tea.mathoverflow.net - Discussion Feed (Poincare/Hadamard survey redux?)

Jon Bannon comments on "Poincare/Hadamard survey redux?" (13706)

Jon Bannon — Sat, 19 Mar 2011 10:43:31 -0700

These are all good suggestions. One thing could perhaps be usefully gleaned from the survey I suggest: First, how have the habits/thinking patterns of mathematicians changed from then to now (e.g., is language more important now?)

What really interests me is the "behind the scenes" activity of mathematicians...as suggested in Bill Thurston's question linked to by Joseph O'Rourke above. I wonder if there is any direct advice on pedagogy that would bring us closer to what mathematicians, especially those of Thurston's caliber, actually do all day.

Thanks for the suggestions, all. I'm not going to post anything like this, yet. If anyone wants to, though, feel free.

Joseph O'Rourke comments on "Poincare/Hadamard survey redux?" (13660)

Joseph O'Rourke — Wed, 16 Mar 2011 16:15:43 -0700

Here's the Thurston question to which Gerhard refers: http://mathoverflow.net/questions/38639/thinking-and-explaining .
Perhaps several Gower's questions are relevant; at least this: http://mathoverflow.net/questions/40005/generalizing-a-problem-to-make-it-easier .
I guess Jon's question would be best phrased by citing and contrasting with these and other related MO questions. Otherwise many responses will be, "Haven't we discussed this before?"

This is a partial answer to Qiaochu's request:
http://en.wikipedia.org/wiki/Jacques_Hadamard#On_creativity .

Qiaochu Yuan comments on "Poincare/Hadamard survey redux?" (13659)

Qiaochu Yuan — Wed, 16 Mar 2011 15:31:32 -0700

For those of us who are unfamiliar with it, could you briefly summarize what this survey is about?

grp comments on "Poincare/Hadamard survey redux?" (13656)

grp — Wed, 16 Mar 2011 14:01:24 -0700

Write the question up, and get Bill Thurston to post it.

Better yet, try to extract the information you want from similar questions posted by Tim Gowers and Thurston. I think Gil Kalai and Richard Stanley have posted questions that border the topic.

Gerhard "Reduce, Reuse, Recycle Questionable Content" Paseman, 2011.03.16

Jon Bannon comments on "Poincare/Hadamard survey redux?" (13654)

Jon Bannon — Wed, 16 Mar 2011 13:02:48 -0700

This forum is certainly not appropriate for surveys, but the access we have to so many mathematicians suggests that the survey conducted by Hadamard in "The psychology of invention in the mathematical field" could be run again electronically. Perhaps there is no reason to do this, as the answers may not have changed much.

I wonder if this possibility has occurred to anyone else.

I am inclined to misuse of MO for the purpose of probing for intuitions about meta issues, and so won't post the question myself.

Another (related) question/problem I wonder about is this: Mathematics education seems to be concerned with our learning how to think like students, whereas it seems more appropriate for students (and us) to learn how to think like the masters. Compile a source of math education tips from expert mathematicians.

Obviously, the latter question shouldn't, as is, be asked.