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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.
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
52
votes
What precisely Is "Categorification"?
One way to think of categorification is that it's a generalization of enumerative combinatorics. When a combinatorialist sees a complicated formula that turns out to be positive they think "aha! this …
- 28.1k
33
votes
Examples of great mathematical writing
Silverman and Tate's "Rational Points on Eliptic Curves."
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 …
26
votes
Most helpful math resources on the web
Videos from MSRI.
24
votes
Generalizations of the four-color theorem
The chromatic polynomial of any planar graph has no real roots that are greater than or equal to four.
Note that the four color theorem says that 4 cannot be a root, and it's well known that the root …
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 …
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, …
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 …
17
votes
What are some of the big open problems in 3-manifold theory?
Rob Kirby has a huge collection of open problems: http://math.berkeley.edu/~kirby/problems.ps.gz
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.
16
votes
What would you want on a Lie theory cheat poster?
The Vogel plane.
.
Image stolen from Bruce Westbury
12
votes
Mathematical Advice for Interested Highschool Students
There are a number of excellent summer math programs for advanced highschool students. I have my own opinions of which are better or worse, but a quasi-objective list of the programs you'd want to co …
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
12
votes
What are some applications of other fields to mathematics?
This blog post of Kenny Easwaran suggests a mathematical result that can be explained using economic intuition. It's more an interesting isolated example than a genuine application, but it's still in …