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Hilbert’s Sixth Problem

A section of Axioms (ISSN 2075-1680).

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A special homepage, 6th.org, for Hilbert’s Sixth Problem has been set up, where the major research news, information related to symposia, and topical collections of journals will be presented.

In the year 1900, Hilbert presented his problems to the International Congress of Mathematicians. The sixth problem “Mathematical Treatment of the Axioms of Physics” concerns the axiomatization of those parts of physics which are ready for a rigorous mathematical approach. This Section covers all areas of Hilbert’s Sixth Problem, including:

a) Axiomatize Classical Probability and Axiomatize the New (Quantum) Probability:
Quantum mechanics; quantum theory; axiomatic approach to quantum probability; quantum computing; quantum cryptography; axiomatic treatment of probability with limit theorems for the foundation of statistical physics; the axiomatic foundation of probability; measure theory; algorithmic probability.

b) Physical Axioms:
Analytic machinery (formalism); physical interpretation; Boltzmann equations; fluid equations; higher equations of hydrodynamics; Hilbert’s sixth problem in statistical mechanics and machine learning; the rigorous theory of limiting processes ‘which lead from the atomistic view to the laws of motion of continua’.

c) Axiomatic Approach to:
Mathematical logic, algebra, functional analysis, differential equations, geometry, probability theory and random processes, theory of algorithms and computational complexity, etc.