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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.
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 …
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 …
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 …
-3
votes
Describe a topic in one sentence.
QFT — every expression converges after a Wick rotation.
1
vote
What is the first interesting theorem in (insert subject here)?
Algebraic geometry: points are prime ideals.
13
votes
What is the first interesting theorem in (insert subject here)?
Computer science: sort requires n * log n
5
votes
What is the first interesting theorem in (insert subject here)?
Algebraic number theory: Hilbert 90.
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 …
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 …
- 15.1k
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 …
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.
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 …
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 …
3
votes
Where does a math person go to learn quantum mechanics?
There's quite a variety of resources available for learning quantum mechanics. Since you're interested in the mathematical perspective, my suggestion would be to start with one of the mathematically-o …
3
votes
One-step problems in geometry
I think the question Is it possible to capture a sphere in a knot? is an excellent one-step problem.