Mathematician:Karl Theodor Wilhelm Weierstrass

German mathematician whose main work concerned the rigorous foundations of calculus.

Known as "the father of modern analysis".

Nationality
German

History

 * Born: 31 Oct 1815, Ostenfelde, Westphalia (now Germany)
 * Died: 19 Feb 1897, Berlin, Germany

Achievements

 * Pioneered the $\epsilon-\delta$ definition of continuity.
 * Was able thereby to formulate proofs of the Bolzano-Weierstrass Theorem (which had been proved earlier, independently of Weierstrass, by ), the Intermediate Value Theorem and the Heine-Borel Theorem.
 * Made significant advancements in the field of calculus of variations.

Theorems and Definitions

 * Weierstrass Approximation Theorem
 * Weierstrass-Casorati Theorem (with )
 * Weierstrass's Elliptic Functions
 * Weierstrass-Erdmann Corner Conditions
 * Weierstrass Function
 * Weierstrass M-Test
 * Weierstrass Preparation Theorem
 * Weierstrass Factorization Theorem
 * Weierstrass Substitution
 * Bolzano-Weierstrass Theorem (independently of )
 * Enneper-Weierstrass Parameterization (with )
 * Hermite-Lindemann-Weierstrass Theorem (with  and )
 * Sokhotski-Weierstrass Theorem (with )
 * Stone-Weierstrass Theorem (with ) (a generalization of the Weierstrass Approximation Theorem)

Books and Papers

 * 1854: Zur Theorie der Abelschen Funktionen
 * 1856: Theorie der Abelschen Funktionen
 * 1894: Abhandlungen-1
 * 1897: Abhandlungen-2
 * 1902: Vorl. ueber die Theorie der Abelschen Transcendenten
 * 1915: Abhandlungen-3
 * 1927: Vorl. ueber Variationsrechnung

Notable Quotes

 * "A mathematician who is not also something of a poet will never be a complete mathematician."

Also see

 * : Chapter $\text{XXII}$
 * : Chapter $\text {A}.33$