Interaction Mathematics, Physucs and Phykosophy, 1860-1930

The main theme of this book is the unique interaction between mathematics,
physics and philosophy during the beginning of the 20th century. In this period seminal theories of modern physics and new fundamental mathematical
structures were discovered or formed. Significant physicists such as Lorentz
and Einstein as well as mathematicians such as Poincar´e, Minkowski, Hilbert
and Weyl contributed to this development. They created the new physical
theories and the mathematical disciplines that play such a paramount role in
their mathematical formulation—and in other areas of mathematics. These
physicists and mathematicians were also key figures in the philosophical discussions of nature and science—from philosophical tendencies like logical
empiricism via critical rationalism to various neo-Kantian trends.
During the first half of the 20th century relativity theory and quantum
mechanics raised different kinds of philosophical problems. This compilation primarily deals with the philosophical issues related to relativity theory.
Their root in the 19th century considerations of the nature of space, time,
mechanics and electromagnetism is the subject of the first papers. Hyder analyzes Helmholtz’s proof of the centrality of forces and its equivalence to the
conservation of energy. He connects it to Helmholtz’s changing adaptation
of Kantian epistemology and shows that these physico-philosophical considerations form the basis of his later papers on geometry. L¨utzen argues that
Hertz’s philosophical theory of images, presented in his book on mechanics, had their origin in Hertz’s work on electromagnetism and was aimed
at presenting a mechanistic foundation of all of physics. After Hertz several
physicists tried to replace this mechanistic philosophy by an electromagnetic
program. This is at the heart of Janssen’s and Mecklenburg’s paper on the
electromagnetic models of the electron in which they give a detailed account
of the transition from classical to relativistic mechanics.
Also Pulte’s and DiSalle’s papers connect post relativity ways of thinking with 19th century ideas. Pulte discusses Schlick’s changing philosophy
of spatial intuition and the foundation of geometry relating it to his reading
of Helmholtz and DiSalle argues that the creation of a mathematical relativistic world structure was a continuation of the epistemological reflections
of Helmholtz and Poincar´e.
Hilbert’s axiomatic program has often had a bad press in so far as it deals
with physical theories, but Majer defends Hilbert’s views while explaining
in some detail how Hilbert imagined one should go about such an axiomatization.
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