Linked Questions

134 votes
69 answers
222k views

Mathematical "urban legends"

When I was a young and impressionable graduate student at Princeton, we scared each other with the story of a Final Public Oral, where Jack Milnor was dragged in against his will to sit on a committee,...
168 votes
50 answers
56k views

17 camels trick

The following popular mathematical parable is well known: A father left 17 camels to his three sons and, according to the will, the eldest son should be given a half of all camels, the middle son ...
106 votes
15 answers
36k views

Most striking applications of category theory?

What are the most striking applications of category theory? I'm trying to motivate deeper study of category theory and I have only come across the following significant examples: Joyal's ...
77 votes
15 answers
14k views

Each mathematician has only a few tricks

The question "Every mathematician has only a few tricks" originally had approximately the title of my question here, but originally admitted an interpretation asking for a small collection ...
67 votes
16 answers
8k views

What do named "tricks" share?

There are a number of theorems or lemmas or mathematical ideas that come to be known as eponymous tricks, a term which in this context is in no sense derogatory. Here is a list of 11 such tricks (the ...
153 votes
4 answers
11k views

Analytic tools in algebraic geometry

This is not a very precise question, but I hope it will get some good answers. As someone with a background in smooth manifold theory, I have experienced algebraic geometry as a beautiful but foreign ...
Tom Goodwillie's user avatar
43 votes
3 answers
5k views

Is there a systematic method for differentiating under the integral sign?

This MO question by Tim Gowers reminded me of a question I've wondered about for some time. In the delightful book Surely You're Joking, Mr. Feynman!, Feynman praises the technique of differentiating ...
Timothy Chow's user avatar
  • 79.5k
14 votes
1 answer
3k views

How is the "conformal prediction" conformal?

The question is clarified by Prof.V.Vovk. See his answer below for discussion. Recently, early works of Gammerman, Vanpnik and Vovk[4] are rediscovered by Wasserman et.al[1] and proposed it as a ...
Henry.L's user avatar
  • 8,011
2 votes
2 answers
1k views

What is a simplified intuitive explanation of conformal invariance? [closed]

Can the concept of conformal map and conformal Invariance be explained in very general terms, preferably in high school/undergrad-level Mathematics? Abstracting away from the applications in physics (...
Sohail Si's user avatar
  • 157
17 votes
1 answer
864 views

Proof of certain $q$-identity for $q$-Catalan numbers

Let us use the standard notation for $q$-integers, $q$-binomials, and the $q$-analog $$ \operatorname{Cat}_q(n) := \frac{1}{[n+1]_q} \left[\matrix{2n \\ n}\right]_q. $$ I want to prove that for all ...
Per Alexandersson's user avatar
3 votes
0 answers
791 views

Hard problems solving tricks

This question is motivated by this one that I posted on math.stackexchange. When I fail to solve a hard math problem (like the ones I presented in the linked post), I read a solution and I noticed ...
Michelle's user avatar
  • 161
10 votes
0 answers
382 views

Is there a general theory for Wilsonian renormalization?

I know that Wilson's renormalization group is not a theory per se and that there are many ways to implement it in a given system. Also, renormalization group techniques are applied in a large number ...
JustWannaKnow's user avatar