Question of the Week, 26.4.2011
The Hilbert’s sixth problem [1] is one of the 23 problems in mathematics presented by Hilbert in 1902 [2]. It is about axiomatizing branches of physics with mathematical background. The explicit statement reads:
To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.
Hilbert worked on this extensively: firstly on general relativity with A. Einstein and later on quantum mechanics. Interestingly, in 2008 Schiller proposed in context of combination of general relativity with quantum theory, that the sixth problem cannot be solved. However, Schiller’s argument is not generally accepted.
In fact, the search for an axiomatic description of fundamental physics can be seen as the search for the theory of everything, which is one of the unsolved problems in physics.
References:
[1] http://en.wikipedia.org/wiki/Hilbert%27s_sixth_problem
[2] http://en.wikipedia.org/wiki/Hilbert%27s_problems
Libor Veis