Karl Weierstrasse

Karl Theodor Wilhelm Weierstraß (written Weierstrass when the character «ß» is not available) (Ostenfelde, October 31, 1815~Berlin, February 19, 1897) was a German mathematician often cited as the "father of modern analysis". His most notable achievements include defining the continuity of a function, proving the mean value theorem; and the Bolzano-Weierstrass theorem used later to study the properties of continuous functions on closed intervals.

Biography

Weierstrass was born in Ostenfelde, Ennigerloh, province of Westphalia, then part of Prussia. He was the son of Wilhelm Weierstrass, a government official, and Theodora Vonderforst. His interest in mathematics began when he was a student at the Theodoriamun School in Paderborn. He was sent to the University of Bonn to prepare for a state civil servant position. His studies were focused on law, economics and finance, which conflicted with his desire to study mathematics. He resolved this conflict by paying little attention to his college career, studying mathematics in private. He ultimately left college without a degree. After he studied mathematics at the Münster Academy and his father got him a teaching position at a Münster school, he was certified as a teacher in that city. During his study period, Weierstrass attended Christoph Gudermann's lectures and became interested in elliptic functions.

In 1843 he taught in Germany and West Prussia, and from 1848 he taught at the Lyceum Hosianum in Braunsberg.

From 1850 Weierstrass suffered a long period of illness, but was able to publish papers that brought him fame and distinction. The University of Königsberg awarded him an honorary doctor's degree on March 31, 1854. In 1856 he obtained a place at the Gewerbeinstitut, which would later become the Technical University of Berlin. In 1864 he became a professor at the Friedrich-Wilhelms University in Berlin, an institution that later became the Humboldt University of Berlin. The last 3 years of his life were spent without being able to move, and he ended up dying in Berlin of pneumonia.

In addition to his prolific research, it should be noted that he was a professor at the University of Berlin, where he had among his disciples Georg Cantor, Ferdinand Georg Frobenius, Wilhelm Killing, Leo Königsberger, Carl Runge, Sofia Kovalévskaya and Edmund Husserl.

Contributions in mathematics

Weierstraß gave the definitions of continuity, limit, and derivative of a function, which are still used today. This allowed him to address a set of theorems that were then not rigorously proven, such as the mean value theorem, the Bolzano-Weierstrass theorem, and the Heine-Borel theorem.

He also made contributions in the convergence of series, in the theory of periodic functions, elliptic functions, convergence of infinite products, calculus of variations, complex analysis, etc.

Selected Works

• Zur Theorie der Abelschen Funktionen (1854) (in German)
• Theorie der Abelschen Funktionen (1856) (in German)
• Abhandlungen-1Math. Werke. Bd. 1. Berlin, 1894 (in German)
• Abhandlungen-2Math. Werke. Bd. 2. Berlin, 1895 (in German)
• Abhandlungen-3Math. Werke. Bd. 3. Berlin, 1903 (in German)
• Vorl. ueber die Theorie der Abelschen TranscendentenMath. Werke. Bd. 4. Berlin, 1902 (in German)
• Vorl. ueber VariationsrechnungMath. Werke. Bd. 7. Leipzig, 1927 (in German)

Eponymy

In addition to the different mathematical concepts that bear his name, one must:

• The lunar crater Weierstrass bears this name in his memory.
• The asteroid (14100) Weierstrass also commemorates its name.

Additional bibliography

• Weierstrass, Karl Theodor Wilhelm. (2018). In Helicon (Ed.), The Hutchinson unabridged encyclopedia with atlas and weather guide. [Online]. Abington: Helicon. Available at: http://libezproxy.open.ac.uk/login?url=https://search.credoreference.com/content/entry/heliconhe/weierstrass_karl_theodor_wilhelm/0?institutionId=292 [Accessed 8 July 2018].
• O'Connor, J. J.; Robertson, E. F. (October 1998). "Karl Theodor Wilhelm Weierstrass." School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 7 September 2014.
• Biermann, Kurt-R.; Schubring, Gert (1996). "Einige Nachträge zur Biographie von Karl Weierstraß. (in German) [Some postscripts to the biography of Karl Weierstrass]". History of mathematics. San Diego, CA: Academic Press. pp. 65–91.
• Gillispie, Charles Coulston. Dictionary of scientific biography. New York: American Council of Learned Societies. p. 223. ISBN 978-0-684-12926-6. OCLC 89822.
• Grabiner, Judith V. (March 1983). «Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus». The American Mathematical Monthly (in English) 90 (3): 185. JSTOR 2975545. doi:10.2307/2975545.
• Cauchy, A.-L. (1823), "Septième Leçon – Valeurs de quelques expressions qui se présentent sous les formes indéterminées ∞ ∞ 0... Relation qui existe entre le rapport aux différences finies et la fonction dérivsiée", Résumé des leçons données à surique l'école royale poly-01 (in French)