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Results tagged with soft-question
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user 1463
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.
5
votes
Accepted
Why do branches of math vary in proof styles and what category are different branches in?
The only thing this reminds me of is Tim Gowers's nice article on the two cultures of mathematics, in which he compares and contrasts "geometry" (very broadly defined) and combinatorics.
The categori …
11
votes
Math Vs Social Science
There's nothing wrong with this question per se, but you're asking the wrong audience. Mathematics is used all over the sciences, and mathematicians themselves have relatively little to do with most …
9
votes
What should be offered in undergraduate mathematics that's currently not (or isn't usually)?
Igor Rivin has a whole diatribe on this topic!
17
votes
A single paper everyone should read?
Stallings's How Not To Prove the Poincare Conjecture (cached at Citeseer) is the funniest paper I've ever read.
4
votes
"negative" vs "minus"
I always think of it as a British vs American thing. British students say 'minus 6', and all the American students I've taught say 'negative 6'. Presumably, as Carl Weisman says, this can be ascribed …
5
votes
Most important mathematical results in last 30 years
Agol's proof of the Virtual Haken conjecture was a wonderful application of the tools developed by Wise and his coauthors in geometric group theory to 3-manifold topology. The Virtual Haken conjectur …
6
votes
Most important mathematical results in last 30 years
Perelman's proof of the Geometrization conjecture (see here, here and here) was the crowning achievement of decades of work. It was the most important of Thurston's conjectures about the topology of …
3
votes
Most important mathematical results in last 30 years
Kahn--Markovic's proofs of the Surface Subgroup conjecture and the Ehrenpreis conjecture.
10
votes
Research-level mathematical bookstores
I haven't been there in a while, but Foyles (in London) used to have an excellent selection of mathematics books.
13
votes
The work of Thurston
This isn't a direct answer to the actual question, but in your first sentence I think you're alluding to Thurston's article On proof and progress in mathematics. In section 6, entitled "Some persona …
- 25.2k
47
votes
Most interesting mathematics mistake?
Not just a great mistake, but also a great documentation of a mistake: Stallings's How not to prove the Poincaré Conjecture.1 (I think this paper is my answer to every community-wiki question.)
1Here …
37
votes
What are your favorite instructional counterexamples?
The Baumslag--Solitar groups have presentations
$BS(p,q)=\langle a,b\mid a^p=b^{-1}a^q b\rangle$.
They have the following nice properties:
they're two generator, one relator groups;
they can be wr …
4
votes
Introductory text on geometric group theory?
It's not an introductory text, but if you're trying to get a feel for the area you could look at the GGT Open Problems Wiki. It's still rather incomplete and patchy; a more coherent and shorter alter …