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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

17 votes

How difficult will it be for me to switch fields (details below) after my Ph.D. in pure math...

I switched from theoretical physics to math, long time ago, it has been a very painful experience (and I had a double graduation). But after 20 years, now, it's OK ;-) I have a good friend who switche …
1 vote

What is the definition of "canonical"?

It is not an answer but it must have to do with the way our brain pick up a sample between a few ones. It must be the minimum of some function which can be implemented for real in the brain. I do not …
7 votes

A book you would like to write

After reflexion, I think I will reduce my contribution to this: Don't think too much about the book you want to write, just write it down. Don't wait that everything is perfect, just begin. Anyway, it …
3 votes

What does the word "symplectic" mean?

The word "sum-plectic" as a greek translation of "com-plexus" was needed also to differentiate the study of "complex geometry" (complex numbers etc) from the study of "complexes de droites" (the geome …
Patrick I-Z's user avatar
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5 votes

Why should one still teach Riemann integration?

In Cartan calculus, integrating a $k$-differential form $\alpha$ on a $k$-cubic chain $\sigma$ doesn't need more than the Riemann integral: $$ \int_\sigma \alpha := \sum_{i=1}^N c_i \int_{I^k}\sigma_i …
9 votes

Which mathematicians have influenced you the most?

Joseph-Louis Lagrange For his modesty as a human being, and his great mathematical work, on almost every field of mathematics, but especially in mechanics.
4 votes

How do you keep your research notes organized?

I work on paper notebook with a pencil (I put date here and there as markers). When something is ok I write a small paper (in TeX) with most of the details. Sometimes I publish it. I put everything va …
3 votes

Theorems that are 'obvious' but hard to prove

In the same vein, chating: My advisor used to say "An interesting theorem is a theorem true which looks false". Well, tastes and colors... ;-)
5 votes

On referee-author communications

I think nothing must be changed in the present procedure. 1) We send a paper to a journal when we think that the paper is ready for publication, if it is not, we don't send it. We spend more time on …