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Results tagged with big-list
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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
8
votes
Ingenuity in mathematics
How about the fact that in hex the first player has a winning strategy?
7
votes
LaTeX based document editors
The usual Mac software for this is TeXShop, which is ok but not great. Ben swears by emacs.
16
votes
Are there other nice math books close to the style of Tristan Needham?
I haven't read Needham's book so I'm not totally sure what you mean, but it sounds like you might like "Three-Dimensional Geometry and Topology" by Bill Thurston and Silvio Levy.
12
votes
What practical applications does set theory have?
One cute application of Cantor's results in set theory is the existence of transcendental numbers. Since the set of algebraic numbers is countable while the continuum is not there must exist uncountab …
- 28.1k
8
votes
Examples of great mathematical writing
Another paper that I really like, because it makes a lot of things that are muddled in the literature very clear, is Sawin's Quantum Groups at Roots of Unity and Modularity. In particular the lesson …
18
votes
Examples of great mathematical writing
Dror's paper Khovanov's homology for tangles and cobordisms is one of the papers I loved back when I hated all math papers. In particular it's a paper that has a really good use of diagrams, a lot of …
33
votes
Examples of great mathematical writing
Silverman and Tate's "Rational Points on Eliptic Curves."
7
votes
What would you want on a Lie theory cheat poster?
Probably you want the dual Coxeter number as well.
20
votes
How should the Math Subject Classification (MSC) be revised or improved?
I would add a top-level subject code roughly corresponding to the arXiv math.QA. Currently my field (quantum groups, knot invariants, TQFT, monoidal categories, etc.) is listed under 16T, 17B, 20G42, …
16
votes
What would you want on a Lie theory cheat poster?
The Vogel plane.
.
Image stolen from Bruce Westbury
139
votes
Accepted
What's the "best" proof of quadratic reciprocity?
I think by far the simplest easiest to remember elementary proof of QR is due to Rousseau (On the quadratic reciprocity law). All it uses is the Chinese remainder theorem and Euler's formula $a^{(p-1 …
- 28.1k
12
votes
Which journals publish expository work?
The Moscow Journal of Math says they publish "research-expository articles."
"An important specific trait of the journal is that it especially encourages research-expository papers, which must cont …
30
votes
Favorite popular math book
Title: Journey Through Genius
Author: William Dunham
Short Description: A fencepost history of mathematics. For each highpoint it describes some fun history and then the actual math. Examples of t …
21
votes
What programming languages do mathematicians use?
There are lots of subject specific packages written by mathematicians out there: GAP, PARI/GP, SnapPea, Macaulay (1 and 2), Magma, Singular, etc. Sage is a new python based open-source project that i …
9
votes
Where does a math person go to learn quantum mechanics?
I took undergraduate quantum mechanics as the only Physics class I took in college. You're in better shape knowing linear algebra well and not knowing any physics than you would be the other way arou …