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The Saw-Toothed Function That Broke Calculus
In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.
Though he showed an early aptitude for math, his father pressured him to study public finance and administration, with an eye toward joining the Prussian civil service. Bored with his university coursework, Weierstrass is said to have spent most of his time drinking and fencing; in the late 1830s, after failing to get his degree, he became a secondary school teacher, giving lessons in everything from math and physics to penmanship and gymnastics. Mathematicians were forced to follow in Weierstrass’ footsteps, further sharpening their definition of functions, their understanding of the relationship between continuity and differentiability, and their methods for computing derivatives and integrals.
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