Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A counterexample to Borsuk's conjecture   Let $f(d)$ be the smallest number so that every set in $R^d$ of diameter 1
can be partitioned into $f(d)$ sets of diameter smaller than 1. Borsuk's
conjecture was that $f(d)\! =\!d\!+\!1$. We prove that $f(d)\! \ge\!
(1.2)^{\sqrt d}$ for large~$d$.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga