Weierstraß

Karl Weierstrass was a German mathematician widely regarded as the "father of modern analysis." Born in 1815, his early career was marked by teaching secondary school mathematics due to his lack of a university degree. However, his self-published work on the theory of elliptic functions gained him recognition, eventually leading to an academic position.

Weierstrass's most significant contributions lie in the rigorous formulation of calculus and mathematical analysis. He is credited with developing the epsilon-delta definition of a limit, which provided a precise and formal way to define continuity, derivatives, and integrals. This work was crucial in eliminating the intuitive and often flawed reasoning that characterized earlier calculus.

He also made advancements in the study of functions, including the Weierstrass M-test for uniform convergence of series and the Weierstrass function, a continuous function that is nowhere differentiable. This latter example was a groundbreaking counterexample, demonstrating that continuity did not necessarily imply differentiability. His work laid the foundation for many areas of modern mathematics, including real analysis, complex analysis, and functional analysis. Weierstrass's influence extended through his many students, who became prominent mathematicians in their own right. He died in 1897, leaving behind a legacy of rigor and precision that continues to shape mathematical thought.