Summary:
Calculus was historically founded on shaky intuition rather than precise definitions. French mathematicians applied calculus to physics, while German mathematicians like Weierstrass challenged and revolutionized its core concepts. Weierstrass introduced a function continuous everywhere yet differentiable nowhere, a shock to the mathematical community. This “Weierstrass monster” forced mathematicians to redefine continuity and differentiability, leading to the establishment of a more rigorous standard for calculus. Weierstrass’ function, though initially rejected, eventually found applications in modeling complex phenomena like Brownian motion and financial markets. His work marked a shift towards more analytical approaches in mathematics and continues to shape the field today.
https://www.quantamagazine.org/the-jagged-monstrous-function-that-broke-calculus-20250123/