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How to deal with a student who harasses the (inexperienced) teacher during class?
I am a young teacher at college. I have to go way too long, I know but I have the following problem.
In one of my classes, I have this guy who pecks at me for everything I say. He is surely conceited, but it hurts like hell when he makes fun of me in front of the whole class.
However, I take no note of it in class, but later I feel very sad. This makes me frightened to go to that class at all.
He is overconfident and imposing and seems to have got a big gang behind him. He is a threat and he disturbs me. Please help me tackle this situation.

Can you provide some specific (anonymized) examples of the kind of thing that this student does/says?

Is this not heckling? (A milder offense.)

@Raphael "harass" was my word; I used it in the sense of "to annoy or bother (someone) in a constant or repeated way"

Many schools have teacher-training courses for new professors and for TAs/RAs. Can you attend one of them? There are also professional coaching services.  You could also watch a lot of military films and look for what is called "command presence."

How do the other students react? In my experience as a student, the few cases that I have seen were very much frowned upon by their peers.

I'm not a teacher, so take this for what it's worth. When I've seen this sort of thing happen before, usually the teacher takes the student aside after class and lets him know that he's disrupting the class and asks him to save his comments for after class. If they have merit, you'll bring them up next time. If the student does not listen to this, the teacher will announce this in class that they are being disruptive and ask them to stop. If it continues after that, the student is asked to leave the classroom for being disruptive. Only when that fails to work do they get someone else involved.

It usually works, BTW. Usually you don't even go to asking them to leave. You just mention that they will be asked to leave the next time they disrupt, and that's enough. And often it doesn't even go that far.

Step 1. Warn him. Step 2. Threaten him with exclusion from the class. Step 3. Kick him out. Problem solved.

If he goes overboard, invite him to give the lecture ;)

@BenCrowell Kicking out students from class is not unheard in the US, neither.

Just be professional and straight forward with that student. If the student says something correct, then you can acknowledge that in a professional manner. If he simply makes silly jokes or trivial comments/questions, then command the class to focus on business. You can pull him aside to let him know that everyone's time in the class is precious. If he keeps making silly comments, then you can cut his comments/questions short by saying "You and I can have a chat after class on those comments/questions because other students need to focus on this lecture, and we are running out of time".

As a first step you could ask one of your more experienced colleagues to observe your teaching. Let the students know the colleague is there to evaluate your teaching. While it is obviously not a formal evaluation, it is an evaluation of how you handle a difficult teaching situation. You want to tell the students that you are being evaluated so that the trouble makers feel like they can sabotage you. If they do not know why they are being observed, the trouble makers may behave better. The goal is not to "catch" the student behaving badly, it is to have an example of bad behaviour so you and the evaluator can work through possible responses after the class.
Hopefully the trouble makers will try and "undermine" you and act out. With first hand knowledge the colleague may have specific suggestions of how to deal with the student. If the student does not act out you can then discuss the types of behaviour the student shows with the colleague.
Ideally the observer would be from your department, but if it is difficult to find someone, the observer does not need to be from your department nor understand the material you are teaching. They do not need to commit to the entire lecture, 15-30 minutes is often enough. The key thing is they need to be experienced enough to be able to provide suggestions and someone you respect enough to take the suggestions on board. If they understand the material even better, but you want someone that you respect with the needed experience.

I think this is really good advice in general.  Two points: (i) if the desired goal is to get a witness to the behavior, perhaps do not announce the purpose of the visitor.  (Also, honesty check: is the visitor really there to "evaluate your teaching"?  Better to say nothing than to mislead, IMO.)

(ii) I see no advantage in having the visitor be from another department and/or not understand the material being taught.  In fact, I think it would be hard to evaluate the situation without being able to evaluate the intellectual merit / relevance of the comments being made.  Which is not to imply that the behavior is acceptable if the comments are correct, but it may well make a difference in the approach taken.

The likelihood is that the problematic student will alter his behaviour when there is an observer in the classroom. Partly because he is unsure of the reaction of the observer, and partly because his motivation for being disruptive is that he wants his peers to think his is the "cool guy" - but that does not extend to being so disruptive that the teacher is disciplined or fired.

@PeteL.Clark good points. I edited to clarify.

@bain it is easier if the observer sees the bad behaviour, but just observing class can give the observer ideas about how to deal with problem students and if they no who the problem student is, they can watch him/her on good behaviour, which can also be insightful.

@PeteL.Clark One benefit of having an external visitor is that it places them on even footing with your students, rather than with yourself. Since they don't know the material, they can better judge whether you're transmitting it well to others in a similar situation.

@eykanal: An external visitor need not be on an even footing with the students.  If the OP is teaching, say, real analysis and the external visitor is a random college professor, then she will probably be totally lost.  I find your suggestion that teaching can be better evaluated by outsiders to the discipline a bit alarming: that is not in fact how faculty-evaluating-faculty-teaching works, in all my experience.  If you want to know how students are responding to your teaching, you get evaluations from the students.  You don't try to find the most student-equivalent faculty....do you?

@PeteL.Clark - I stated "equal footing", what you describe is clearly not that, and I would not advocate that. Even in that case, though, it is very common for a master teacher in one discipline to evaluate teachers in other disciplines. Many teaching fundamentals are shared across disciplines, allowing any experienced teacher from any department to provide useful feedback to a new teacher. Techniques like classroom management, lesson planning, and general presentation are not wholly unique to a single discipline.

@eykanal: Your phrasing indicated to me an implication: if the visitor is external to the department, then they are on even footing with the students.  I pointed out that was false.  And I find the idea that there are faculty in other departments who are on "even footing" with undergraduate students so iffy -- please find me a faculty member who knows as much as a student who is halfway through undergraduate linear algebra, for instance --  that I would be surprised if any university used this as a principle of teaching evaluation.  Please let me know of any specific examples to the contrary.

"Even in that case, though, it is very common for a master teacher in one discipline to evaluate teachers in other disciplines." Everyone who has ever evaluated my teaching or had their teaching evaluated by me has been in my academic department.  Again I would be interested to hear specifics: this time I find it more plausible that the practice might actually exist in smaller colleges, for instance.

"Many teaching fundamentals...are not wholly unique to a single discipline." Yes, I agree.  One can learn a lot from a good teacher in a different discipline, especially from what they do differently.  But I don't see that that's advantageous in this situation.  You simply don't know how obnoxious the student is being without understanding the content.  For instance, see https://www.youtube.com/watch?v=etbcKWEKnvg.  How out of line is the student (during the lecture itself)?  It seems to me that in order to properly answer, you need to know some homological algebra.

@PeteL.Clark I just asked about who should observe ones teaching http://academia.stackexchange.com/questions/26913/what-is-the-purpose-of-peer-evaluation-of-teaching.

@PeteL.Clark but after the lecture the observer and teacher can talk about what happened and why a question was off base or not. In this case I think you just need to observer the behaviour, with the added insight from the teacher about which questions/comments were relevant. If the issue between the student and teacher focused on the "correctness" of the lecture, then a deep understanding of the material would be key.

@StrongBad: in my experience, the correctness of the lecture is usually at least part of the issue with an interrupting student.  Although the given question is really rather vague, I get the impression that's part of the issue in this case.  As always, I cannot claim universality of my own experiences...

The following are slightly generic remarks. They may not help much in this particular case (first impressions being so persistent, you may have lost this particular charmer), but might be helpful in future.
Remember we all of us are apes, and have ape-like notions of territory.  He is acting as if the classroom is his territory, whereas it is in fact your territory.  But how do you establish that?

Often inexperienced teachers stand right up at the blackboard, apparently as far away from the students as they can possibly get.  Move forwards.
If you can get into the class before them, welcome them in – nothing fancy, just generic "good, good, come in, hurry up... hello..."  You're giving them permission to be in the room.
Look into their faces as you talk; you're the authority figure, and you get to choose who you look at.  Apes really react to being seen.
I generally start a lecture by deliberately and obviously moving to the front of a class, just in front of the front-most rows, and just stand waiting expectantly but alertly.  The students I'm looming over shut up promptly, and a wave of silence spreads outwards.  If people are still talking, look right at them; others will follow your gaze, and there's nothing apes notice more quickly than people looking at them. If they keep talking, keep on looking, in a "you're wasting all these people's time" way. It takes real aggression for someone to blatantly keep talking in those circumstances. If you just keep standing, impassive, repeating in your head "you are a stupid little dick, boy; you are a stupid little dick, ..." you'll freak out the class and they will probably suppress misbehaviour themselves.
Move into the class.  This is your territory and not theirs, remember, and so you can walk into the middle of it and they can't. If the layout permits, teach from the centre of the class occasionally. If you're explaining something on the board/screen, perhaps do so from half-way up the side of the class, facing in the same direction as them (apart from anything else, this provides variety and stops them or you getting bored!).

This doesn't have to be some massive mind-game, and it doesn't have to be and shouldn't be some sort of contest (which is the sort of game where social aggression wins). And I'm not suggesting you spray on the walls! But teachers often forget that physical presence and movement, and where you choose to stand, can send very powerful signals to creatures of all shapes and forms.
Building confidence is hard; moving a couple of metres forward is less so.
An exercise: assemble four or five friends in a row of chairs in front of you, looking straight at you. Stand in front of them, looking back into their faces in turn, in a nice friendly way but saying nothing.  It's weird how difficult it is to keep this up for even one minute. Part of what's initially challenging about teaching is the discomfort of having a room-ful of people looking straight at you, and if you can get used to this (in this context, without the distraction of having to teach at the same time), and if you remember the feeling of being looked at, you'll become more able to deploy the gaze in your territory.

This is very good advice! You've put into words some of the things that I've experienced and witnessed, but that I didn't know how to explain.

The way you refer to students as apes makes me uncomfortable, to say the least.  +1 anyways.

Ah, but the thing is that we're apes, too, which is why we have our own territorial anxieties about moving into the middle of the class, and our own acute sense of where we and others are looking, and at whom. I'm not suggesting we run around the classroom hooting and scratching ourselves (entertaining though that might be, on occasion), but there's a subtle but powerful back-channel here, which we can gently exploit to surprising effect if we're aware of it. Saying 'be in charge' or 'be confident' is one thing (and true); but 'stand in the middle of your classroom' is immediately actionable.

Also, to be honest, who wouldn't prefer A to B as a teacher?  Oook!

Good advice (for any presentation situation, not just a teaching lecture). I do many of the things mentioned. I don't remember if I learned this somewhere, or if it's instinctive. If the latter, I guess my ape is showing.

"and there's nothing apes notice more quickly than people looking at them". Priceless.

To be honest, sometimes you just get a dick. However, I have seen more often that the students merely thrive on the attention and have little regard to how you perceive it.
Without examples of what this student does it's hard to give great advice but here are some of my suggestions based off of observing both confident and in control teachers and those who are timid and meek.
I'm assuming this student asks questions designed to throw you off or tries to contradict you/ correct you at every turn. To this I ask "does it throw you off and is what he says accurate and you were wrong?"
If he's trying to throw you off just tell him that his question isn't applicable to the lesson. If he wants to talk about it later on in more depth, then invite him to discuss it further after class or during office hours (they 99% of the time never do). This can keep you on task and not battling the everlasting "but what if" questions.
If he's correcting you, is he right or wrong? If he's wrong then don't be afraid to tell him so (or that both answers are correct). If he's right, well, to be honest, that hurts your credibility a lot. No teacher that I've ever seen who is consistently wrong has the respect of their students. You really need to evaluate how/ why you're teaching and perhaps need to brush up more on concepts you don't know.
If he simply disrupts class, then you need to take charge and be the leader of the room. When you have someone interrupt you and let it continue happening without saying anything, obviously that sets a precedent. The teachers that I've seen where this happens are quiet and meek and usually try to laugh it off while feebly getting the class back under control. Does this sound like you? Once this precedent is set, it is very hard to go back. I would advise working on that for the next term (assuming you are closer to being done and can just wait it out until this class is gone).
Bottom line, it's your job to be in charge. Some students will walk all over you if you let them. Don't give them that chance. You can be respected and in charge without being a jerk or overly strict. The best teachers are the ones who are confident in their subject and respect their students, which, in turn, reciprocate with respect for the teacher. It's like the old saying goes "Those who have to say they're in charge are clearly not".

Telling "it is your job to be in charge" to someone ho clearly struggles to be does not seem particularly helpful and specific to me.

Like I said, without specific examples to the OP's case, I can't exactly be more helpful. Some go in to teaching thinking that the students will just naturally respect them and behave. You can't go in that way, you need to go in knowing you are in charge and that you're supposed to be. Usually those who don't feel like have a hard time telling people no or being firm because they don't in any other aspect of their life or feel like they will come across as being mean.

I agree with Jen: the OP has framed the problem in very general terms, so at the moment can only get general advice.  I also think that "Bottom line, it's your job to be in charge" is helpful: it reminds the OP that he is both empowered and obligated to take control of the situation.

This is clearly the best answer on this thread. If the student is constantly proving the teacher wrong, then it's the teacher's job to get better at what he/she does. If not, then the student should be told to shut up, or leave the classroom.

Exactly. If the situation gets out of hand, a firm invitation to leave the room can go a long way.

I think you have a potential ally in the rest of the students, if you treat them correctly. You are in a university, not in a troubled high school from a bad film: most of the students are mature persons, that are there because they want to learn.
When I was an undergrad, I had a few friends in class, but most of the people were from completely strangers to no more than acquaintances towards the end of the degree. This means that I don't have any kind of loyalty or tolerance towards them: if you are annoying me, I am not going to like you.
What do you think would happen if an outsider interrupted the class saying that the Apocalypse was going to happen in four months and you are all going to be abducted by UFOs? And what if this happened every week? Do you think your students would like it?
It is important that you don't turn them against him, but instead give them the chance to do it. Put them on your side by engaging in a good interesting lesson. If you are teaching one of these subjects that nobody likes, try to make it more appealing by doing an experimental demonstration every now and then.
If you try to actively turn them against this annoying subject, he will get angry, and things will get worse. And the students may misinterpret what you are trying, not like it, and things got even worse. Instead, you have to bring them in your boat because they want to learn and you are there to teach them. That guy is the enemy just because he is getting in the way, but you are a magnificent god, and he is welcome if he stops acting the way he is.
Your mindset has to be that you are there to teach the class, and you have to take whatever means are necessary for it. If someone comes in late, making a lot of noise, and disturbing everybody, you have to show them you don't accept it and even tell them off. If someone consistently asks stupid questions, you can tell him to shut up. If someone is derailing off topic, you should kindly invite them to discuss after class. If someone starts to make political interpretations of Matrix Algebra, tell them that is not the place or the moment to discuss it. If someone is willingly hurting you, you may consider telling them that it is not nice and they should stop it. If you firmly invite an offending person to leave the room, they would either do it, or chicken out and apologise. If he just refuses, or decides not to acknowledge your request, or attack you verbally, his peers will see it as childish behaviour.
Any confrontation you have with a student, is it not you, Name Surname; it is the lecturer of Your Subject. Once you step out of the building, you don't personally hold any grudge against them. This is where your power comes from, and also your shield: it is not you, it is the lecturer.
You need confidence before getting in that class, and the best you can get is with passion for your subject and teaching. Prepare and rehearse your class beforehand, make sure you know everything you want to say, prepare the questions they may have; and when the day comes, go into that room knowing that you are going to nail the lesson, no matter what.

I didn't know this was in a university, are you sure about that?

@Mehrdad per the first line of the question, "I am a young teacher at college."

Wow, really sorry, I'm not sure how I totally missed that. Thanks.

Offtopic, but I'm curious, how can anybody make "political interpretations of Matrix Algebra"; I mean, it seems that it is as objective as it gets ?

@Dangelov it was an impossible example, but you can find people making political claims about nearly everything. The point is, unless you are in a politics class, it is not the place.

@Davidmh, thanks for your explanation. I understand now what you meant.

As @bain said, do not engage in bickering.  I would like to pick up on this and amplify it a bit.
My suggestion is: whatever the student says, take it seriously - even if he clearly does not mean it seriously.  Do not take it as an attack on you - even if he clearly means it as such.  (Or, if you can't help taking it as an attack on you, at least try not to show that in front of the class.)
When I say "take it seriously", I mean something like this: if you express an opinion and he says "that's a really stupid comment" - don't retaliate, but ask him politely, "Why do you think it's stupid?  What is your opinion on the question?"  If he replies with evasion or further abuse, quietly but firmly repeat the question.  If he tries to get out of it by saying "well the whole question is a waste of time" you can ask "What do you think are the important questions, and why do you believe they are important?"  Make him commit himself: let the whole class see that he is the one being unreasonable, not you.
It is important, however hard it may be, to stay calm and polite.  You may at present feel that the situation is you against him, but I can assure you that many students in your class will want to learn the subject and will be on your side, even if this guy and his gang have scared them into not admitting it.  If he is abusive and you are polite, the class will be even more on your side - nobody really likes this kind of behaviour.
Sometimes (I don't know how it is in your subject) the line between robust discussion and personal attacks can be fuzzy.  If, however, he engages in definite personal abuse (of your race, gender, appearance, manner of speech and so on) then he has clearly crossed the line and has forfeited his right to be in your class.  Get the authorities to remove him.  And if it results in his being tossed out of his course, don't even think of being sorry for him.
Another thing: if the situation is seriously making you sad and frightened to go into class, then this could be turning into an occupational health and safety issue.  Those who are in charge of such things in your institution may be able to help you.
Finally I would like to support what others have said - if you could give more specific examples of what this student is doing, then you will probably get some more useful advice.  I am sure that many people on this site have been in the position you describe and would love to be able to help you.

I think this is the best answer yet. Almost every other answer emphasizes on confidence and (dominant) body language, but a teacher shouldn't have to be a natural brute to be able to teach.

The problem is one of basic psychology. In a classroom environment, an effective teacher needs to be respected as the leader - either respect for the authority of the position itself, or respect for the knowledge, or just basic good manners. By being disrespectful and undermining you and your authority, the student is implicitly challenging you in an attempt to elevate his social standing within the group.

it hurts like hell when he makes fun of me in front of the whole
  class. However, I take no note of it in class, but later I feel very sad.
  This makes me frightened to go that class at all. He is overconfident
  and imposing and seems to have got a big gang behind him.

Your main problem is that you are under-confident, and your authority has been challenged by someone who is more confident, more imposing, and better able to "work the crowd". You need to regain the respect of the  students. How you do this is up to you, but I would note:

Be confident. Act confident. Act like you are actually in control. When you begin to act like you are in control, you will begin to appear like you are in control, and, eventually, you will be in control.
Stop being scared. This person can not physically hurt you. If he can mentally hurt you, then that is because you allow that hurt to happen. You need to find a technique to reduce your fear. Some people do this through contemplation, some through repetition of phrases like "I am a tiger", some through more physical techniques like study of martial arts. Do whatever works for you.
Play to your strengths. You are the one who is an expert in the subject that you teach. The student is not. In this domain, you are the more powerful one. If you choose to engage him, do not engage in bickering, because that is his domain. Engage him in the domain where you will win - in the exercise of academic and technical excellence.
One option is to ask him if he knows the answer to a particular question, and ask him to explain it to the rest of the class on the board. This does not require singling him out - you can ask other students to also answer questions - but what it does is put him on the defensive. Either he admits that he does not know the answer, or he has to get up in front of the class and explain it.
If the latter, then you have turned the focus of attention towards his knowledge and his teaching ability. It might help him to realise that he does not really want to be the leader in the domain where the leader has to stand and teach everyone else. He will probably get parts of the answer wrong, or have an incomplete answer, and afterwards you can probe this, and ask the other students to explain where he went wrong. This re-establishes you as being in control, and turns the focus of the class to subject knowledge and academic ability. You do not need to undermine him, just encourage him to demonstrate his lack of knowledge, and then let the other students demonstrate their own  ability. This is enough.
Be interesting. Boredom is a driver of problematic behaviour. The fact that other students are following your problem student indicates that they perhaps are not being challenged by the lessons. If you see the eyes of your students glazing over as you begin to speak, then change direction, and structure your lessons to directly engage the students. One technique is to have them work on problems in pairs, and then randomly choose one of them to present the solution to the rest of the class. This forces them to work, and forces them to come up with an answer that they not only understand, but understand in a way that they can explain to everyone else. Nobody wants to stand up in front of the class and look like an idiot. It takes the focus off you and your teaching and knowledge, and puts it back on the class, which helps to make the lessons more social and interesting.
Take control. Changing the structure of the class and engaging the students in a way that allows you to demonstrate your leadership may encourage your problem student to back off. He is a part of the class, and if you have control of the class, it is likely that he will defer to that. But if he does not, you may consider a more direct approach:

The warning. Confront the student outside (or at the end) of class. Tell the student that his constant undermining is disruptive to the class and you are not going to stand for it any more. Tell him that if he can not be respectful, and does not value your teaching, then you do not want to see him in your class. Do not be angry or scared or emotional - just be straight - you are done, this is not a negotiation, this is the way it is.
The appeal to authority. Tell the student that you are not going to stand for his behaviour any more, and if it continues you will report him to the disciplinary authorities. All institutions have formal mechanisms for dealing with discipline. The threat of this may help him to temper his behaviour.
Remove the student from your class. Not always possible, but, either officially or unofficially, get rid of him. Officially, you can request a formal transfer. Unofficially, you can tell him that you will keep his name on the register but you do not want to see him in your class again.

I physically cringe when terms like "alpha leader" get thrown around (bonus cringe points for "alpha male"). Also, telling a scared and under-confident person to stop being scared and start being more confident seems ... relatively useless.

@xLeitix Then call it something else - call it whatever you feel comfortable with. The terminology is not particularly important. What is important is the recognition that this problem is fundamentally that of a young man asserting his dominant personality and influence in a social group of his peers. I will only note that the question states "He is overconfident and imposing and seems to have got a big gang behind him" - which is pretty much the definition of an alpha in any species. But if you do not like the term, just substitute it for another. "A rose by any other name.."

@xLeitix Whether advice is of use or not ultimately depends on the response of the person asking for the advice. Fear and under-confidence are psychological issues, and the answer is to become more confident and less fearful. How that can be done by an individual person is another topic. I did suggest some techniques that are successfully used by some people, but ultimately each person has to figure out what works for them.

How can a teacher assign a grade to a student they unofficially kicked out of the class? My school would not allow me to do that. Are there schools that give teachers the option to remove any student?

@Village if the student is not allowing you to teach the class, there has to be ways in place to stop it. Depending on the rules, you may not be allowed to force him outside, but you an surely strongly suggest him to take on your invitation to leave the class at once.

It's dangerous to become obsessed with confidence in front of a classroom. What if you make a mistake, or you don't know the answer to a question? A good teacher should admit this immediately, and involve the class in the process of correcting the mistake and finding out the correct answer. If you feel that losing your authority will turn the class into a bunch of heckling jackals, it might lead to these kinds of things: http://xkcd.com/803/ Real confidence comes from being very honest and very much yourself. These kinds of confidence-building techniques tend to have the opposite effect.

How can a teacher assign a grade to a student they unofficially kicked out of the class? — By giving them an F.

Yeah this is not /r/redpill.

@xLeitix There's the term "alpha" for crazy people who think you have to be a dominant person that does whatever you want and doesn't care about others, usually contrasted with "beta", which means complete wuss. There's the term "alpha" in its original ethological sense which means the leader of a group, and carries some connotations of how someone stays/becomes the leader of the group (because the term seems to come from the study of animals), contrasted with beta, the second-in-command, and omega, the one eveyone picks on. Is even the latter use cringeworthy to you?

@Peter I agree with everything your saying, but acting, talking and walking confidently certainly helps, especially when you haven't reached the point yet where you're genuinely confident in what you're doing or who you are. These things reinforce each other. I also use the "wrong" response from that xkcd a lot, because sometimes the answer is complicated and we need to move on (because I don't want to lose a large part of the class by talking for an extended period about details that are ultimately not important.)

Maybe you have been out of luck and got the 'bad' class (my teacher friends always have one from time to time) but if this problem is recurring, there is probably something you can do to improve yourself.
I also think @StrongBad answer is a good way to find help to solve your problem with this guy in particular.
As student, I have observed some attitudes were much more prone to gain the respect of the class.

Confidence (really the most important): Of course it was more present with older teachers who commend their course content and have a lot of teaching hours behind. This is cruel, but this is played in the first 30second you meet your new class. The way you speak and hold yourself in this period can go a long way...
Ask questions: when you know the teacher might ask a tough question at any time, you follow much more and it usually avoid too much discussion. As student, often you don't want the teacher to see you and ask you to answer a hard question in front of every one. If really one guy is bothering you why not call him in front of the class and ask him to do a tough demonstration?
It is sad to say, but the harder/more important courses will always be more quiet than the easy one even if the teacher is bad.
Make it interesting: if the content is interested and well presented most student listen.

Again this is only my observation from the bench point of view...

@Lynda “Never argue with stupid people, they will drag you down to their level and then beat you with experience.”

I agree that confidence is key.  Ultimately it is a battle of dominance and currently the student has the dominant personality.  Once you are more confident with your teaching (NOT your mastery of the material but rather your ability to present it) things should get easier.  I used to dread teaching too, but after a semester or two I found my confidence and now enjoy it

Asking questions is good, but be careful, no one should be scared in your class. Some students have issues with their personality and confidence, if you force a random student (not one that is outrageously annoying) to speak up in front of the class, he may feel embarrassed and not go back to your class.

There are some good tips in the existing answers, but I would give the following advice as a crucial first step: be very careful with your iterpretation of the situation.
You've already branded this guy as "out to get you". That means you've made it personal, which is a bad place to get to. Not only because it leads to nasty behaviours and escalations on both sides, but also because that's what allows him to get at you confidence.
Being in front of a classroom enhances certain signals and dulls others and can make you very paranoid. I've had situations where I couldn't figure out what was going on and why people were laughing and as soon as the class was over I suddenly realized that someone was making a simple joke. Not at my expense, nothing to do with me, just a normal joke. And of course, to make it worse, the students have no idea how blind you are to social cues up there (at least when you're starting out) so they think you're a total dork.
A lot of things that feel like heckling can actually stem from other reasons. It may be that he's just a little socially awkward, and asking real questions. It may be that he's actually nervous and it's coming out in a strange way, and it may well be that he disagrees with something, but doesn't yet have the academic skill to show it in a civil manner.
However, even if he is just out to bully you, and you see no point in trying to understand where he's coming from, it's best to hold on to your detachment. Don't let him him drag you down to his level. If he is heckling, he's basically brought high-school level behaviour to a university. I would prefer to act with almost astonishment. Let him explain himself, and really act like you'd never expect anyone to behave this way. Don't be indignant, or in any way affected, just act as if he's just sat the wrong way around in his chair or drawn on the table with crayons. Convey in your attitude and body language, as much as you can, that he's behaving very out of place and very childish. Ask him to explain (in a gentle tone, like you genuinely don't understand and want to find out) and don't be afraid to leave long pauses.

Read When I Say No, I feel Guilty by Manuel J. Smith.
I realize that this book sounds like it has nothing to do with your situation, but before you dismiss it out of hand, I implore you to read some of its customer reviews on Amazon.
Note that it's a book that is best read backwards, from the back of the book, where the examples begin, to the front of the book, where the theory is actually discussed.
On that note, someone else mentioned using sarcasm, but the book and I would advise against that. It's important that you do not throw verbal stones back at him and it's important that you do not scold him and make him lose face in front of his classmates. If or when that student crosses the line, ask to speak to him privately. Once alone with him, assuming you feel safe enough to meet him privately of course, he won't have an audience to play for, so he's much less likely to act out if you can be assertive about what you want from him.
Next, I'd suggest that you take up some kind of combative sport, like martial arts, or boxing, or even a sport like rugby. This is not to encourage you to fight, please do not misrepresent my intent, this is just to teach you how to carry yourself with confidence and to mitigate some of the fear of a physical confrontation.
Next, I'd suggest that you practice public speaking in a safe environment. The best place for that is http://www.toastmasters.org/ (it's a non-profit club, so it's a cheap way to practice public speaking and to bring up some of the problems you've been having in class and discuss possible ways to address them).
Just one warning thought. Not all Toastmasters clubs are equal. If you don't like the vibe in one, try another one, and if you don't like that second one, try a third one. They're basically everywhere and there are many to choose from. The key is to keep on going, and to participate, even if you don't feel comfortable at first. If you go frequently enough, you'll feel comfortable enough and it can become like a second home to you.
Next, and this is the most difficult challenge I can give you, so I don't really expect that you'll do it. But once that you've done all those three things I've suggested, I'd encourage you to take it up a notch higher, and that's to join a comics class sponsored by a night club, or to participate in poetry slams, or even to sing at Karaoke clubs, all the while staying completely sober. I'm not saying any of these things are going to be easy, especially not for the type of personality I envision you to have, but if you can do any of these things (without the help of alcohol), handling a single heckler in your class will seem like a real walk in the park after that.
Please note that these things are worth doing, even if that guy ends up dropping your class. Our society tends to reward confident and extroverted people. And aside from the book I've suggested, which is one in a million, nothing beats practicing frequently and sharpening yourself against the brunt force of a real live audience.

Another way to deal with this sort of a problem is to only engage with students' questions when they have questions that (in your judgment) are of direct relevance to the lecture. You can tell before you start that you're running a bit behind and that you'll now limit discussions during the lectures, students who have additional questions will be able to discuss that during the break.
Then when a question is asked or a remark is made that you feel is not constructive, you'll just say so (e.g. you can say that you can't address this right now, but you're happy to discuss this in detail after the lecture). If you think that you're losing control of the class due the problem student having a following and they then start discussions in class among themselves, then a very effective way is ignore what's going on and to lower your voice so that you make yourself a bit more difficult to hear.
This "lowering of the voice-method" is often used by professors when teaching to first year students who come straight out of high school. The alternative would be to ask the students to be quiet, but this then opens up a discussion about keeping order in class and that's not the ideal position to be in. You have your job to do which is to teach the subject, you're not a Kindergarten nanny. It's the student's job to master the subject and part of that job is attending college to follow the lectures. If they can't hear you because other students are talking they can ask them to stop talking, lowering your voice will force their hand immediately.
Exerting your authority explicitly is best done at the first lecture the moment you address the class. At that point there is no problem at hand, so the ball is firmly in your court. You can then explain the rules for the exams and the consequences of failing the exam. Here it helps if the subject you teach happens to be one which is difficult to pass and there are a limited number of make-up exams. This puts a lot of pressure on the students to act in a serious way. Also it would help if attending the lectures is not compulsory.
But suppose that the subject you teach is easy to pass and that attending lectures is compulsory so that you're going to get quite a few bored students in class. In that case you should consider modifying the lecture plan so that it includes additional tests. You then make it a requirement that students are allowed to sit the exam if they have done sufficiently well on the tests. You make it clear that this is going to be purely your judgment, that no appeal is possible. Also, you can mention that you have the right to deny a student the right to participate in a make-up exam. This can happen if the student does not show up at the exam and doesn't have a valid excuse (to be judged by you).

I think the best way you can react is not to take personally his "attacks". Act like the guy does absolutely not touch you, that his questioning comments and remarks are useless and uninteresting. But for that, you should trust yourself and abilities. Don't let him spread doubt in you.

Giving authority to problematic students often helps as delegating responsibility will put him under pressure and divert his mind from generating devilish ideas towards escaping / fulfilling the responsibility that you have just burdened onto him. Example: Make him a Class Representative or a leader of the course.
OR
Reverse Psychology - Applaud his comments, Use sarcasm, intelligent phrases or sheer innocence to mess up his "efforts".
This will not only eliminate the problem but also set an example for other students.

A class representative exists to fulfil a role, and he may be needed at some point, and when that occasion arrives, I wouldn't want him to be there. Also, the example you are setting is "be a $#%& and get promoted!"

@Davidmh I'm not sure this is promoting a $#%&. It really depends on the details which are missing. It could be the student is quite advanced and sincere but does not know well how to ask questions delicately and the OP might be a little more sensitive than others might be. If the student is advanced (if he is often more right than the teacher) then having him use his knowledge and energy can be beneficial to all, including the other students. More details from the OP would help.

@earthling just tactless advanced students can be annoying, but leaving the lecturer in the verge of crying takes more than that. I am all for re-conducting behaviour, but there seems to be an underlying problem that should be tackled before. If I am brilliant and I want to show off, I can do it without making fun of the lecturer.

@Davidmh I agree. However, just because you can do it does not mean everyone else has those same social skills. In my undergraduate days I was sincerely confused why the lecturer was doing something (programming) in a way which was clearly not ideal. From his looks, I could see quickly he was not happy with my questions. So, I stopped asking after my 2nd question. But I can imagine students who would not stop (being less sensitive) because they wanted better information. Is the student wanting an ego boost or wanting deeper information? If only the OP gave us that information.

Can a TA make somebody a class representative? In all the universities I have worked, the students elect their class represenative. Apart of that, I don't think it is a good idea to promote for bad behaviour.

That can be brutal.  Two possibilities:

You have just stumbled upon a "worthy opponent" which offers you the best opportunity for your academic life:  a chance to master the skill of dialectic in a war for nothing less than your intellectual integrity.  This requires building the skills of ruthlessness and patience.  Take care not to let ruthlessness devolve into cruelty.  And you'll have to master timing for it not to blow up in your face.  Forewarning:  this could take months.  Time it for the end of the semester.  :)
Don't fight him in the slightest, but humor him.  But do talk to the Chair.  Try to engage him/her on the problem since they are responsible for assisting you in exactly these issues by position of their office.  If they can't help you, you can be sure that they don't deserve the office, because this is one of the most important issues for building the integrity of a university program and it is their job to help their faculty.

I am pretty sure a dean is at least a couple of levels to high to go to about a problem student with peers, teaching mentor, director of teaching, director of undergraduate/graduate studies, and department chair all coming first.

I'm referring to a Dean as the head of the Department, but I suppose I should say Chair.  Will revise.


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Bonus Quizzes to entice students to read their syllabus?
As I'm sure many lecturers/professors would attest, one of the frustrations of teaching can be the continuous asking of questions that had a student read their syllabus and/or navigated the online learning site, would have most likely been answered.
I teach a social science class and I spend a lot of time on my syllabus, and even more time on the learning site we use. I have an abundance of extra resources to help students out and everything is neatly organised. Regardless, I still receive countless emails and questions not about the content of the course, but when my office hours are or where my office is, or when is the assignment due, or do they have to attend class, and so on.
In speaking with a number of academics, some of the solutions have been creating assessments based solely on the syllabus, such as a 5% quiz in the first week of class. A colleague of mine who was concerned about students not knowing how to navigate the library created an assessment where students had to go to the library and answer a set of questions.
My faculty is quite strict about assessment tasks though, and I've been informed I can only have a max of 2-3 in my unit, so I'd rather not waste them on a syllabus test.
I was thinking about setting up some online bonus mark quizzes where students who wanted to earn a little extra credit could complete them. They wouldn't be worth much, maybe .5% per quiz, perhaps totaling to a bonus of 2.5% or something similar (my best student typically has a grade of around 94%). They'd be on the syllabus, the learning website, perhaps a research bonus quiz (navigating online databases) and so on.
I will consult with local faculty and check my institution's policies. But beyond that: does this seem like a good idea? What factors should I consider?

When I get such questions, I refer students to the syllabus rather than providing the answer.  After a while, they get a clue. Sometimes.

It sounds like spoonfeeding, is this community college, 4-year college, undergrad, grad student or what? Is teaching them how to use the library (for your course and discipline) your job or the library's job?

The standard time-honored solution is to write a class FAQ, make that one of the first class handouts, read it in class, reference it in your email SIG, just reference the URL in response to any questions covered by it. Make sure it's clear, concise and covers the questions. Break stuff into sections like "How to Use the Library", "Assignments", "Grading", "Attendance" etc. etc. Ask your students and TAs in your end-of-term assessments how the FAQ can be improved.

Another standard technique was on the first couple of assignments, to give them some basic tasks (e.g. "Using the library, find the answers to X, Y, Z") which carried no weight, or almost no weight - but don't necessarily tell them that upfront. Or tell them (in the FAQ) that if they're borderline at the end of semester, you may take their responses in assignments into consideration.

I'd avoid setting summative assessments (i.e. for course credit) on topics other than the subject material you expect the students to learn. Doing so might come back to bite you, even if you keep the relative contribution to a final grade as low as you are suggesting.
Perhaps you could spend half of your first lecture rhetorically asking the sort of frequently asked questions that get your goat, while at the same time navigating your course webpage, to show where a student will find the answer to your questions. After  reading out five or so of the most commonly asked questions, the students will get the message:- the answer is likely to be on the webpage. Look for it.

That's a good idea. I do have a FAQs up on the learning site but perhaps actually reading them aloud/showing students exactly where things are on the learning site will get the message across :)

As I'm sure many lecturers/professors would attest, one of the frustrations of teaching can be the continuous asking of questions that had a student read their syllabus and/or navigated the online learning site, would have most likely been answered.

Ha ha! Yes, it really happens all the time.

Regardless, I still receive countless emails and questions not about the content of the course, but [...] where my office is

My students typically wander at the opposite side of the university with respect to my office and when they eventually succeed in finding me, I ask them: haven't you read the location of my office on the syllabus on the course website? I let you figure out what the answer is...
Students simply don't read page-long bureaucratic information.

In speaking with a number of academics, some of the solutions have been creating assessments based solely on the syllabus

I don't like this idea nor that of bonus quizzes.
To solve this problem, this year I've decided to remove the syllabus altogether (no one reads it anyway) and to send updates by email to all the students (e.g. hey guys, the new homework is online and is due by etc.). Every email should contain just one piece of information and have a length of just a couple of lines. As for the office hours, they are by appointment and I give office directions when they ask for it.

Gosh I would love to not have a syllabus. Unfortunately, the faculty stipulates that everything important must go in the syllabus in addition to the learning website and we can't get rid of the syllabus. The problem with email is that I have 300+ students in my classes, so while I utilise the posting system on the learning website which automatically emails all students, they still feign the old 'oh I didn't get the message'.

I have indeed given bonus points for questions from the course syllabus and it seemed to resolve the problem that you described (although I never did a formal before-and-after test, I did get a subjective impression that after I implemented this, I was much more rarely bothered by students asking questions on what is clearly on the syllabus).
However, I implemented my system with some slight but very crucial differences from what you described, that seem to have resolved your concerns:

First, some background: in many of my classes (mainly for undergraduate students), I begin the class session with a reading quiz of around 5 multiple choice questions. These are low-level comprehension questions based on the assigned reading simply to make sure that they read the assigned material. I do not ask any tough questions that require deep understanding--only very surface questions with the aim that if they actually read, they should get 4/5 or 5/5, but if they didn't read, they should not be able to guess more than 1 or 2 correctly.
To this reading quiz, I add a bonus question taken from the course syllabus (e.g. when are my office hours; or what is the deadline for the 1st milestone of the semester project). With this bonus question, there are 6 questions in the reading quiz.
I still score the quiz out of 5. So, if they got 4/5 of the regular questions plus the bonus syllabus question correct, their score is 5/5. (If they get 5/5 + the bonus correct, I still give them 5/5, not 6/5.)

The advantages of this system:

I do not dedicate any extra time, whether as a dedicated assessment or class time, to getting them to read the syllabus. I simply inform them of the bonus questions from day one and then the syllabus assessment is built into whatever assessments I've already designed.
Because I give my regular quizzes throughout the semester, students are motivated to read the entire syllabus early on in the semester and they are also motivated to refresh themselves on the details all the way up to the last regularly scheduled assessment.

All that said, as you have noted, the idea of assigning course credit points for syllabus content is controversial to some people. However, I have no problem with it. I firmly believe that students who are well aware of the syllabus learn more in the class, because the syllabus is designed to maximize their learning experience. So, I believe that giving bonus points for knowing the syllabus content indirectly but very meaningfully increases their learning, and so is well justified.

Not sure if this applies, but any school that would support tangential "assessments" such as a participation/attendance score would surely fund no fault with this second cousin, which would have the fringe benefit of raising awareness of the very sort of policies that such a participation score is likely to be measuring.  I have taught at numerous universities that have tried both ends of this assessment spectrum, from read-for-detail "quizzes" in the first week to contract-mimicking "I read it and understand" signature pages to detach and turn in.
I'm contemplating one that forces a detailed perusal: burying a code phrase, Waldo-style, in  a random location deep within the syllabus along with instructions to send me that code phrase in an e-mail (to establish their knowledge of my e-mail, at yet another school in which at least two colleagues have nearly identical addresses) after receiving verbal instructions to read the syllabus cover to cover "and do what it asks you to do" on opening day, just to try out such a novel approach.

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text:
How does it affect the treatment of a mathematician's results, if that mathematician was a Nazi?
I've been studying uses of quaternions to study various types of orbifolds. The important thing here though is that I came across an absolutely incredible result due to Vahlen in 1901, that apparently received no attention until Ahlfors revamped the idea in 1985 using more contemporary methods. The result (Vahlen matrices) is central to my research.
The problem with Vahlen is that he was about as much of a Nazi as a person could be. He was in the SA, the SS, accused brilliant Jews of plagiarizing Aryans, helped the Third Reich expunge Jews from the scientific community, etc. He even supported the Nazi party before its infamous rise to popularity.
My questions are:

What is the likelihood that Vahlen's results were neglected due to this political misfortune?
What are some similar instances, particularly in mathematics?
What is the etiquette of discussing a great result by a person who lead a morally reprehensible life?

Regarding the third question, Ahlfors simply writes about his math, which I think is the right way to go for a journal article. But what about a lecture or more general discourse among the community? I would feel weird if I were to give a lecture where I'm praising a guy who may have contributed to the extermination of an audience member's family. I have kind of a dark sense of humor, so I'm likely to mention the Naziism and poke fun at it ... maybe use it as an example for why you have to check everyone's results regardless of their other results. Personally I would find it funny to denote the Vahlen matrices by a swastika, but obviously this would be extremely inappropriate.
A more specific issue I'm having is that there is a lot of conflict about the notation for Vahlen's discovery, as other notation was developed for 84 years without it. It is an obstacle because we literally have different definitions for identical symbols all over the place. My feeling as that the clearest notation would be to use a $\mathcal{V}$ for the Vahlen matrices (which I have not seen in any papers thus far) and move on, but I wonder if there is a tendency in the academic community to avoid even that. I don't want even an iota of a suspicion of being sympathetic to this man's priorities.
An important note here is that Vahlen's matrices are in the domain of pure math. That means their development had nothing to do with any sort of experimentation, and are quite disjoint from these other aspects of Vahlen's life.
Follow-up: Without naming any names, some very established mathematicians I've been discussing my work with have unequivocally recommended omitting Vahlen's name from any constructions I use in my paper, specifically because of the political history. As in, don't call them "Vahlen matrices," call them "Ahlfors matrices," and things like that. Regardless of whether or not one agrees with that sentiment, to me it is concrete evidence of Vahlen's Naziism's effect on what credit he might receive for his mathematical work.

Comments are not for extended discussion; this conversation has been moved to chat.

Reminder that we can only move comments to chat once, so comments that are not requesting clarification or suggesting improvement will be lost. If you have an example of a "similar instance" that you would like to add, please add it as a bullet to the community wiki answer (note that this is a bit of an exceptional case; we do not generally take questions that ask for lists of things).

Could you call them Ahlfors matrices instead of Vahlen matrices?

I think there is no academic issue here.

The problem with Vahlen, as you may have guessed by the title, is that he was about as much of a Nazi as a person could be. He was in the SA, the SS, accused brilliant Jews of plagiarizing Aryans, helped the Third Reich expunge Jews from the scientific community, etc. He even supported the Nazi party before its infamous rise to popularity.

I looked into Theodor Vahlen, and I agree that he was a morally reprehensible individual.  But this is irrelevant to a discussion of his work: he proved the theorems that he proved whether he was good, bad, or whatever.  As is well known, the Unabomber is a published mathematician.  His six papers have eight citations on MathSciNet, three of which came long after his capture, e.g. see here.  (Though I do not know for sure that the author of this paper was aware that the T.J. Kaczynski whose work is cited is the Unabomber, it seems likely: the author is an American, and among Americans this name is well known to say the least.)

I was wondering what the likelihood is that his results were neglected due to this political misfortune. I was also wondering if people know of similar instances, particularly in mathematics. It seems like whenever I look up the politics of a respectable mathematician, they are either nonexistent, or equally respectable. I don't know if we tend to discredit people like this, or if people like this tend to not produce good results, or what.

In my opinion this is unlikely.  There are very famous mathematicians who were, to lesser or greater extents, participaters in the Nazi movement.  Perhaps Ludwig Bieberbach and Oswald Teichmuller are the two leading examples: these are household names in mathematics, and that they were intimately (and reprehensibly) involved in the Nazi movement is also very well known.  (For that matter, I am not convinced that Vahlen's work is so little known.  It is described in the wikipedia article linked to above, for instance.)
In my personal opinion, it is worth knowing when a mathematician (or other academic) has done reprehensible things in their personal life.  Some years ago I compiled a list of "greatest mathematicians" on MathOverflow: I limited myself to choosing at most one mathematician born in a given year, but in some cases I included "honorable mentions."  When I got to Teichmuller, I did not want to use the word "honorable" to describe him, so I wrote "dis/honorable mention."  That was a personal decision (and by the way, I am partially of Jewish descent, so it is really not for me to forgive or forget such things).  But I included him on the list anyway: that he was a terrible person does not influence his mathematics one way or another.

I'd like to just use a big-ol' script V for the Vahlen matrices (which I have not seen in any papers thus far) and move on,

There is no problem with this.

but I don't want even an iota of a suspicion of being sympathetic to this man's priorities.

We don't endorse the life of Teichmuller when we talk about Teichmuller space or Bieberbach when we talk about Bieberbach's Conjecture.  We credit them with their work, as we must.

It would also be hilarious to just use a swastika, but that joke might not be funny to some people (understandably).

I am not laughing at all.  Please do not do this.
Finally, you can read much more about mathematics in Nazi Germany from this book.  Again, I think it is good to know these things.

There is also a book "Mathematicians Fleeing Nazi Germany", or something similar, though I cannot recall or locate the details just now. From it, I learned that Hausdorff took his own life, for example.

Thanks for this. As far as using a swastika, of course I would not really do that. But I do want to emphasize my motivation for that idea, which is basically this: the last thing the Nazi's would want is for us to be laughing at them after their downfall. They would want their symbol, or anything, to continue to bring us down. As I said I have a dark sense of humor and personally it's gotten me through a lot of hardship, so please don't interpret that joke as a sign of disrespect.

@paul: Yes, I knew that about Hausdorff.  Of all places, I learned that in the big colorful book "Chaos and Fractals" that most American mathematicians who were high school students in the early 90's paged through.

See: Alan Beyerchen: Scientists under Hitler

@j0equ1nn Even if you indent to use the swastika in a humorous way, to make fun of it, it is still going to bring some people down. So, as stated in the answer, pleas do not do this. Some people will just not be laughing, others will be worse.

Apologies for adding to chatter, but I can confirm that Kaczynski = Kaczynski. (It was even mentioned in Good Will Hunting, so it must be true.)

@PeteL.Clark I would rephrase the first line of your answer to: "This shouldn't be an academic issue." However in the field I work in, (biomedical research; hoping you guys consider it academic as well ;) ), there is a growing movement of people who do see academics and 'politics' (better: social theories) as being interwoven. Interesting stuff has been written by Latour (https://en.wikipedia.org/wiki/Bruno_Latour) on this. Also, in the Netherlands we have the "Science in Transition" movement which highlights how social tendencies (incl. personal fame/infamy) influences scientific endeavours.

@IWS: I hope it was clear from the rest of my answer that I don't regard information about the lives of academics to be categorically "out of bounds" in discussions among academics.  In "I think there is no academic issue here," you should understand "here" to be referring to the OP's main question: is it an issue to cite the work of a Nazi mathematician?  I am saying that it isn't.  Of course the claim that it isn't an issue is a claim about the sociology of mathematical practice.  We could make an issue out of it, but as a community we have decided not to.

(Still less am I claiming any kind of fundamental "independence" between mathematics and political/social forces.  Paul Garrett's answer gives an extreme example of that: that which costs mathematicians their lives obviously influences the discipline of mathematics.)

@IWS In biomedical research, you get a moral dilemma that you don't get in mathematics: While a mathematician might have commited atrocities and advanced science, a physician may very well have commited atrocities in order to advance science, and if you take results from those atrocities and use them like any results at all, shaking your head sadly about the atrocities, you create a trade-off where people obsessed with advancing science may come to the conclusion that the advancement of science is well worth whatever personal retribution commiting atrocities will bring down on them.

@sgf I will definitely acknowledge that. However I was trying to say that imo any science is (somewhat) influenced by social theories (as explained by Latour). For example, which prominent scientific leaders (also in mathematics) get to further advance their fields is most often a money-issue, where different stakeholders get to decide which scientist to back.

@IWS thank you for the interesting perspective. We understand your position, but please put a bit of trust in the mathematicians here when they tell you that pure math is by and large a discipline devoid of any connection whatsoever to politics or "social theories". Mathematicians are interested in math, and while many of them are also interested in politics, history, social theories and whatnot, they simply don't think those things should influence a discussion on math. Maybe one can find one or two small exceptions to this rule from WWII or the Cold War era, but Pete is essentially correct.

@DanRomik I believe you misunderstand IWS's point. What he's trying to say, I believe, is not that fads in maths are engineered by social theorists, but that fads in maths are social theoretic entities and that therefore there is a social theoretic aspect to what happens in maths.

I generally agree with the answer, but not the very last part. Many spaces and conjectures are not referred to by the name of the person who introduced/worked on/conjectured something. Terminology is already established in some areas, but if one finds an interesting conjecture in the work of a reprehensible person, one might exercise creativity in naming the conjecture (of course, one still has to cite the originator).

At least the author of one of the papers citing Kaczynski is very well aware of who he is, as indicated in the footnote.

I was wondering about the etiquette of discussing a result by such a person. Ahlfors simply writes about his math, which seems probably the right way to go. But it still feels weird if I were to give a lecture where I'm praising a guy who may have contributed to the extermination of an audience member's family.

You need to remind yourself why you are there giving a lecture to this audience member in the first place. What is the goal that your lecture is trying to achieve?
Is this a lecture about mathematics?
or
Is it a lecture about the history of Nazism?
If this is a lecture about mathematics, talk about mathematics. Think about it this way: if you invited a speaker to give an algebra seminar at your department and they instead went on a 10 minute digression about the history of automobiles and inserted icons of automobiles to stand for mathematical objects instead of Latin or Greek letters, would you think that was appropriate, or would you think that it detracted from the goal you had in mind when you invited them to give a talk, namely to learn about their work and mathematics related to it?
It's okay to tell little historical anecdotes about the people behind the mathematics in talks; we are humans, not robots. Nonetheless, I'm willing to bet that your hypothetical audience member whose family was exterminated by the Nazis is still there primarily to hear about interesting mathematics and not about historical anecdotes or to see cheap gimmicks ostensibly making fun of the Nazis, and ultimately doesn't care that much to have any of that stuff brought up. Your use of a swastika as a mathematical symbol may or may not offend him; will certainly not strike him as funny; and will probably just annoy him for being a distracting gimmick that undermines the primary goal of the talk.
To summarize, no one really cares what "feels weird" to you - that's your own private feeling; to the extent that that feeling is causing you to want to give an unfocused talk that goes on irrelevant tangents and annoys people, the correct thing to do is to ignore that feeling and instead give the best mathematical talk, which focuses -- as a mathematical talk should -- on the mathematics. (Hmm, and that's basically what Ahlfors is doing in his writing isn't it...?)

To summarize, no one really cares what "feels weird" to you — Best. Summary.. Ever. (+1)

@MadJack Not really. The post mainly inquires about the history and current common practices, and their effect, regarding this type of information. My post was not to the effect of "I feel weird, does anyone care?"

@j0equ1nn you seem like a nice and quite interesting guy (I looked at your web page and academia.se history, some of which I feature in), but you take things a bit too literally for your own good. Lighten up, we are here to have fun and enlighten each other with interesting discussions and witty banter. You did mention feeling weird, and I was trying to be helpful by pointing out that in the context of the question, no one cares. Likewise MadJack was trying to be helpful to others by commenting on it in a humorous way that pokes a bit of fun at your expense. No one here wishes you any ill.

@j0equ1nn ... The bottom line is that witty banter aside, you may notice that essentially everyone here actually took your question quite seriously and gave their best shot at addressing the concerns you brought to our attention. I hope you appreciate that.

@DamRomik I do appreciate that and yeah it's not really a big deal what Mad Jack said. I think I've become defensive though due to some posts that are a little too insulting and patronizing to be called "witty banter." It gets hard to tell what I'm supposed to be doing within the range from rigidly conforming to the site's guidelines to avoid my question being closed, to relaxing and letting silly comments fly.

@DanRomik I don't mean to come across like I think people are conspiring against me or something. I just mean to stand up for myself and the legitimacy of my question.

Find the integral of 2 Honda Saab squared delta Saab.

As @Rudiger says, we should tell the truth so far as we know it (and make an effort to know it!), and give credit where credit is due, regardless of the possible failings in the other parts of a person's life.
I disagree with @Rudiger's claim that mathematics has nothing to do with politics, at least insofar as all these things are mixed together and affect each other in the larger human enterprise. After all, Nazism affect mathematics profoundly, by affecting mathematicians profoundly (killing some, driving some to suicide, and driving others to the U.S. and other places far away from Germany).
So far as I know, in Vahlen's case, the lack of attention is not so much about his abhorrent politics but that people did not find his mathematical work terribly useful (whether or not you yourself do).

I appreciate this and respect your opinion. I'm coming at this as a new mathematical researcher in my first postdoc, encountering something like this for the first time, so I'm confused why anyone who would feel the need to insult me because of this post. Regarding usefulness or otherwise of Vahlen's work, I have noticed a lot of results from that time period that are worth another look (for me, especially due to the modern development of topology). And that does seem to happen independently of this Nazi issue so... I think you're right.

Yes, it is palpably true, though apparently not widely appreciated, that people 100 years ago were doing sophisticated things... not just proving basic theorems that are now in every textbook. :)  There is a "Whiggish" tendency implicit in the over-simplifications suggested by, if not literally asserted in, many textbooks that leads people to believe that everyone nowadays is far more sophisticated than everyone in the past, in particular, people were dopier the farther back one looks. This simplistic outlook has an obvious appeal, but is crazily misleading...

Right on. My PhD thesis was germinated by taking a paper from 1900 (by Macfarlane), updating the notation and methodology, then seeing what I could do with it. The more research I conduct, the more important it seems to start by digging.

This community wiki answer was created from answers-in-the-comments.

What are some similar instances, particularly in mathematics?

At least according to Wikipedia, the non-subscription of "Deutsche Mathematik" outside Germany caused problems in the development of Teichmueller theory, as many of the papers of Teichmueller's were thus not available for researchers in the field.

Wagner's music was not publicly performed in Israel before the current century.

Alexandre Grothendieck's "political views were radical and pacifist", to the point of quitting academics, harassing people trying to publish his work, and living into reclusion. That did not prevent him from getting prizes (that he refused) nor to be abundantly quoted. He is often referred to as one of the founder of modern algebraic geometry. He was the opposite of a nazi, but actively involved in political activities that may shock / derange. If anything, this added to the awe that the mathematical community has for him.

Werner Heisenberg. Fortunately the uncertainty principle is no less amazing and cool because its discoverer was working to help the Nazis develop an atomic bomb.

Lev Pontryiagin

Johannes Stark

Philipp Lenard

Serge Lang had some pretty scary views about HIV/AIDS

Helmut Hasse. Prolific twentieth-century mathematician at the university of Göttingen. He was a nazi, which allowed him to survive the "great purge" that happened at Göttingen in 1933.

The fact that you would make a joke because of someone's political attitude shows that you lack professionalism. Mathematics has nothing to do with politics, and it is totally inappropriate to mix it with politics/ideology. Not giving credit to someone just because you don't agree with his personal opinion is also disingenuous. Richard Feynman and many other scientists worked on the atomic bomb; would you try to ignore them because of this?
"It would also be hilarious to just use a swastika [...]".
This speaks for itself.

Okay, 3 things. 1- "Political attitude" feels insufficient to describe active Naziism. 2- Humor is important especially within topics that can be difficult and make listeners feel alienated. 3- I never said I wouldn't give the person credit, rather I asked if he may have been denied credit historically. Okay, 4- you seem to get upset easily and the insulting nature of your "answer" is unprofessional.

I agree with "Mathematics has nothing to do with politics" and "Not giving credit because you don't agree". The other arguments are not really appropriate. Whether a joke concerning political attitude is suitable or not has nothing to do with professionalism. In this particular case, the joke may be inappropriate, but this is not how the response has been phrased. And Feynman and others racing Germany on the bomb is really not the right comparison - these guys (as Feynman himself makes clear) were the guys who would be killed first if Nazism had won. They had a very strong reason to go for it.

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