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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

1 vote

To what extent is it true that "number theory = mathematics"?

I was wondering, in what way is this dichotomy between "top-down" and "bottom-up" mathematics related to the distinction between mathematicians who, deep down, prefer the Continuum Hypothesis to be tr …
20 votes
6 answers
872 views

Hamiltonian paths where the vertices are integer partitions

I have been working on this problem for several months now but have not made much progress. It concerns the set of all integer partitions of n. Let the vertices of the graph G=G(n) denote all the p(n) …
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