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Foundations of the Exact Sciences

Ever since the birth of science, mathematics and physics have gone hand in hand. Pythagoras of Samos, Aristotle, Zeno of Elea, Euclid of Alexandria, Archimedes of Syracuse, to name some of the great Greek scientists, were mathematicians as well as physicists and addressed fundamental questions. Some of these problems are still or again actual (e.g. Zeno's paradox in quantum mechanics).

When modern science started in the 17th century, mathematics and physics kept influencing each other fundamentally. Isaac Newton and Gottfried Wilhelm von Leibniz, both studying classical mechanics, and later Augustin Louis Cauchy, working on continuum mechanics, developed classical differential and integral calculus. The concepts of 'continuity', 'differentiability', and 'integrability' were only formalized by the end of the 19th century, after they had been used for a long time in a fertile way in classical physics. Carl Friedrich Gauss, Janos Bolyai, Nikolai Ivanovich Lobachevsky en Georg Friedrich Riemann formulated non-Euclidean geometry and Albert Einstein used it to develop general relativity theory during the first quarter of the 20th century.

In the 19th century Arthur Cayley discovered matrix theory and it was recognized by Max Born as the mathematical foundation to Werner Heisenberg's first quantum mechanical calculation in 1925.

Paul Adrien Dirac intuitively introduced the delta-function, which is not a function, and Laurent Schwartz later formalized it in a strict mathematical sense to give rise to the theory of distributions.

There are many more examples of the intertwining of mathematics and physics throughout the history of science. The interaction happens in both directions. Mathematical structures, invented for pure reason and beauty, often turn out to be the building blocks for new frameworks in physics. And mathematical entities, introduced in a non-rigorous way in physics, often give rise to deep and beautiful mathematical theories. In our research group FUND we want to study the foundations of physics and mathematics respecting the ancient historical bond between the two.

FUND is one of the research groups of the Department of Mathematics in the Faculty of Science of Brussels Free University.

The research group FUND has a close collaboration with the Center Leo Apostel for Interdisciplinary Studies (CLEA) at Brussels Free University. Some menbers of FUND are also scientifically active in CLEA and vice versa.

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Last modified October 27, 2001, by Diederik Aerts