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This is (sort of) continued from the highjacking of Urs’ thread on his talk. It threatened to become a debate about beamer versus chalk until Urs told us to go play in our own backyard! Rather than try to pick up threads, I thought I’d start afresh. This is something I want to know because I want to make my own talks better, whether as presentations or as chalk-and-talk.
I’d like to steer clear of the “beamer vs chalk” bit, at least for a while, and start with the simple question of the title:
What makes a good seminar talk?
Ideally, I’d like concrete answers to this. Also, I’d like answers both from the perspective of the audience and the speaker. What is it about a talk that makes you glad you went to hear it? What is it about a talk that you’ve given that makes you feel like you’ve done a good job in giving it?
If you had to design a questionnaire to “rate my talk”, what questions would you ask on it?
My difficulty with the whole beamer vs chalk debate is that I just don’t know the answers to those questions, but without them it’s hard to reliably assess whether or not my chalk talks are better or worse than my beamer ones.
What makes a good seminar talk?
Off the top of my head, I would say that a good seminar talk should:
But perhaps those are not concrete enough?
I can think of one thing that has made some of my talks bad or at least not great: trying to say too much. In the first place, going overtime is, in my experience, usually considered a big no-no (although some cultures might be more loose about time and schedules). Going too fast for the audience to follow is another.
Realistically, I think for a hour-long (or 50-minute-long) seminar talk, you can only get across a small group of ideas, examples, and some idea of proof or methodology. Since things often take longer than you think they will (e.g., if an audience member asks something unexpected), it’s probably a good idea (let’s say in my case) to prepare something I think I can get across in 30 minutes. And then take your time doing it, with deliberate, measured pace and with lots of space to give due emphasis. The time will often expand anyway to the allotted amount, and one has room to throw in an extra little goodie or two that come to one spontaneously, or at the end if there’s time left, or to give a personal reminiscence or feeling about the subject, etc.
(Someone who I think gives very nice seminar talks in category theory is George Janelidze. He is sort of a model for the firm, unhurried pace that I like, and with effective pauses to give strong emphasis where needed. Steve Lack is also someone I find very good.)
As far as chalk or whiteboard talks go, an absolute must is very clear, neat handwriting on a clean (or at least very well erased – I want to say well brushed) blackboard, and go sequentially, left-to-right, left-to-right, in smallish chunks. Sometimes one can do a little calculation off on a sideboard, if one wants to keep the main development on the main boards – but be mindful of the fact that as an audience member, it’s annoying to have to look back and forth a whole lot. Also, avoid too much shorthand or abbreviations, and don’t write super-fast.
For overhead talks (meaning either prepared slides or beamer or whatever), don’t cram in a lot of information on the page, and don’t rush through pages with a lot of meaty math. Act as if someone in the audience is trying to take notes on what you have, in other words give them time to catch up by keeping a smallish chunk of information on the page and then amplifying on it (as opposed to just reading the words on the page).
(For some reason, I tend to like to use about four different colors when I’m making e.g. overhead slides. I don’t know if this is good or irritating for others, but I wouldn’t mind some feedback. For some reason I think it helps break things down into small edible chunks.)
I don’t know if this is all that concrete, but worse, I feel as if all these remarks are no-brainers. But maybe these simple precepts get violated often enough that there is no harm in repeating it! I should say that a lot of this advice is informed by memories of how I’ve done things wrong (and I suppose I’ve made almost every mistake in the book at one time or another).
In the first place, going overtime is, in my experience, usually considered a big no-no (although some cultures might be more loose about time and schedules).
If there is anything I despise about some academia is the assing about not going over few seconds. For a positive example, at IHES a seminar at 11 is supposed to be until 12. The lunch is at 13, so people would get uneasy if they do not have time to go back for few minutes to their office before lunch. That means, one should not go over time by more than 30-40 minutes. Similar relaxed timing end is at many places, in many groups and at many conferences, as it was at all 3 conferences I helped to organize. Those big-no-no implementers should relax – they can always get out of the conference room at the time they like to. I mean the rooms are usually not locked, and if the rest of the speaker and the audience are not used to the natural act of leaving when it is needed or convenient, they should simply be used, like whites in the south got used to the end of segregation. And THIS should also not be an offense to the speaker. I was leaving graduate seminars if too busy to stay, even when I was an undergraduate intruder to those. Good seminar atmosphere is one in which everybody feels happy leave the seminar talk when he likes. Then the pressure to stop the questions should not be there either.
Acting “lecturing authorities” is something what should be expelled from good seminar and academic communication. I will tell couple of negative examples from my graduate school which are in sharp contrast with my general recollection where I recall UW as an excellent intellectual environment, specially as most mathematicians are concerned, and general conditions, like library, computer and other services. However there was plenty of nonsense coming from central administration of the campus, and some indoctrination practices. As a foreign TA I had to take a foreign TA special indoctrination course in which we were told by English department special agents that in other cultures like in Iran people are supposed not to question authorities. However, my experience at the same university was that the authorities where more irritated by being questioned than I lived through at my institution which was in supposedly non-democratic system. For example, that same English agent was very irritated when I told her that her claim that every language has schwa-like phonem in the system was not in agreement with my own language, and my quantum mechanics professor has forbidden me publicly to ask questions in public after I pointed in the class the second error in the exam which he has given to us, graduate students, because pointing out to the truth is confusing to the audience. He was supported by a fellow student who thrown his pencils at hearing that there is a second mistake after he spent time trying to understand the solution to the wrong posed problem. In another course I was TA and a math professor close to the retirement wrongly solved the problem; after consultations with other TAs we saw that the error is obvious. I came to the professor and explained him, and then he told me that his (incorrect) procedure (for evaluating double integrals) is actually correct as it is in the book. On that he started yelling at me in front of the students who were taking the actual exam that I should not be his TA. So I went to the office to take the book, and shown him that the procedure is in fact the way TAs say. Then he told me, look NOT, the picture with the number of the problem in the book has the opposite system. Then I shown him that the picture number 6 is related to problem 7 (what shows it is really bad – he relearned the elementary subject at the end of the career wrong way on the basis of automatically accepting the misread answer from the undergrad textbook!), after what he admitted the mistake. I said, OK never mind, it is early morning, on which he told me that it was not early morning for him, as he came earlier than me to the exam.
As I said, going overtime might not be considered a big no-no in some cultures. (And I personally don’t mind people going over a few minutes. Going over by 20 minutes certainly verges on rudeness, at least in the cultures I am accustomed to.)
I do stand by what I said about trying to say too much. You will lose people. One way you can lose people is, like it or not, via the annoyance they may feel if you go overtime – they will stop paying attention, and the feeling this leaves in the room can be palpable. There are other (perhaps more substantive) ways as well.
Sorry about your negative TA experiences.
Sorry about your negative TA experiences.
As I said I just discussed negative exmaples, I have many good experiences there.
One way you can lose people is, like it or not, via the annoyance they may feel if you go overtime
Many people whom I appreciate the most I appreciate just because they gave such seminars. Like when a person from California came to Madison and gave two smeinars on the same day scheduled plus that one went 30 minutes over time. If I leave because I am tired or have to go somewhere that means that I regret that I did not sleep enough and have enough time to catch the whole thing.
On the other hand I WAS ANNOYED by many hosts who would stop the speaker or stop the questions after a couple of minutes and make the talk unrounded by not being able to extensively answer questions. Some conference organizers who done that in past LOST me: I will never go again to conferences organized by certain people of that kind.
Even one of my mathematical idols, I won’t name, stopped Serre (!!) asking questions in a talk about Serre’s conjecture. The amount of intellectual joy which the audience lost because he thought that Serre asking more than 3 questions in public is not good is far bigger than can be loss of those few minutes.
Going over by 20 minutes certainly verges on rudeness
This happened to majority of talks in conferences I organized, and I recall that the people were very happy with those conferences.
Back to the topic: my experience with listening math talks with technology was mainly negative. I get much more from chalk talks. One of the rare mathematcial opinion things I do side with Doron Zeilberger. For physics talks elaborate pictures are needed, but in math if the picture is more complicated than can be drawn in real time, it is rarely needed for a seminar talk. There are few people who do not put too much on the slides and do not go too fast. The same is with conferences; those I learned the most are the least technological ones. I was very annoyed with incomprehensibility at ICM 2002, where all talks had some technology (overhead if nothing else). That is why I skipped ICM 2006, and ICM 2010 (of course, the financial expenses added to the decision).
Yes, I would like to keep this on topic. I think that the “going over time” issue is perhaps too contentious. My aim in starting this is to learn how I can improve my talks by getting ideas and the like from others. I certainly try to not go over time, but that is my rule for myself.
(That said, I suspect that whether or not someone thinks going over time is acceptable or not might be more to do with how they learn. I am very bad at being told stuff. I need to hear something and then go away and think about it. So if you tell me too many things, I won’t be able to keep them all in my short term memory long enough that I will be able to ponder them later.)
What everyone says about putting too much on slides is something I definitely agree with. In fact, I’m giving a lecture course now which I gave last year and I’m using the same slides. But I’m going through them taking out as much as possible. I take out sentences, I take out extraneous words, I replace “if this then that” by “this that” (I still say the sentences and so forth).
So I’m still of the opinion that all the negative experiences of beamer presentations are more due to the speaker’s unfamiliarity with the medium than with the technology itself and that it is possible to give as good, if not better, talks with beamer as with chalk (indeed, I would say that I give a better beamer talk than I give chalk talk, but then I’m not in the audience of one of my talks so it’s hard for me to say).
I might paraphrase what I think Zoran is aiming at, which I much agree with, as follows:
Of course speakers should give brilliant talks. Sure enough.
But their scientific audience is hopefully not there for entertainment reasons and in the hope not to be bothered with too much math. What drives the audience is hopefully curiosity in the subject. They could have gone to the movies instead, and would have gotten there colorful slides with little information per frame and guarantee that nothing goes over time. That they instead went to a math conference is hopefully a sign that they are interested in using every spare second of their lives to learn-learn-learn about the secrets of the universe, and be it by way of trying to understand what others have already extracted, no matter how they mutter, if only what they mutter brings mankind closer to the truth.
A colorful beamer presentation with plenty of pictures and little information per slide, easy to follow for everybody and finishing before anyone’s attention span is exceeded can be just as well a waste of time. There is no way around the fact that communicating the secrets of the universe requires effort also on the part of the listener.
(Exasperated reaction heavily redacted.)
Of course communication requires an effort from the listener. Consider that as read. The problem for the speaker – which is what Andrew wanted to discuss, isn’t it? – is to find methods that will help the listener in this effort to understand ideas being presented. What the listener can do is also an interesting question, but it’s not what we were discussing.
I strongly suggest that we quit the topic of the ethics of going overtime. The ethical question is something I never wanted to get into to begin with, and as I keep saying, different cultures develop different ethics. But the fact that differing opinions exist, whether right or wrong, are some facts on the ground that speakers might wish to consider or might need to work with as they prepare their talks.
Thank you for making an effort to listen.
Todd,
I am sorry for having caused these feelings with you.
but it’s not what we were discussing.
The discussion is about what makes a good seminar talk. I think a good seminar talk may be and should be demanding on the audfience at some point. Otherwise, why bother with it?
I thought (Andrew, correct me if I am wrong) that the focus was to be on the criteria for assessing the performance of the speaker, both from the speaker’s point of view and from the audience’s point of view. In addition, I thought Andrew wanted to use this discussion largely with the goal of improving his own performance as speaker, or anyone else’s. (No, I do not mean ’performance’ strictly from the standpoint of entertainment value, although that might be one of the criteria.) These are the parts we actually have some control over. We don’t have control over the collective internal states of audience members.
I fear my words (e.g., about colors on slides) were misconstrued, and even parodized by your #9. But I’ll take your “demanding” in comment #12 in the sense that the audience should be given something substantive to think about, and not merely entertained. Of course, I agree. At the same time, the speaker should try to remove aspects which make the talk unnecessarily demanding, such as difficulty in reading a poorly written overhead projection or a sloppy blackboard, so that the only difficulties reside in inherent difficulties in the mathematics. And I was attempting to offer some concrete recommendations to achieve this.
In any case, I thought comparing the colors I like to put on slides with the colors you see in Technicolor cels (or whatever) was unfair, and missed the point I was trying to make. I hope the previous paragraph removes unnecessary difficulties in following what I was driving at.
Hi Todd,
thanks for the clarification. I wasn’t actually reacting to what you had written, but had meant to expand on what Zoran had written, as I said in my first line. Using lots of colors is a wide-spread tool that I didn’t associate specifically with your comment. So that was a misunderstanding.
My impression was that Zoran had pointed out that sometimes the catering for the well-feeling of the audience is put above the interest in the mathematics itself. I thought that was a good point to keep in mind.
So I am sorry that my comment hurt your feelings. It wasn’t written with anything specifically you had said in mind.
I should have stuck to my initial hesitation to participate in this discussion. Which I will do from now on… I’d rather discuss some math here on the nForum ;-)
Jim says ideas and only outlines of the proofs. If one is to compare this with speakers who spend the hour on technical detail they struggle in chapter 6 (to paraphrase Noam Chomsky) I agree. But this is not necessarily the best option. I listened a number of seminars in operator algebras at Purdue in Spring 2002, and the lecturer was usually Marius Dadarlat. I am not an expert on operator algebras. Marius definitely is. The setting was rather specific - another expert (Brown) 1-2 grad students and me, so speaker +4 people typically. He would come with having prepared for about 10 seminar hours at the time, do blackboard talk and at 2-3 points in the lecture he would give us option. Like do you ant to see the proof, or an example or a next chapter of the theory. So one would have to choose what to dismiss and what to hear out of large amount of prepared material. Say we said we want a proof. Then he would go into many details but giving intuition for every step, at the blackboard pace. I mean I was not an expert at all and could follow ideas of proofs of extremely complicated theorems, due this willingness to give feeling for every step he was doing. At the end of the seminar I would feel a bit overwhelmed but also with very useful impressions on a number of new techniques and constructions. This is amazing, how even a very technical and detailed presentation can be so exciting. And of course there was reasonable interaction (besides voting for next subtopic).
So I do not think that being dry and technical in boring and oppressing sense can be pinned down to rule of a thumb criteria like mere speed, mere amount of detail and mere length of the lecture. Honest speaker willing to express his intuition can make excessive sensible. Of course some people have more talent than others, it is not just good will. Seeing his writing and clarity of thinking I am sure Todd is an excellent speaker. and it is a pity not to give talks for years…maybe online technology could help prevent such losses of opportunity in new ways. If I look at my own talks some were disasters and some went pretty well off, but I can say that the worst ones are those when I felt a bit insecure with the audience; like expected that the audience wanted to see more interesting topics and will be bored with introductory and paceful presentation and when I realized I needed to add some intro then I would spend too much time and screw up my own plan. This is sort of bad response to pressure. I also have rather inconsistent experience about last minute preparation. Sometimes preparing much in advance makes me talking from older memory (the repetitions before the talk are too automatic so they do not help) and feeling like I do not reason but rather talk mechanical. When preparing the night before, sometimes I am really on top of things and control the talk so well as I feel refreshed and excited with the last minute preparation. But sometimes this makes me confused, the refreshing of too much material. I am yet not experienced enough there.
Todd, that is what I’m trying to do. Your interpretation is correct.
Urs and Zoran, maybe part of the difficulty is that there is such a large range of circumstances in which we give talks and what works well for one does not work well for another. A seminar series is completely different to a colloquium talk, for example, so what is appropriate for a series of three or more lectures is not appropriate for a one-off.
So let me make it more specific. In January, I’m going to be giving a talk in Sheffield on something to do with loop spaces. Now, although the conference is about loop spaces I imagine that there will be many people there who are less familiar with them than, say, Urs or myself. I don’t want to give a talk about some interesting-but-technical piece of the theory, I would rather give a more general talk that any topologist could follow. Moreover, I would like it that any topologist could follow the whole talk. Of course, the specialist will get more out of it, but I don’t want to essentially say, “The next bit is only for people who actually work with loop spaces” at any point.
You can disagree with me as to whether or not that is the type of talk I should give, but that’s not the debate for this thread. That’s a debate over a pint in a pub! Under the above assumption, I’m asking for advice on how to improve my talk, and as part of that I’m interested in how people measure the success (or otherwise) of their talks. Thus:
When you hear a talk that is not in your speciality area (though maybe in a nearby one), what is it that makes a talk one that you’re glad you went to?
When you give a talk to a general audience (for example, a colloquium), what signs do you use to decide whether or not it was a good talk?
Lastly, I hope that Urs doesn’t stop participating in this discussion. Communication of mathematics is extremely important, but is one of those thing that we’re meant to pick up “by osmosis”.
(Actually, it’s hard to think of any aspect of this job that we’re ever actually taught!)
When you hear a talk that is not in your speciality area (though maybe in a nearby one), what is it that makes a talk one that you’re glad you went to?
Freshness. If the talk gives me new vista. So the talks which repeat standard mantra by which most lecturers introduce some area than it is not a good choice. For example, I am rarely at a talk about vertex operator algebras. Not my specialty. But here and there sometimes I get to such a talk. The last talk of that kind I heard was introducing the subject for general audience. It done it exactly the same way I heard the introductions on that in late 1990s. The same examples, the same emphasis and the same fascination with historical wonders on j-function and the dimension of certain representation of monster group. Having not being an expert does not mean that the listener never had a talk in some area.
With Zoran, I hope you don’t stop participating either, Urs (although I understand if that’s your prerogative)! As some regulars know, I have to work on my reactions sometimes. :-(
Also with Zoran, I agree that giving detailed proofs can certainly be okay. More than okay: sometimes exactly the right thing to do. But I generally wouldn’t try it on an audience that I didn’t feel confident about. When I was very active in the Chicago category seminar in the mid-to-late 90’s (of which I like to think of myself as a co-founder, although the principal credit would have to go to Saunders Mac Lane), we only ever had about 5 or 6 people, and I wound up giving a great many talks (this is at the blackboard, somewhere in Eckhart hall). Sometimes it was part of a mini-series, and I would use the opportunity to give highly technical accounts. Sometimes Saunders (then in his late 80’s) would nod off, but occasionally I would see some payoff as well (and it certainly paid for me).
I happen to love details that I can follow; in fact I get strong cravings for detailed proofs; that’s very much my own nature as a mathematician. Indulging in those cravings and meeting a creative challenge of organizing such details for a seminar series teaches me so a tremendous amount. But it’s very far from a universal taste in public talks, and I recognize that intellectually, this is a particularly demanding challenge for the audience to rise to.
BTW: for what it’s worth, I always prepare at the eleventh hour. Not literally, but I have frequently banged out an all-nighter to prepare for a talk. Even for my thesis defense. This is probably not a Good Thing! :-)
(Written before I saw Andrew’s response, which I may respond to in turn.)
When you hear a talk that is not in your speciality area (though maybe in a nearby one), what is it that makes a talk one that you’re glad you went to?
Definitely I want strong motivation, and a coherent story with a good punch line. Strong narrative drive. Why are you interested in loop spaces? How do they relate to other general areas of mathematics?
The first time I met John Baez was in 1997, at a workshop on methods of higher category theory, which gave rise to one of the Contemporary Mathematics volumes, edited by Getzler and Kapranov. This was also where I first met Jim Dolan. Jim Stasheff was there, too. The workshop was only for two days, but it shines in my memory: John outlined the n-opetopic approach to higher categories that he and Jim had worked out. There the interest of the program was made quite obvious by John (although I think that mine was a mind prepared), and it culminated I believe in finishing the outline of the complete definition in (I believe) an hour. It was a tour de force performance. Interestingly, the Baez-Dolan paper that appeared in the volume is ’Categorification’, but John drew on the material there, (the general idea of categorification, relations to homotopy theory, the parable of Bo Peep, etc.) to motivate the talk about the Baez-Dolan definition.
Ross Street also spoke: his was on Batanin’s definition of higher categories. Ross gave this in two talks, and his approach was much more technical. Nowadays the approach is very streamlined (see Tom Leinster’s book), but at the time there was a lot of extra stuff about monoidal globular categories, nothing about cartesian monads, and it looked at the time like demanding stuff.
Jim Dolan did not speak, but I spoke with him at that conference for (what is in my mind) hours and hours. He was trying to teach me about opetopes, and I was trying to teach him my stuff.
That’s what a good talk should do: really get people talking afterwards.
I spoke as well, on surface diagrams. This talk does not shine in my memory. But I tried to convey the right pictures in three dimensions. A good talk should plant effective images, where applicable – they are often easier to store in the brain, especially for non-experts.
When you give a talk to a general audience (for example, a colloquium), what signs do you use to decide whether or not it was a good talk?
I sense that a talk went over well if someone comes up later and doesn’t say just polite things, but we have a good conversation. It doesn’t have to be right away; some days or weeks elapse might elapse, or it might be in email later. It also doesn’t have to be glowing; I’ve had good post-talk discussions where some skepticism is expressed (but I feel much better about that if I manage to be persuasive in the end).
You can get some idea from the quality of the questions. I got some very good reaction from Martin Hyland after I gave my 1999 talk on the definition of n-category that has since had my name attached. (Eugenia and Tom were in the audience, and it was very pleasing to me when they both discussed this definition in later articles!)
Again, some of these might be no-brainers.
This thread seems to have stagnated a bit – apparently we’re all more interested in arguing about beamer vs chalk than we are in discussing what makes a good talk in general. (-:
Here’s a concrete question for the gallery: should every math talk include at least one proof?
I feel like in general, the trend of my own talks has been away from giving any proofs at all. I try to give sufficiently precise definitions that people know what I’m talking about, I state theorems, talk about the idea of constructions, and give examples. Perhaps this has something to do with the sort of math I talk about, where getting the right definition seems to be at least as important as finding the proof.
However, I still feel that it’s a good idea to include some sort of proof or argument at some point. Not as a hard and fast rule to follow slavishly, of course, but something to aim at. A short proof or argument, of course – one that fits on a single slide, if using slides – and one that is easy for the audience to follow. I feel as though doing this gives the audience confidence that they understand the definitions, concepts, and methods, and makes them more willing to take on faith the other theorems that I state without proof. But this could be just something that I’ve made up with no justification – what do others think?
A lot of the beamer-vs-chalk discussion has been oriented towards teaching, whereas this thread started off being about seminar talks. Naturally, these are hugely different circumstances. I guess, speaking somewhat off the cuff, I’d say:
For the classroom, for upper-level undergraduates and graduate students, it’s hard for me to imagine doing away with the sheer process of reasoning, in detail, before one’s audience. (I’ve never attended a math camp. I imagine it might work a little differently there.)
For a seminar series on a specific topic before an audience with a serious interest, I would also roll up the sleeves and get on with the serious business of techniques, proofs, and calculations.
For a one-time seminar before a more heterogeneous crowd, detailed proofs and calculations are mostly to be avoided, I think. A general overview of the proof is generally fine. More finely grained arguments that are short and clear are fine. Short calculations (say a string diagram calculation) can be okay.
For a conference talk before a larger (and heterogeneous crowd) in category theory, mostly the same as in the previous, except maybe more gingerly approached. Mostly it should be about the ideas or general program.
For a colloquium talk, be even more careful. You have to hop lightly through arguments, as it were (and if at all).
Re the last, I’m thinking of two talks that I’ve given, with some proof, which had very different outcomes. One was a talk before the Macquarie University math department (I guess you could call it a colloquium), where instead of trying to describe my general area of research, I tried to give an idea of a random problem from “real (mathematical) life” being solved with the help of category theory. (The actual problem was drawn from Halmos’s autobiography. On one of his take-home finals, he gave the problem: is there a connected Hausdorff topological group of exponent 2? I showed how to solve this using category theory. Andrew Stacey may remember my bringing up this talk in another discussion.) There I had to skip lightly through a series of functors which translated a solution to an easy problem into a solution of the harder problem given by Halmos. That talk was generally well-received, perhaps because I wanted to solve a problem, not just build a theory. I also gave a spurious argument (clearly identified as just a sketchy possibility) for the opposite conclusion beforehand, to give them some extra time to think.
The other talk was a colloquium talk before the Loyola University (Chicago) math department, where I was then teaching. I wanted to talk about species, and how they figure in Joyal’s beautiful demonstration of Cayley’s formula for the number of trees. Of course, that’s a demonstration (a proof), and I attempted to build up to it basically from scratch, addressed at the level of a Loyola graduate student largely innocent of any category theory. A completely abysmal failure of a talk. Maybe two professors there were at all sympathetic to where I was going. From other faculty, I got what was perhaps the most unfriendly reception I’ve ever had to a talk I’ve given – even to the point of openly hostile and critical reactions right to my face immediately after, over wine and cheese. And I had tried really hard to prepare well for that talk!!
In this case, I don’t know if giving Joyal’s argument itself decisively ruined the talk (how could it? it’s such a fantastic proof!). Perhaps, looking back, I was trying to be too precise and formally correct in my statements, and that was the real problem – as well as being ambitious and going maybe 10 minutes overtime (bringing us back to that thread!), which I think I was hated for doing. (It’s a pretty bitter memory, I have to say, and my blaming myself goes only so far: I am largely inclined to blame the audience in this case for being mental pygmies.)
Anyway, if the proof is just really nice, and pretty light on technicalities, I think you can do it, even in a colloquium. If you’re careful.
My inclination is that for the first two in Todd’s list then all bets are off. The circumstances are likely to be so special that almost no general advice could (or should) be given.
For the others, I think I agree with what Todd says. If I could try to summarise it in a single sentence, it would be that in these more general talks then the rule-of-thumb should be: no proofs unless the whole talk is the proof.
Of course, there’s a spectrum between a vague hand-waving “this is why you should believe it” and a full, detailed, every i crossed and t dotted, proof. So “no proofs” could actually include quite a few so long as each is treated quite lightly.
(And, to avoid a resurgence of vehemence, these are simply my working guidelines and I’d feel happy breaking them if I felt that I should. But I only would if I were absolutely sure that I ought to.)
It feels very curious having this discussion with half a dozen people, none of whom I have ever seen give a talk. We should really have an nConference some day and meet each other in person. (-:
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