Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tschirnhaus transformations after Hilbert   Let RD(n) denote the minimum d for which there exists a formula for the roots
of the general degree n polynomial using only algebraic functions of d or fewer
variables. In 1927, Hilbert sketched how the 27 lines on a cubic surface could
be used to construct a 4-variable formula for the general degree 9 polynomial
(implying $RD(9)\le 4$). In this paper, we turn Hilbert's sketch into a general
method. We show this method produces best-to-date upper bounds on RD(n) for all
n, improving earlier results of Hamilton, Sylvester, Segre and Brauer.

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The categories of this paper are: supr-con
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an