Abstract
On the occasion of an international congress of mathematicians that was taking place in Paris in 1900 David Hilbert gave his famous lecture on “mathematical problems”. In this lecture he addressed a number of questions, the answers to which he considered to be most important for the further development of mathematics. Problem number 6 is concerned with the mathematical treatment of the axioms of physics. Hilbert himself has considered this problem in detail. In 1924 he published a paper entitled “Grundlagen der Physik” (Engl.: “Foundations of Physics”) in the “Mathematische Annalen” (Hilbert 1924). In this paper he proposed a system of axioms that is based on field theoretical considerations. This system of axioms was aimed at overcoming the predominant mechanical point of view on physics at this time. However, the fast development of Quantum Mechanics that passed off in parallel soon led into a total new physics that could neither be explained in terms of particles nor in terms of fields. This new branch of physics came along with new mathematical structures whose epistemological consequences are still under (sometimes quite controversial!) discussions. At this congress Hilbert advocated also a strict axiomatic and self-contained foundation of mathematics—the so-called “Hilbert’s program”. But this program was soon overthrown by Goedel’s incompleteness theorems.
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Rother, T. (2017). Prologue. In: Green’s Functions in Classical Physics. Lecture Notes in Physics, vol 938. Springer, Cham. https://doi.org/10.1007/978-3-319-52437-5_1
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