Hilbert's sixth problem

[5] At the same time, but independently, Dirac formulated quantum mechanics in a way that is close to an axiomatic system, as did Hermann Weyl with the assistance of Erwin Schrödinger.

Since the 1960s, following the work of Arthur Wightman and Rudolf Haag, modern quantum field theory can also be considered close to an axiomatic description.

In the 1990s-2000s the problem of "the limiting processes, there merely indicated, which lead from the atomistic view to the laws of motion of continua" was approached by many groups of mathematicians.

Main recent results are summarized by Laure Saint-Raymond,[6] Marshall Slemrod,[7] Alexander N. Gorban and Ilya Karlin.

[13] Nevertheless, in recent years it has fostered research regarding the foundations of physics with a particular emphasis on the role of logic and precision of language, leading to some interesting results viz.