Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Why and whence the Hilbert space in quantum theory?   We explain why and how the Hilbert space comes about in quantum theory. The
axiomatic structures of a vector space, of scalar product, of orthogonality,
and of the linear functional are derivable from the statistical description of
quantum micro-events and from Hilbertian sum of squares
$|\mathfrak{a}_1|^2+|\mathfrak{a}_2|^2+\cdots$. The latter leads
(non-axiomatically) to the standard writing of the Born formula
$\mathtt{f}=|\langle\psi|\varphi\rangle|^2$. As a corollary, the status of
Pythagorean theorem, the concept of a length, and the 6-th Hilbert problem
undergo a quantum `revision'. An issue of deriving the normed topology is
likely solvable in the affirmative and has been stated as a mathematical
problem.

14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci