to one. This is MUCH easier to manage. But digital content will never replace the physical book experience, with a good cup of coffee.

1000 of 1100 books are electronic. Only 100 physical books. On my shelf right now I have maybe 30 books of various types, far from them all being math though many of them are at least in math-heavy fields if not pure math. So that's 3.3 times more books. They may also be lighter/thinner. Could pack it into a few boxes. Compared to the amount of junk we as a family had that is not hard to move. Just don't carry junk around with you.

30+ years ago I injured one of my knees lugging boxes and boxes of books up stairs during a move, and I'm still affected today.  Hiring movers is a great idea!

One possible interpretation is that the professor felt uncomfortable because he has far fewer books than you do, despite him having had years more to accumulate them. That implies he's less dedicated to the subject than you, which threatens his status. The only other way he can frame the situation is that you have too many books, and he has the 'normal' number.

People get insecure for all sorts of (mostly immature) reasons, no matter how educated or old they are. This answer isn't saying he's less dedicated but that he might have felt uncomfortable because he felt like him owning less books about the subject matter might imply it. I know people who might act like that for that reason and whether or not the professor in this case was one of them, I don't see how this possible interpretation would be stupid. You might get away with calling the professor feeling that way stupid, but even then, insecurities have very little to do with intelligence.

Do you need professional help because I buy math books regularly?
As long as you think your habit of buying math books is useful to you, given what your goals in life are, you don't need to seek professional help. Even if many other people besides your professor say that your habit is out of line, and even if they can motivate why that's the case, that is not necessarily a good reason why you should change your habit or seek professional help in doing so.
This is true in general, whether it's about you buying lots of books or something else. You should take serious any arguments presented and then see if that would impact your assessment on whether or not your habit is useful to you. Changing a habit simply to fit in better with how other people are going about their business, is never a good idea.
Just think about what would have happened had “Paul Erdős sought professional help to become a more "normal" person:

Paul Erdős was one of the most brilliant and prolific mathematicians of the twentieth century. He was also, as Paul Hoffman documents in his book The Man Who Loved Only Numbers, a true eccentric—a ‘mathematical monk’ who lived out of a pair of suitcases, dressed in tattered suits, and gave away almost all the money he earned, keeping just enough to sustain his meager lifestyle; a hopeless bachelor who was extremely (perhaps abnormally) devoted to his mother and never learned to cook or even boil his own water for tea; and a fanatic workaholic who routinely put in nineteen-hour days, sleeping only a few hours a night.

Erdős would have lived a healthier lifestyle, and been more self-reliant. He would have been more mentally healthy. People absolutely should have offered him counsel to seek some therapy, everyone can benefit from it (when they find the right therapist). This is not a good example to model ones life by.

@BenjaminR Maybe, or maybe no therapist would have gotten through to him and the attempt would just have broken his creativity. I'd agree it's not a good idea to model one's life after somebody like Erdős, but then, the answer didn't suggest that either.

It's rare to find a healthy lifestyle when it comes to doing exceptional Mathematics. Math history is filled with stories of such mathematicians, be it Erdős or Cantor or Ramanujan. Tragic lives from some perspective. But who are we to judge? They experienced something tremendously beautiful and spiritual. I think the sacrifice they did was every bit worth it.

I read that the famous computer scienist and mathematician  Donald E. Knuth owns a large personal library. He is notorisouly known for a series of books with the aim of covering a large portion of computer science and having a very detailed bibligraphy.
In my studies I once visited a professor of statistics from the psychology department. As I entered his flat, books where laying, open, on the corridor. He had a personal library, spanning across multiple rooms, guess way more than 300 books. He was a great person!
I, for myself, also collect books. But I limit myself to hard-to-get and out-of-print ones. I have a collection of some old books from my field that are hard to find otherwise, bought over time at ebay and other online-shops. Furthermore, I would also suppose I have an "above-average" math book collection. In terms of physical books maybe not that much as you own, but I also own a big ebook collection.
Beside from that, I also have, permanently, a collection of 40-50 books loaned from the library. That even caused me some trouble recently in the corona crisis, as libraries shut down and I am not that much around the university anymore. So, I totally understand your passion for books.
If you would tell me about your book collection I would see it very positively, and maybe you can be of great help to your colleagues if they search for literature or need access to a particular book.

If it was spread across multiple rooms, there's a good chance that it was well over 300.  If you have a moderate size bookcase (6 shelves, 3' wide (~91cm)), and books are 1 to 1.5" wide (2.5 to 3.75cm), that's 140 to 210 books per bookcase.  Even a small bookcase (4 shelves, 2' (~61cm) wide) would hold about 48 thick (2" / 5cm wide) books.  Although in practice it's a good idea to not pack an individual shelf too tightly

Probably, I just gave a conservative guess without doing the actual math. But the point is, he had lots of books ;)

When I was early in my studies (physics) I had a real hard time with computing integrals. I simply would not "see" how to go from that weird integral to the nice ones and solve the equation.
Our teacher (a prof that was doing both the lecture and the practical exercises) told us that we need to do at least 50 integrals to "get the vibe" (or something like that).
I did I think 2000 (well no, 2000 is probably the effect of my memory and the trauma, let's say a shitload, which will be probably hundreds) of them (all the books I could find, it was in the very early 90's so no internet) and when the exam came and I was struggling with an integral, he told me in a disappointed tone that he warned us about the 50 to do. I took off my bag the pages and pages of integrals I was training on and he said without smiling

yes, some people should seek medical help to understand when to stop

I think this is close to what was told to you.
I got a great mark, it was his weird way to acknowledge the huge effort I made to try to solve integrals.
You did not mention the country, such wording would not be surprising in a country like France (where what we call "second degree" (in terms of meaning) is part of the interactions between people).
So just relax - he was probably complimenting you.

In my friend circle personal jokes are very common. But I can't see any way the comment above was done in a good faith. There are some people who are truly impolite or have personal dislikes for whatever traumas they personally have. But it is nice that you didn't take it personally. When acting as dickheads, they usually talk to themselves. Probably he himself needed medical help to understand that he needed to stop teaching, not you.

Simple answer.  Anyone who loves a discipline is likely to want to own a part of it.  Whether its owning a piece of a '58 Ford, a 2 million year old fossil, or a piece of the coliseum, tangible objects brings us closer to our fascinations.
Your fascination with owning mathematics books, whether or not you've even read them, is just proof that you are a lover of math.
This is something to be proud of.  So go buy more, add to your collection, and tell everyone else to go read comics.

No. Not anyone who loves a discipline wants to own part of it. If you think so, please provide a reference. Also, what does it have to do with comics? And is it really a recommendation to tell a professor (who is higher up in the university hierarchy than OP) to go read comics, and to what goal?

In my opinion you do not need to seek help. It is normal for some to have high amount of interest in their work. Just remember that other things in life are good too. I myself forgot about many things because I was so focused on academics which for me was also math.
It seems to me that two things are important here. Firstly, graduate math and science fields seem to be an extremely cruel, cut throat, rat race today. These fields are highly sought after today and correlated often with power. It is because of this that a wide range of people enter them. And this brings me to my second point. S.T.E.M. today is highly populated with mediocrity at best and more probably what should be called complete incompetence. Often the race for power is more about social dynamics of regular people that otherwise would not have anything to do with the field if it were not for the hope of power and influence. All to often you will hear about relationships and other things, which is an example of how unrelated these things are to competence in S.T.E.M.
So while I don't think you are crazy, the out look is not always good.
On other hand professors have to sometimes deal with witty energetic students, to appear to be outsmarted is often taken poorly, though such behavior on both parties is extremely childish in my opinion and lacking of perspective. The professor is a working person perhaps short on patience, and couldn't entertain such things any longer. So no big deal then.
Also in my opinion the number of books is pointless metric. Only good texts are of value, and any amount of them is always in short supply.

Also too I find you kind of have to throw away money on bad texts to finally come across a good one. But for someone who actually cares and takes deep interest in or still does, it is worth it to learn topics.

Also I site Gregory Pearlman himself as well as his words and comments on higher levels math academics, to support my views and opinions on S.T.E.M. which otherwise might be attacked for being prejudice, condescending or derogatory.

I am bothered by the comments on 'incompetence' and 'mediocrity', because this attitude can smother passion and participation in those fields. Learning mathematics is a lot like learning a language or a musical instrument. Not all are gifted, but many find fluency with time and effort. Even those who never transcend mediocrity find enrichment from the study, whatever their reasons for entering the field. Condemn not the art lover who can't paint, nor the music lover who fails Mozart. Time and perseverance brings their own rewards to those of passion, even for those lacking native talent.


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What role do universities play in weapon manufacturing, design and research for the military?
I was reminded of a conversation I had with a professor while I was searching for a book on weapon physics and design for an unrelated application in designing an online RPG game.
It was during a grad interview at a top public university in the states when I mentioned that I became fascinated with laser sensing and radar technology due to the Israel-Palestinian conflict during 2013 when I saw how the Iron Dome technology was so effective at protecting the civilians from rockets fired across the gaza strip. I was expecting him to go deeper into the applications of his research focus in these areas but to my surprise he quickly switched the topic.
I had always interpreted this encounter as his lack of interest in discussing anything related to warfare and technological possibilities to that end and not his own personal politics (I would be extremely surprised if he had deep opinions on the conflict itself). For years I had taken the assumption that academics in general averts any discussion to military applications of their research and "things that can kill people". After all which department across North America would boast having research in machine vision for surveillance drones or deadly biological toxins?
But needless to say in the real world there are a lot of research into weapon, weapon making and theoretical weaponry as evident by the host of military weaponry technologies ranging from autonomous military robots, laser weapons, drones, algorithms for missile tracking that are coming out each year (sometimes on Youtube!). The Iron Dome technology didn't pop out of thin air. Someone smart had to design the system, someone rich had to fund such research.
I am curious as to the role that universities play in research into weapons and other military technology. I hope someone can provide me an answer to clear up the following questions:

Can we think of university and the military as two separate spheres
or are they intricately meshed together? Through what means?
Are there any programs or departments in public or private
universities in North America and elsewhere that place emphasis on
research into military applications?
Are harmless research results and findings from universities later on
weaponized at weapon research centers, military colleges, etc.? Or do weapons solely come out of weapon research facilities?
What is the general stance or attitude in academia with respect to research for military applications?

I think that this question is too broad for this site (even considering the formulated specific sub-questions). a relatively comprehensive answer to this question IMHO, probably, would be a candidate for a long paper or a book chapter, if not a whole book on the topic.

I like the question. But, it is indeed too broad. Sorry about the close vote.

@AleksandrBlekh I think the sub-questions are difficult to answer, but not too broad. Especially #2 and #3 are quite specific. I agree that a full answer would be very long and detailed, but that shouldn't be a reason to close the question. For this site, a pointer to maybe existing previous studies could make a good answer.

BTW, we have related questions (or answers): http://academia.stackexchange.com/questions/4954/military-usage-of-scientific-work, http://academia.stackexchange.com/questions/28462/why-would-a-security-agency-distribute-research-funds/28474#28474

This question is too broad, but I think its pieces should be answered.  Can you please split each bullet point into its own question?  People may be reluctant to answer some of them because these are very uncomfortable topics for academics, but they are also very important.

@silvado: Fair enough. But, I think that my point still holds, even for less broad, but difficult to answer questions - if it is challenging to answer a question, it might require a more comprehensive discussion, hence the "too broad" attribution. However, I don't insist on closing the question, if some people can answer it well enough (as a whole or in parts).

I think the first question is too philosophical to answer as it stands. Sometimes there are connections or relationships between universities and militaries, but I don't know whether that makes them "meshed together" or how one would determine that. And I'm not sure what one can say to #4 except that "academia is comprised of individuals, all of whom have their own feelings on this issue".

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How do people in academia know whether their research, result, theorem or thesis is original work?
I am curious as to how academia continues itself without replication or reinventing the wheel. So many academicians in so many areas of work, how would one ever find out whether the work he or she is about to embark on can be considered an original work? That someone didn't already publish the very same result?
In engineering, we have all heard the story of Cooley-Tukey's method of Fast Fourier Transform. The story goes Tukey has been applying his own method of FFT for years without recognizing that the implementation was a fundamentally original approach. Until he brought it up in a meeting in the 1950s, he had always thought that this method was used widely given its extraordinarily simple implementation. Only later did everyone realize that Gauss had used the very same method 160 years earlier.
The same goes for the famed Wiener-Khinchin theorem in stochastic analysis. After two most ingenious mathematicians ever graced this earth came up with this theorem did they realized that Einstein had already published it a decade ago.
Doubtlessly, there are thousands of examples in all branches of natural sciences. It is less clear whether the social science encounters this problem since no two times and places are ever alike, and the social reality keeps on changing therefore novel results is always promised.
So how can one find out in the quickest way possible that his or her work is original work? Original in the sense that the end result is something that improves upon an existing result or opens up an entirely new field without duplications from other people. Does there exist a database somewhere to categorizes all recent and historic progress in a certain field? Are there people who are employed in academia or elsewhere to do this very task?
Edit: I guess same goes for asking a question without looking at the other questions first...seems like this question was resolved in another post T_T

"I am curious as to how academia continues itself without replication or reinventing the wheel.": Unfortunately, academia has reinvented the wheel many times (and sometimes it invented less "efficient" wheels) :-(

I don't know if Wiener-Khinchin is a good example; Wiener's 1930 paper cites Einstein, so he evidently knew of the latter's work (though conceivably he discovered it during the preparation of the paper).  But Einstein merely stated the claim without proof, so Wiener's proof was a genuine advance.

Sometimes, they just don't know: https://www.google.com/?q=medical+invents+newton+integral+gets+citations

I think that to answer this effectively, one needs to carefully distinguish between two concepts that are often conflated in discussing research: originality and significance.  The originality of a piece of work is the degree to which it is distinguished from other pieces of work, while the significance of a piece of work is the intellectual impact that it has.
I think that these two tend to get tangled up because what typically concerns us is significance, but significance can only actually be measured in retrospect.  Originality thus gets used as a proxy for determining significance.  Intuitively, it makes sense: the more creatively different an idea is, the more likely it seems that it will have an impact.
Originality, however, is a matter of both perspective and scale of measurement.  Newton's famous quote: "If I have seen farther it is by standing on the shoulders of giants", summarizes that no intellectual work exists in a vacuum: the myth of the lone genius is just that, a myth.  Edison did not invent the lightbulb, he made a significant improvement in its design which moved it past the tipping point; Einstein did not invent relativity, he had a mathematical insight which crystalized a collection of growing problems that many were starting to pay attention to; Hopper did not invent the compiler from whole cloth, she simply was the first to achieve that milestone amongst a number of others who were working on the automation of computer control. Reinvention, at this gross intellectual level, is not only frequent, it is to be expected.
At a finer granularity of measure, however, pretty much every non-plagiarized work is quite original: even if two people come up with effectively the same approach to a problem, how they approach it and how they validate their approaches will generally end up being very different, simply because the space of possible viable realizations of a program of research is so large.  Likewise, even a highly "unoriginal" idea at the grand scale may have great impact when introduced to an area where it is not commonly used, such as the recent Bayesian revolution in cognitive science.
So, originality per se is not a very useful measure; instead, you really want to be able to evaluate the likelihood of intellectual significance in your work.  For that, there is simply no substitute for getting to know the community that you want to impact.  You can do the most beautiful and elegant research in the world, but if it does not connect with intellectual issues that matter to others, it will remain in a sort of limbo... perhaps to be revived in 100 years (cf. the swing between frequentist and Bayesian statistics), or perhaps simply to be forgotten in the archives of history.
Thus, when it comes to evaluating one's own research, the thing you really should be worrying about is not unoriginality, but insignificance.  If you are working honestly, you will be original.  To estimate the significance of a piece of your work:

Know who you are trying to affect, and learn how to speak their language.  This typically involves reading relevant parts of the literature.
With respect to that literature, be able to explain how your work changes how people in that community should be thinking and acting.

And that's the (perhaps unsatisfying) long and short of it: if your work is done honestly and has an impact on the scientific community, then its originality is sufficient.

You can never really find out for sure (which is why it's not uncommon for things which are not really original to be published). However, when a scientist has an idea that they would like to publish, it's expected that they be reasonably confident that it has not been published before. Someone who works in that field of research will have been keeping up with the latest developments, and should therefore know (99% of the time) whether their idea is new or not. If they don't know of any prior instances of that work, they should then search the standard references in their field, and these days, probably search the internet as well (e.g. Google Scholar) to see whether anything in a different field comes up.
When the paper is finished and sent for review, the reviewer(s) will go through the same steps; perhaps less rigorously, but still, there will be multiple people checking any given paper for previous work on the same topic. By the time a paper makes it to publication, one can be fairly confident that it contains something original.

Often anther field has discovered the same thing but using different words to describe it.

Indeed this happens sometimes, but many research problems are so specific that it's exceedingly unlikely they would show up in another field.

A simple example, is that software wrote as part of research on DNA, is now used  to work out how hand written books have changed over 1000 of years.   We just DON'T know how many other cases of the same solution working for problems in different areas, most of the time when you reinvent the wheel, you never find out that you have.

@Ian I'm not sure if it's clear, but I'm not disputing your claim that there are many cases in which results are rediscovered in different fields, often because of conflicting terminology. But I'm saying there are also many cases, probably a majority, where this does not happen.

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Do I still need a PhD to do research if I have double honours in CS and Pure Math?
I'm planning to get double honours in CS and Pure Math. I'm confused what's the biggest benefit of Ph.D. will be for me? People say you learn to do research, but I can do research(as I have the appropriate background, CS and Math) sitting at home or in industry. Then what's the biggest benefit of Ph.D.? Why should I do Ph.D.?
EDIT1: The only thing that is stopping me from getting a PhD is time.
EDIT2: Link to my new post.

Also see Doing research outside of academia, without a PhD?

The biggest reason to get a Ph.D. is either 1) To teach, or 2) because some jobs require it.  If you have no interest in either you certainly don't need a Ph.D. to do research.

Just focusing on the title: Depending on the university it might be a requirement to teach. If you want to apply for funding it might be required too by certain programs.

It depends very much on what you mean by “research”. Of course anybody can do any research they want at any point, at any time. If, instead, you want your research to be published and reviewed, you most likely need Academia to recognise you in some way, that can be entering or possessing an academic title.

"The only thing that is stopping me from getting a PhD is time." A little humility wouldn't hurt, either.

@DaveKaye is on the right track. Do you need a PhD to do research or even to publish it? No, plenty of people do that without a PhD. It's not like a PhD is some uber-mysterious thing that grants you mad leet research skills that you can't possibly learn anywhere else. A PhD does help a great deal if you want to get grant money, faculty posts, or space to do research.

Actually you can teach without a PhD, although it may be not as common, especially not the higher level courses like MSc and PhD level. Biggest difference is some positions of employment may require a PhD and to be eligble to apply for your own grants in funding bodies you will typically need a PhD. Nothing stopping you from seeking employment as a research engineer helping out doing research in groups where a PhD has gotten grants.

I will raise a point for you to think about it: collaborative networking. When you are getting a PhD, you will cross paths with people who could help throughout your research. And yes, this is a big deal. Although I'm sure you're very capable to gather knowledge into CS and math field, there are many things only a experienced advisor could lead you to.

If you don't have time for a PhD, you don't have time for research.

I could not disagree with @DaveKaye more. I did a PhD in pure mathematics and now work as a Data Scientist (was at NYT now at Conde Nast). His answer basically says the reason to do a PhD is for a) teaching or b) jobs. This is wrong - you mostly do a PhD because you are passionate about research and want to pursue the subject. Never pursue a PhD for teaching or for a particular job. That being said, many jobs will only be accessible with a PhD - having only a masters indicates a lack of context with the subjects you'll be using. Doing a PhD for teaching/for a job are two reasons not to.

@DaveKaye for many types of research, being part of a PhD program or being an acclaimed researcher (with PhD) is the only way to get paid to do such research - so in essence that is a requirement unless you're independently wealthy and can spend a few years on unfunded research. And no, doing it as a hobby after a full time job doesn't really count, proper research by itself is more than a full time job.

I can do research sitting at home

Read a few research papers published in highly regarded venues in your field of interest. Are you capable of producing that kind of work at this point in your training?

Do you know how to identify important and original research questions?
Do you know how to select an appropriate methodology for answering a particular research question?
Do you have a "toolbox" of methods you can apply to different research questions as appropriate?
Are you able to critically evaluate your own and others' work as experts in the field would?

If not: a PhD is an apprenticeship in which you learn how to do the things mentioned above under the guidance of an expert advisor, in an environment that is designed for learning those skills, hopefully with a salary that allows you to focus on improving your research abilities.

Thanks for the advice! The only thing that is stopping me from getting a PhD is time. I have excellent grades(almost perfect GPA). I'm very motivated to launch startup after graduating(maybe after working for a year or so). The only thing that's worrying me is that if I get stuck on a problem while working at my startup and the problem involves some sort of research, Will I be able to do research and solve that problem with my background(CS and Pure Math)? Say that problem is related to machine learning and involves creating a more intelligent machine.

@GaryGrey It sounds like your real question is "Will a PhD help me as a startup founder?" I suggest you ask that as a new question since it is substantially different from what you've asked here. (P.S. perfect grades are not really an indicator of research ability; a good understanding of the basics is necessary, but not sufficient, for doing research.)

"Will I be able to do research and solve that problem with my background?" - @GaryGrey Only you can answer that.  I will say that it is extremely difficult to get hired for machine learning jobs without at least a MS.  Everyone has good grades, CS/Math background. You need to find a way to stand out and graduate work is one way path to do that.

@Gary: I am a little puzzled by your last comment.  Working at a startup and doing mathematical research seem very different.  Is there some connection between the two that you envision?

@ff524 even just a phd is not enough to build all those skills!

As far as the capability and talent for doing research is concerned good grades mean next to nothing. I have seen plenty of graduate students, some of them my own, who have come in with perfect grades, but ultimately were incapable of the kind of independent, original thought that is a sine qua non for a researcher, and a PhD student. So, long story short, there is no way for us to tell whether you would be able to do research work, nor is there a way to do so for a potential employer. If the job in question requires the proven ability to do such work, you will not be considered as a candidate

@ff524 I've posted it as a new question here - http://academia.stackexchange.com/questions/80227/will-a-phd-help-me-as-a-startup-founder

@GaryGrey Problems presented to you as an undergraduate and graded are almost uniformly problems that the instructor knows can be solved, and how to solve.  Usually they are problems where they have already taught you the techniques to solve them, or use techniques you are presumed to know from prior classes.  A PhD teaches you how to solve problems nobody knows how to solve, and (in some cases) nobody even knows the techniques required to solve them because they haven't been invented yet.  Undergraduate "problems" are mostly toys meant to teach, not real problems.

Benefits of PhD:

an expert advisor training you to do research.
a workgroup and peer students to collaborate with.
a salary/stipend (hopefully) while you do it.
shiny title on your business card.
being a student, you can obtain discounts in conferences. It is often assumed that all "early-career participants" are students, because it's the most likely path.
in the industry, having a phd might unlock higher salaries.
if you want a career in academia, it's a sort of certification that you had some research training. Not having one is unusual. Of course, once you have a few journal papers published it starts to matter a lot less.

Thanks for the advice! The only thing that is stopping me from getting a PhD is time. I have excellent grades(almost perfect GPA). I'm very motivated to launch startup after graduating(maybe after working for a year or so). The only thing that's worrying me is that if I get stuck on a problem while working at my startup and the problem involves some sort of research, Will I be able to do research and solve that problem with my background(CS and Pure Math)? Say that problem is related to machine learning and involves creating a more intelligent machine.

Research, by definition, is supposed to be challenging. If I can guarantee that a graduate student can solve it quickly, then it's probably not a research problem. :) That said, with your background it's likely that you can read and understand (with proper effort) most of the research books and papers that you are going to need in your startup job, and come up with something now if you need it.

Sorry, typo: last sentence -> something *new.

Thanks Sir. I've posted it as a new question here - http://academia.stackexchange.com/questions/80227/will-a-phd-help-me-as-a-startup-founder

@GaryGrey and while I have no experience in that, not all research is successful in the sense that it yields a useful working result. Think of all the times Edison messed up a lightbulb. It's research sure, but it just doesn't work because it's a matter of figuring it out. Granted, if research refers to reading and doing citations and things from previous publications with some original thought sprinkled in to glue it together, then I would say that it's a matter of how dedicated you are to those sorts of things.

In general:
Research is a social process.
Hypothetically, you can prove theorems at home and submit them to journals and review journal papers from home. The industry is unlikely to support pure maths during your work time. But there are not so many people worldwide who are able to do research without verbal communication. The majority of researchers need a social working environment to some extent, at least every while and then. And get financed as well. (Submitting a paper without an institution name on it looks strange, btw.)
PhD is sometimes related to science (always in pure maths). PhD is something you cannot do without being associated to a university. What you get from a PhD degree has been mentioned in other answers.

Within a startup as you suggest you may hit a problem that requires research.
Without research training you may not have enough breadth or depth in your field to estimate the scope of the problem i.e whether the solution is well known in the field, the solution is at the edge of current knowledge or whether the solution is currently intractable.
The issue that bedevils all computer science / software engineering problems both in academia and from an entrepreunurial perspective is estimating how long it will take to solve a given problem and how much it will cost.
Typically the issue here is the less knowledge one has about a given problem domain the lower the time estimate given and the higher the potential for getting the estimate wrong. Development time estimation is an almost intractable problem in it's own right for various well known reasons, that the agile methodology has grown up to address.
So what are the benefits of a PhD: wider and deeper domain knowledge obtained from the literature review, a set of research tools, ability to formally present solutions, a measure of mentoring and having been able to tackle a problem in a relative "soft environment" of academia, together with the enhanced credibility of the qualification.
If of course the problem you want to solve is not at at or beyond the current research wavefront for your field, has a tractable solution you may be able to achieve a quick implementation and get to market in short order. Clearly only you can asses that in first instance. However if you have no commercial experience and no higher  academic qualification where will you get your venture funding from?

In pretty much any field you need a terminal degree (usually but not always a doctorate) to get a teaching position.
But you can indeed do research without a terminal degree --or even no credentials at all-- though you probably won't be able to get paid for it, or published, unless you have a Master's.

A PhD is not just a credential that you need in order to get certain jobs (or to get published - you certainly don't need a PhD to publish your work, if it's high quality work.)

There are journals that won't allow someone to publish unless they meet an arbitrary standard.  As an example, Richard Bernstein MD could not get his paper published because he was an engineer at the time, not an MD.  His paper was on the role of carbohydrates in the progress of diabetic debility, and his research was rock-solid.

While there may be some journals with unusual policies, the statement "you probably won't be able to get... published, unless you have a Master's." is just not accurate as a general rule. See Do journals in general have any kind of policy regarding papers submitted by someone without a research affiliation?

We seem to be talking at crossed purposes.  I'm talking about credentials, which aren't the same as affiliations.

The questions asks about "e.g., if a carpenter were to perform a study on memory". Presumably the carpenter is not assumed to have any academic credentials. The answers there are generally in agreement that most journals judge the quality of the work, not the author (indeed, many use a double blind review process, and do not know the author's affiliation or credentials.)

@MMacD: I also strenuously disagree that one cannot get published for research without a master's degree.  Every year there are math papers published in reputable journals authored (only) by current undergraduate students, i.e., by people with no academic credentials whatsoever.  In fact I know of no reputable mathematics journal in which the "credentials" of an author play an explicit role in the evaluation of their work.

I'll probably have to let it drop here, since I only know about my own field, psych, and about those individuals in other fields I've heard about, like Dr Bernstein, who couldn't get published despite the quality of their work.  If you guys know something different from your own fields, Fairy Nuff.