Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: What is a proof? What should it be?   Mathematical proofs should be paired with formal proofs, whenever feasible.

5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol