[cholmon]

1) Lecturing - Every lecture should make only one main point - Never run overtime - Relate to your audience - Give them something to take home

2) Blackboard Technique - Make sure the blackboard is spotless. - Start writing on the top left-hand corner

3) Publish the Same Result Several Times

4) You Are More Likely to Be Remembered by Your Expository Work

5) Every Mathematician Has Only a Few Tricks

6) Do Not Worry about Your Mistakes

7) Use the Feynman Method

8) Give Lavish Acknowledgments

9) Write Informative Introductions

10) Be Prepared for Old Age

[joe_the_user]

A good portion of these points involve "integrate into the mathematical exposition methods of your time" and become useless as exposition methods change. If blackboards are supplanted by digital whiteboard that autoerase or autoscroll, exposition may different - slide techniques would be useful to include.

Another portion involve the "exposition culture" - that the greatest of a given mathematician still has to interface with mathematics proper (or at the limit, a mathematician who is "outre", "out-there", may publish a theorem and have mathematics simply throws up it's hands as happened with ABC theorem - at least so far). Essentially, have a strategy that lets you keep working on the hard stuff but without getting entirely lost on it.

But I think the really cool parts involve rules of thumb for going through life and solving a few hard, important problems. This reminds me of Andrew Wiles talking about the problem that really, really smart math grad students have when confronted with problems that they can't solve in 24 hours.

Edit: and naturally, it's worth noting that exposition method and culture are important for anyone also working on hard problems since knowing the "smell" of good or bad proofs is crucial if one is going forward towards a really big proof - see the point that most good proofs can survive a little bit of error.

[jacobolus]

Blackboards are much better as lecture tools than digital whiteboards with autoscroll, or most uses of powerpoint, or whatever else people try, in my experience.

I wish that more lecturers would consider returning to blackboards, instead of the lazy slides they currently do. It would both improve their talks and waste less of their prep time.

The nice thing about blackboards is that lecturers don’t try to write every word on a screen, but just talk as normal, only putting up explicitly technical content like diagrams and formulas. They can add or remove things from the board in response to audience feedback, and can improvise new ideas. Maybe most importantly, (sufficiently large) blackboards keep a large amount of context in view at any given time.

Blackboards are especially good as classroom tools because they are a fundamentally improvisational and accessible medium. You can’t prepare all the drawings in advance, which means that anything a lecturer can do on the board a student can in principle also do, and the form of the teacher’s lecture is a direct part of the pedagogy: the student can learn to imitate the same mode of thought with access to the same tools. There can be a drawing- and formula-based dialog between teacher and students in which they are all operating as equal peers, unlike powerpoint where one participant spent hours making a bunch of pretty graphs or typing up formulas in a cryptic markup language, and the other participant gets no insight whatsoever into how.

Making good use of computers would mean handing out interactive demonstrations with their full code available [code might be implemented in some drawing-based environment, not necessarily just lines of ASCII] at every lecture, and then showing how the code works and showing how to twiddle the parameters as part of the lecture, alongside the traditional writing-and-drawing-on-a-blackboard part of the lecture. Ideally students would have some way of also interacting with the same medium during class.

But making good interactive diagrams or writing code whose primary purpose is exposition takes 2 orders of magnitude more prep time than just throwing words and static diagrams up, and is just not feasible for individual lectures in a current education setup. Ideally we would have much better improvisational computer demonstration/diagram tools, but in practice the drawing tools we have are not really designed for a computer medium, and all pretty much suck. (If Bret Victor’s ideas from “Inventing on Principle” and “Stop Drawing Dead Fish” and “Drawing Dynamic Visualizations” were turned into polished, production-ready, mainstream tools, we might have a chance.)

I’ve seen some pretty effective lectures that were done live-coding style, e.g. in some notebook-based tool, but it depends on having the right topic for the lecture.

[WalterBright]

Recently at the NWCPP meeting, the usual presentation was not possible. So I offered to do an extemporaneous one to fill the time. I had no slides and no notes prepared, so I used the whiteboard.

I expected it to be terrible, but was pleasantly surprised how well it went off - it was one of my best presentations. The audience was very much engaged with the whiteboard and I'd erase/adjust things with each point.

I came away thinking I should do that more often.

[kaybe]

It's always impressive to follow someone derive a full theory (general relativity, quantum field theory...) from the basics on the blackboard, and in the end it is off by a factor of 2 or pi, and everyone has to hunt for the place where it was misplaced - demonstrating that this was indeed a live derivation.

[joe_the_user]

Blackboards are much better as lecture tools than digital whiteboards with autoscroll, or most uses of powerpoint, or whatever else people try, in my experience.

If you're down voting me for mentioning these, I have no dog in the fight. I only said that the advice was "learn your tools" - IF the tools HAPPENED to change, the advice would change. If not, sure, use a blackboard well.

[jacobolus]

No idea why people are downvoting you. My comment about blackboards is kind of a tangent.

[soperj]

Agreed, the best exposition style for a digital white board is not to use it.

[virgilp]

> Publish the Same Result Several Times

Is this not frowned upon? Serious question. Serious journals and conferences ask you to certify that you didn't publish that work elsewhere. Yes, you can work around that by doing some extra experiments/ minor tweaks/etc. so that it is "different" .. but I thought that's a sort of "tolerated cheating", not something you'd actively/publicly advise others to do.

[pdpi]

What TFA actually says is that you publish your early ideas on the result in a lower-tier journal, then both things progress side by side——as you refine your ideas, you submit to progressively more prestigious publications.

[NotOscarWilde]

The thing is, you cannot submit to a "lower-tier journal"; once you get accepted to one journal, no other journal will allow you to resubmit the same results (even with readability improvements).

The way I've seen things done in CS these days is not so bad, though:

Iteration 1: When you are done, you submit to arXiv and simultaneously to a conference. Conferences usually have as strict page limit, so many things get swept into the appendix.

Iteration 2: You get review comments from the conference; depending on the rigor of the reviewers, these may or may not be ideas how to improve the text. You submit the camera-ready version of the conference paper.

Iteration 3: If the paper was more extensive, you start preparing a journal version, where you can move things back from the appendix make the text cohesive again. You probably also have feedback from the conference participants, which is often extremely useful.

Iteration 4: You submit to a journal, you get a (usually quite thorough) reviews and you integrate them to the final version of the paper.

---

Bottom line: I'm saying it's not so bad (compared to just a single iteration) but I hate this system. First, it does not allow community contributions from outsiders (such as PhD students who read your paper and notice something small that can be improved) and second, after Iteration 4 it is nigh-impossible to make small improvements to the paper unless it was spectacularly wrong.

[emmelaich]

I'd compare to code that you refine over time. Every release is worth mentioning.

[jimhefferon]

I have a colleague who is very concerned about self-plagarism. Seriously.

An excellent example of forgetting what we are about.

[adrianN]

Rightly so. I once had to review a paper from a guy who only had half a dozen publications that were all but identical. Whole pages were copied between the papers and it wasn't at all clear what the novel contribution of each paper was supposed to be.

You can publish the same result multiple times, but please reference the previous publication and explain exactly what has changed that warrants another paper.

[perl4ever]

Is your implication that self-plagiarism is or is not a serious problem?