"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."
-G.H. Hardy

"I know numbers are beautiful. If they aren't beautiful, nothing is."
- Paul Erdős

Apr
5
awarded Notable Question
Feb
24
awarded Good Answer
Feb
4
awarded Civic Duty
Jan
28
comment Is it possible to formulate category theory without set theory?
I think this answer is so awesome, thanks for taking the time to write it all up. Since posting this question, I have come back and read all these great answers and comments a bunch of times. I have decided to mark this as correct because it is the one that helped me understand the issues that motivated the OP the most, and I wanted it to be at the top.
Jan
28
accepted Is it possible to formulate category theory without set theory?
Jan
21
awarded Nice Answer
Dec
12
awarded Tumbleweed
Dec
5
revised Generating function for the number of ways of writing an integer as a sum of distinct integers from a finite set
added 27 characters in body
Dec
5
revised Generating function for the number of ways of writing an integer as a sum of distinct integers from a finite set
deleted 13 characters in body
Dec
5
revised Generating function for the number of ways of writing an integer as a sum of distinct integers from a finite set
added 1 character in body
Dec
5
asked Generating function for the number of ways of writing an integer as a sum of distinct integers from a finite set
Dec
4
answered JQUERY: Uncaught Error: Syntax error, unrecognized expression
Nov
23
awarded Civic Duty
Nov
18
awarded Nice Answer
Nov
13
comment Is there a (deep) relationship between these various applications of the exponential function?
the words "Landau vol 5" at the end of my previous comment are a link to the relevant pages, in google books.
Nov
12
accepted Is there a (deep) relationship between these various applications of the exponential function?
Nov
12
comment Is there a (deep) relationship between these various applications of the exponential function?
Thanks for the awesome answer to this old question! It's going to take me some time to get through all of these links, but in the meantime I wanted to mention that my favorite derivation of the Boltzmann distribution in physics is directly related to symmetry, the basic idea being that entropy must be an additive integral of the motion, and hence must depend only on energy. It can be found in Landau vol 5
Nov
12
revised Is there a (deep) relationship between these various applications of the exponential function?
fix typo in link to "derivation of boltzman distribution"
Nov
10
awarded Good Question
Nov
9
awarded Popular Question
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