THE MATH
Carl Weierstrass (1815-1897)
The German mathematician Weierstrass was important to the study of infinitesimal and elliptical functions. His continuous but nowhere differentiable functions had a great impact on the development of mathematics, and precipitated a great crisis. Dubois Reymond wrote that, "The metaphysics of these functions seems to hide many puzzles, as far as I am concerned, and I cannot get rid of the thought, that they will lead to the limit of our intellect." The Weierstrass functions are often used to argue for a divorce by mutual consent between mathematics and physics, although Weierstrass himself stressed that the physicist should not see in mathematics a simple auxiliary discipline, and the mathematician should not consider the physicist’s questions a simple collection of examples for his methods. "To the question of whether it is really possible to extract something useful from the abstract theories that modern (=1875) mathematics seems to favor, one could answer that it was only on the basis of pure speculation that Greek mathematicians derived the properties of conic sections long before one could guess that they represent the planets’ orbits."

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