(a) axiomatic treatment of probability with limit theorems for foundation of statistical physics
(b) the rigorous theory of limiting processes “which lead from the atomistic view to the laws of motion of continua”
One of Hilbert’s primary concerns was to understand the foundations of mathematics and, if none existed, to develop rigorous foundations by reducing a system to its basic truths, or axioms. Hilbert’s sixth problem is to extend that axiomatization to branches of physics that are highly mathematical. Some progress has been made in placing some fields of physics on axiomatic foundations, but because there is no ‘theory of everything’ in physics yet, a general axiomatization has not occurred.