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Karl Weierstrass

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Georg Cantor and the Beauty of Infinity

Georg Cantor and the Beauty of Infinity

Harald Sack
On March 3, 1845, German mathematician Georg Cantor, creator of the set theory was born. Set Theory is considered the fundamental theory of mathematics. He also proved that the real numbers are “more numerous” than the natural numbers, which was quite shocking for his contemporaries that there should be different numbers of infinity. “In mathematics the art of asking questions is more valuable than solving problems.” – Georg Cantor, Doctoral thesis (1867) Youth…
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mathematics
Ferdinand Georg Frobenius and Group Theory

Ferdinand Georg Frobenius and Group Theory

Harald Sack
On August 3, 1917, German mathematician Ferdinand Georg Frobenius passed away. Frobenius best known for his contributions to the theory of elliptic functions, differential equations and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms. He was also the first to introduce the notion of rational approximations of functions (nowadays known as Padé approximants), and…
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mathematics
Gösta Mittag-Leffler and the Acta Mathematica

Gösta Mittag-Leffler and the Acta Mathematica

Harald Sack
On March 16, 1846, Swedish mathematician Gösta Mittag-Leffler was born. Mittag-Leffler‘s contributions are connected chiefly with the theory of functions. His mathematical research helped advance the Scandinavian school of mathematics. He is probably best known for founding the international mathematical journal Acta Mathematica. “The mathematician’s best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one…
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mathematics
Felix Klein and the Klein-Bottle

Felix Klein and the Klein-Bottle

Tabea Tietz
On April 25, 1849, German mathematician and mathematics educator Felix Klein was born. Klein is known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day. Klein also devised the Klein-bottle, a one-sided surface which, if traveled upon, could…
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mathematics
Sofia Kovalevskaya – Mathematician and Writer

Sofia Kovalevskaya – Mathematician and Writer

Harald Sack
On January 15, 1850, Russian mathematician Sofia Kovalevskaya was born. Kovalevskaya was responsible for important original contributions to analysis, partial differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe. “Say what you know, do what you must, come what may.” — Sofia Kovaleveskaya, Motto on her paper “On the Problem of the Rotation of a Solid Body about a Fixed Point.” (1886) Sofia Kovalevskaya – Early…
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mathematics
God made the integers, all the rest is the work of man – Leopold Kronecker

God made the integers, all the rest is the work of man – Leopold Kronecker

Harald Sack
On December 7, 1823, German mathematician Leopold Kronecker was born, who worked on number theory and algebra. He criticized Cantor’s work on set theory, and his most cited quote says, “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk” (traditionally rendered: “God made natural numbers; all else is the work of man“.) Leopold Kronecker – Early Life Leopold Kronecker was born in Liegnitz, Prussia (now Legnica, Poland) in a wealthy Jewish…
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mathematics
Ernst Kummer and the Introduction of Ideal Numbers

Ernst Kummer and the Introduction of Ideal Numbers

Harald Sack
On January 29, 1810, German mathematician Ernst Eduard Kummer was born. One of his major contributions is the introduction of ideal numbers, which are defined as a special subgroup of a ring. He extended the fundamental theorem of arithmetic to complex number fields.He also discovered the fourth order surface based on the singular surface of the quadratic line complex. This Kummer surface has 16 isolated conical double points and 16 singular tangent…
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mathematics
Every Set can be Well Ordered – Ernst Zermelo

Every Set can be Well Ordered – Ernst Zermelo

Harald Sack
On July 27, 1871, German logician and mathematician Ernst Zermelo was born. Zermelo’s work had major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. “…self-evidence … must not be confused with … provability.” – Ernst Zermelo The Son of a Grammar School Professor Zermelo was the son of a grammar school professor and attended the…
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mathematics
Sophus Lie and the Theory of Continuous Symmetry

Sophus Lie and the Theory of Continuous Symmetry

Harald Sack
On December 17, 1842, Norwegian mathematician Sophus Lie was born. Lie largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. “In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group,…
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