A German mathematician (1815 to 1897) often called the father of modern analysis. He rebuilt real and complex analysis on a rigorous logical foundation, formalizing continuity and limits, and in 1872 startled the Berlin Academy by exhibiting a continuous function with no derivative at any point, work now known as the Weierstrass function.
Facts
BirthplaceEnnigerloh, Province of Westphalia, Kingdom of Prussia (present-day Germany) 1 Death PlaceBerlin, Kingdom of Prussia, German Empire (present-day Germany) 1 Nationality / Culture Defining ContributionRebuilt real and complex analysis on a rigorous epsilon-delta foundation, and in 1872 constructed the first published example of a continuous function that is nowhere differentiable, now called the Weierstrass function. 2 Notable WorkThe Weierstrass function (presented to the Berlin Academy, 1872), a continuous function with no derivative at any point. 2 AwardHonorary doctorate, University of Konigsberg (1854); Fellow of the Royal Society (1881); Copley Medal, Royal Society (1895) 2 Connections
Associated With
Weierstrass was Cantor's teacher in Berlin; the atlas has no dedicated advisor and student relation, so this is recorded as a general association.
Source Karl Weierstrass, Biography (MacTutor History of Mathematics)
Attributed Works
Source Limit of a Function (Wikipedia)
Source Weierstrass Elliptic Function (Wikipedia)
Source Wikipedia: Weierstrass function
In Branch
Source Karl Weierstrass, Biography (MacTutor History of Mathematics)
Source Karl Weierstrass, Biography (MacTutor History of Mathematics)
Mentored
Source Mathematics Genealogy Project: Adolf Piltz (Mathematics Genealogy Project)
Source Arthur Moritz Schoenflies (Wikipedia)
Source Ferdinand Georg Frobenius (Wikipedia)
Source Hermann Schwarz (Wikipedia)
Source Nicolai Vasilievich Bugaev (MacTutor)
Source Otto Hölder (Wikipedia)
Source MacTutor History of Mathematics: Sofia Kovalevskaya (MacTutor biography)
Principal Result
Source Casorati-Weierstrass theorem (Wikipedia)
Source Weierstrass Elliptic Function (Wikipedia)
Source Wikipedia: Weierstrass function
Proofs Credited
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Source Wikipedia: Karl WeierstrassLead paragraph of the cited Wikipedia articletier 2Quote, Lead paragraph of the cited Wikipedia article
Karl Theodor Wilhelm Weierstrass (; German: Weierstraß [ˈvaɪɐʃtʁaːs]; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".
Sources
1. Wikipedia: Karl Weierstrass
Wikimedia FoundationInfobox: death_place
Berlin, Kingdom of Prussia, German Empire
Lead section
Karl Theodor Wilhelm Weierstrass (; German: Weierstraß [ˈvaɪɐʃtʁaːs]; 31 October 1815 - 19 February 1897) was a German mathematician often cited as the "father of modern analysis".
Calculus of variations
Weierstrass also made advances in the field of calculus of variations.
Infobox: birth_place
Ennigerloh, Province of Westphalia, Kingdom of Prussia
Lead section, gender reference
Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics, physics, botany and gymnastics.
View the Source 2. Karl Weierstrass, Biography (MacTutor History of Mathematics)
MacTutor History of Mathematics Archive, University of St AndrewsOpening summary
Karl Weierstrass is best known for his construction of the theory of complex functions by means of power series.
Honours section
The University of Konigsberg conferred an honorary doctor's degree on him on 31 March 1854.
Berlin period
In 1872 his emphasis on rigour led him to discover a function that, although continuous, had no derivative at any point.
Associated With: Georg Cantor, Students section
In 1870 Sofia Kovalevskaya came to Berlin and Weierstrass taught her privately since she was not allowed admission to the university.
View the Source Nicolai Vasilievich Bugaev (MacTutor)
Mentored: Nikolai Bugaev, Biography, study abroadQuote, Mentored: Nikolai Bugaev, Biography, study abroad
he studied under Kummer and Weierstrass in Berlin
Casorati-Weierstrass theorem (Wikipedia)
Principal Result: Casorati-Weierstrass Theorem, Lead sentence of the article on the resultQuote, Principal Result: Casorati-Weierstrass Theorem, Lead sentence of the article on the result
It is named for Karl Theodor Wilhelm Weierstrass and Felice Casorati.
Wikipedia: Weierstrass function
Principal Result: Weierstrass Function, Lead sentence of the article on the result
In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable nowhere.
Attributed Works: Weierstrass Function, Lead
In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere but differentiable nowhere.
View the SourceWeierstrass Elliptic Function (Wikipedia)
Principal Result: Weierstrass Elliptic Function, Lead sentence of the article on the result
They are named for Karl Weierstrass.
Attributed Works: Weierstrass Elliptic Function, Lead section
They are named for Karl Weierstrass.
View the SourceArthur Moritz Schoenflies (Wikipedia)
Mentored: Arthur Moritz Schoenflies, Biography, teachers (Weierstrass)Quote, Mentored: Arthur Moritz Schoenflies, Biography, teachers (Weierstrass)
He studied under Ernst Kummer and Karl Weierstrass
Mathematics Genealogy Project: Adolf Piltz (Mathematics Genealogy Project)
Mathematics Genealogy ProjectMentored: Adolf Piltz, Advisor 2Quote, Mentored: Adolf Piltz, Advisor 2
Advisor 2: Karl Theodor Wilhelm Weierstra
MacTutor History of Mathematics: Sofia Kovalevskaya (MacTutor biography)
MacTutor History of MathematicsMentored: Sofya Kovalevskaya, Biography, Berlin yearsQuote, Mentored: Sofya Kovalevskaya, Biography, Berlin years
Weierstrass tutored her privately
Otto Hölder (Wikipedia)
Mentored: Otto Hölder, Early life, WeierstrassQuote, Mentored: Otto Hölder, Early life, Weierstrass
he was a student of Leopold Kronecker, Karl Weierstrass, and Ernst Kummer
Hermann Schwarz (Wikipedia)
Mentored: Hermann Schwarz, Infobox, doctoral advisor or academic advisorsView the Source Ferdinand Georg Frobenius (Wikipedia)
Mentored: Ferdinand Georg Frobenius, Infobox, doctoral advisor or academic advisorsView the Source Limit of a Function (Wikipedia)
Attributed Works: Limit of a function, HistoryQuote, Attributed Works: Limit of a function, History
In 1861, Karl Weierstrass first introduced the epsilon-delta definition of limit in the form it is usually written today.
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