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Results tagged with big-list
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user 65
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.
256
votes
41
answers
99k
views
A single paper everyone should read? [closed]
Different people like different things in math, but sometimes you stand in awe before a beautiful and simple, but not universally known, result that you want to share with any of your colleagues.
Do …
238
votes
46
answers
90k
views
Most interesting mathematics mistake?
Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove t …
63
votes
What programming languages do mathematicians use?
People in math seem to be pretty fond of Python (me included).
As an evidence, search on MathOverflow for posts where people mention the fact that they wrote a program, and it's nearly always either …
51
votes
Most helpful math resources on the web
http://jmilne.org has lots of systematic, well-written courses.
35
votes
12
answers
8k
views
How to write math well?
Let's learn about writing good mathematical texts.
For some people it could be especially interesting to answer about writing texts on Math Overflow, though I personally feel like I've already maste …
21
votes
Ways to prove the fundamental theorem of algebra
Pukhlikov has a proof using only real numbers (the page in English, full text in Russian) of the fact that indecomposable elements in $\mathbb R[x]$ have degree 1 or 2 as is part of the 1997 issue of …
16
votes
Examples of great mathematical writing
Well, for me Hartshorne was really the window into the brave new world — and yes, it fits several items from 'acceptable reasons'.
Though this prize should be shared with everyone else who was creat …
13
votes
What is the first interesting theorem in (insert subject here)?
Computer science: sort requires n * log n
12
votes
If you break a stick at two points chosen uniformly, the probability the three resulting sti...
Yes, here's a nice and beautiful argument!
First you should draw a picture of axes a and b. You're asked to select uniformly a point in the square [0,1]x[0,1]. Now because of the symmetry (sic!) it's …
11
votes
What are examples of good toy models in mathematics?
One can think of Grothendieck ring of varieties as a toy model for motives.
11
votes
Best algebraic geometry textbook? (other than Hartshorne)
I enjoyed Griffiths-Harris a lot.
10
votes
Best algebraic geometry textbook? (other than Hartshorne)
Also Eisenbud.
Every algebraic geometer needs to know at least some commutative algebra. And this is
a very good introductory textbook, which teaches commutative algebra rigorously but at the same t …
9
votes
What's your favorite equation, formula, identity or inequality?
For X a based smooth manifold, the category of finite covers over X is equivalent to the category of actions of the fundamental group of X on based finite sets:
\pi-sets …
9
votes
Ways to prove the fundamental theorem of algebra
When you consider how polynomial $f$ of degree $n$ acts on a big circle $R$, it gives rise to a map $S^1 \to S^1$ of degree $n$. Such a map cannot be continued to a map of a disk $D \to D-\{0\}$, thus …
7
votes
Best algebraic geometry textbook? (other than Hartshorne)
Also lots of things on jmilne.org