Balancing Informal Tone with Acceptable Rigor

[Mandelbroth]

This is both a specific and a general advice thread, since I will likely be able to apply this to other discussions than the one in question.

I have a weird situation. I've been asked to give a talk on the research I've been doing as part of a collective celebration of my local university's research. Naturally, and prematurely, I accepted. Some of the professors that I have worked with will be attending, and they are expecting some kind of extravagant bundle of mathematical goodness that they've come to expect from me.

HOWEVER.

There's a catch. The event is also going to be populated by arts and science and psychology and business and (whatever other areas of study the school supports) students. I want to impress my professors, but I also don't want to alienate/bore/confuse/eviscerate the students of the [strike]lesser[/strike] non-math subjects that will be attending. The question comes down to how to give a rigorous talk (assisted by a slide show thing that I have to prepare) that is still interesting and comprehensible to outsiders.

I think this would be a somewhat common debate for teachers. Does anyone have some experience or advice? Any help is greatly appreciated.

 

[micromass]

[strike]lesser[/strike] non-math subjects

Wow. I think you most of all need to work on your attitude. Non-math subject are not lesser.

 

[AlephZero]

Some of the professors that I have worked with will be attending, and they are expecting some kind of extravagant bundle of mathematical goodness that they've come to expect from me.

Have they told you that is what they are expecting, or are you just guessing?

It's quite possible they are there (1) because their head of department told them to be there, or (2) because the free food is good.

In any case, they already know how brilliant you are, so it's the rest of the audience you should be trying to impress. And you won't do that by losing them half way through the first sentence

 

[Lavabug]

Wow. I think you most of all need to work on your attitude. Non-math subject are not lesser.

I second this, very heavily.

I don't know if it will help, but I recommend watching some talks by Roger Penrose, particularly the one at Perimeter on twistors. He does not eschew pretty advanced math topics in his talk but IMO still manages to make things as accessible as possible for a general audience. FWIW, the comments on that video from non-science people suggested they really enjoyed the talk.

 

[Mandelbroth]

Wow. I think you most of all need to work on your attitude. Non-math subject are not lesser.

This was just an attempt at playful banter. I don't actually believe that non-math subjects are less important.

I don't know if it will help, but I recommend watching some talks by Roger Penrose, particularly the one at Perimeter on twistors. He does not eschew pretty advanced math topics in his talk but IMO still manages to make things as accessible as possible for a general audience. FWIW, the comments on that video from non-science people suggested they really enjoyed the talk.

Here's a link, for those who might access this in the future:

I'm not done watching it, but I'm enjoying it too. This was very helpful. Thank you.

Have they told you that is what they are expecting, or are you just guessing?

The people doing the event suggested that I might want to cater to the possibly non-math audience. The professor that is advising my work suggested that I should show off my research contributions to the rest of the department in attendance. That is, sweep them away in a tsunami of "I'm publishing with [professor's name] and you can all eat our dust." I'm not sure how to combine these two.

 

[MarneMath]

In a situation like this I would cater towards the audience not your ego. Why talk to a group of people when only a handful may follow you? Consider this a chance to challenge yourself by explaining difficult and advance topics to a laymen. At one of my former universities, professors used to give little talks to undergraduates about their research. Since most of them knew that no one would understand or learn much of anything if they spoke at the same tone as they would towards graduate students, they often times would ignore the technical arguments and talk about the process of solving the particular problem or break it down to the simplified case and in passing explain that these results can be generalized. As an undergraduate, I enjoyed these little talks and learned a lot about what kind of math research was out there and the difficult in achieving results.

 

[thegreenlaser]

(I'm still an undergrad, so take my advice with a grain of salt)

Aim at the non-math folk. If you're doing something important and you present it well (even at a layman level), your peers with math expertise should be able to figure out how important it is without you rubbing it in their faces.

I think one key thing is to make things simpler without sacrificing precision or correctness. Then, even though you're presenting at a "dumbed down" level, people with expertise in math will pick up on the fact that you really do know what you're talking about.

It's the little things that count. Make sure you use terminology consistently and correctly. Make it clear that you know when you're sacrificing correctness for clarity. Don't give the experts in your audience a chance to think to themselves "well, that's not quite correct." If they're noticing little inaccuracies in your presentation, they're probably not thinking about how interesting and important your work is.

 

[mathwonk]

I agree not to talk to the experts. I am amazed at the advice your advisor gave you -

"I'm publishing with [professor's name] and you can all eat our dust."

That is extremely bad advice in my opinion. I wonder if he was joking and you missed the joke.

The purpose of a talk is to communicate, not to try to snow people. Besides, people are not impressed favorably if they don'r understand. They will not feel it is their fault, they will get the (correct) impression that you don't know how to give a clear talk.

Strongly advise practicing the talk a week in advance at least once, on some kind of audience. That will give you the chance to find out how it is received and what needs to be made more clear. I also disagree about worrying over small points. These talks are so hard to follow that most people follow only approximately. Maybe one genius out of hundreds of potential listeners will follow sow ell that he/she notices tiny exaggerations or imprecisions. But it is ok to just say that you will necessarily ignore some fine points, which you are willing to discuss in more detail with anyone interested in them, perhaps afterwards.

I suggest the most reasonable way to treat your own, presumably very specialized, results in such a talk, is to mention them briefly at the end. I.e. spend 50 minutes making the subject as clear as possible, with examples, and mention some open problems. Then in the last 1 or 2 or at most 5 minutes, just state that you have solved one or more of those, with maybe one sentence about how you did so.

You want to come off as a knowledgeable person from whom it is possible to learn something and a pleasure to do so, not as a snotty jerk. Faculty making hiring decisions ask themselves whether they could learn from, and get along with, this person. They also judge whether he will be able to hold up his end of the teaching load, by being a clear teacher.

That's my advice after 40+ years of giving and listening to these talks.