Karl Weierstrass

Early Life and Education

Karl Theodor Wilhelm Weierstrass was born on October 31, 1815, in Ostenfelde, part of Ennigerloh, Westphalia, Germany. His father, Wilhelm Weierstrass, was a government official and his mother, Theodora Vonderforst, was a school teacher. He was the eldest of four children.

Weierstrass attended the Theodorianum in Paderborn from 1829 to 1834, where he was introduced to calculus. However, his interest in mathematics was not immediately apparent, as he initially studied law and finance at the University of Bonn. His studies were interrupted by the death of his father in 1839, which led him to take a teaching position in Deutsch Krone in West Prussia in 1842.

A historical school building, representing the Theodorianum in Paderborn where Weierstrass studied.

A historical school building, representing the Theodorianum in Paderborn where Weierstrass studied.

Career and Contributions to Mathematics

While teaching, Weierstrass continued to study mathematics and began to publish papers on the subject. His first paper, published in 1841, introduced what is now known as the Weierstrass function. This function is continuous everywhere but differentiable nowhere, which challenged the existing notions of calculus.

In 1854, Weierstrass was appointed as a professor at the University of Berlin, where he spent the rest of his career. He made significant contributions to the field of analysis, including the Bolzano–Weierstrass theorem, the Weierstrass factorization theorem, and the Weierstrass approximation theorem. These theorems have had a profound impact on the field of analysis, particularly in the study of real numbers, complex numbers, and functions.

Weierstrass also introduced the concept of uniform convergence, which is crucial in the study of sequences and series of functions. He was also one of the first to use the epsilon-delta definition of a limit in his work, which is now a standard concept in calculus.

Later Life and Legacy

Weierstrass suffered from a nervous breakdown in 1861, but he continued to teach and conduct research. He retired from teaching in 1891 due to health problems.

Weierstrass died on February 19, 1897, in Berlin. His contributions to mathematics, particularly in the field of analysis, continue to be influential. The Weierstrass Institute for Applied Analysis and Stochastics in Berlin is named in his honor.

A historical university building, representing the University of Berlin where Weierstrass spent his career.

A historical university building, representing the University of Berlin where Weierstrass spent his career.

See Also

• Bolzano–Weierstrass theorem
• Weierstrass function
• Weierstrass factorization theorem
• Weierstrass approximation theorem
• Weierstrass Institute