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Results tagged with soft-question
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user 2284
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.
6
votes
The current status of the Birch & Swinnerton-Dyer Conjecture
There is an article of J.Parson and B.Gross (On the local divisibility of Heegner points) from which I think some very very special instance of r=2, d=2 can be deduced. The argument is a combination o …
- 10.9k
19
votes
Which mathematical ideas have done most to change history?
The idea that new knowledge can be obtained by careful deduction from previous truths has in my opinion had an enormous impact on european history and is certainly not a trivial one. Be it found in th …
9
votes
what is an Euler system and the motivation for it?
A small correction to Hunter Brooks's answer: Kato's Euler system is unrelated to Heegner points but comes from Beilinson's elements on modular curves. The fact that Heegner points form an Euler syste …
- 10.9k
3
votes
Oddities of evenness
The $L$-function $L(A,s)$ of an abelian variety $A/F$ over a number field is conjectured to satisfy a functional equation relating $s$ and $2-s$ (this is known in many cases if $F$ is totally real). A …
16
votes
Biographic Data/Stories about André Néron
According to Colliot (sorry Pete, I missed your warning that you had already asked him), Néron was a very nice person. The fact that he had so few students simply reflect the fact that at the time the …
7
votes
Choosing postdocs
All in all, I had 4 postdoctoral position outside the US, and my experience is very similar to that of Yiftach Barnea. For instance, I had absolutely no problem making a German postdoc start 3 months …
12
votes
Should one attack hard problems?
I think Markus Redeker's answer captures the essential point. If the problem is hard and famous (at least in the relevant sub-field), so a fortiori for a problem like P≠NP, I would add the further res …
13
votes
Books/websites which have motivating stories of mathematicians overcoming hardships in life
Alexander Grothendieck was born the son of Russian anarchist Jew in Nazi Germany, was imprisoned in a concentration camp as a young stateless child, had to hide from the Nazis, lived as a miserable te …
17
votes
Value of "of course" in the mathematical literature
Like Konrad Swanepoel, I have found many mistakes, especially in my own work, around "Of course" or comparable expressions, and the saying from one of my early teacher that I often quote is "If it is …
49
votes
Accepted
History of Geometric Analogies in Number Theory
Treating number and function fields on the same footing or (for instance) the idea that ramification in algebraic number theory and in the theory of covering of Riemann or analytic surfaces are two in …
- 10.9k
25
votes
Work of plenary speakers at ICM 2018
Vincent Lafforgue's work span many topics and contain many striking results but the most probable recent work to be described in the spirit of the question is Chtoucas pour les groupes réductifs et pa …
50
votes
Mathematical habits of thought and action which would be of use to non-mathematicians
Keep in mind that it is easy to make mistakes.
The most striking thing I learned from doing mathematics is that even in an environment entirely devoid of ambiguities and characterized by precise axiom …
17
votes
Most memorable titles
I don't think $\textbf{L'endoscopie tordue n'est pas si tordue}$ (Twisted endoscopy is not so twisted) de J.-L. Waldspurger has been mentioned yet.