David Hilbert

Kurt Gödel Shaking the Very Foundations of Mathematics

Kurt Gödel Shaking the Very Foundations of Mathematics

On April 28, 1906, Kurt Gödel was born. He was one of the most significant logicians of all time. Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics. “Either mathematics is too big for the human mind, or the human…
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Emmy Noether and the Love for Mathematics

Emmy Noether and the Love for Mathematics

On April 23, 1882, German mathematician and physicist Emmy Noether was born, who is best known for her groundbreaking contributions to abstract algebra and theoretical physics. Albert Einstein called her the most important woman in the history of mathematics, as she revolutionized the theories of rings, fields, and algebras. “My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.” Letter to Helmut Hasse (1931)…
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Georg Cantor and the Beauty of Infinity

Georg Cantor and the Beauty of Infinity

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) Georg Cantor…
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Paul Bernays and the Unified Theory of Mathematics

Paul Bernays and the Unified Theory of Mathematics

On October 17, 1888, Swiss mathematician and logician Paul Isaac Bernays was born. Bernays made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator of David Hilbert. Bernays is known for his attempts to develop a unified theory of mathematics. Bernays was born the oldest of five children in London, UK, the son of Julius Bernays, a businessman, and his mother…
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Emil Artin and Algebraic Number Theory

Emil Artin and Algebraic Number Theory

On March 3, 1898, Austrian mathematician Emil Artin was born. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields. Emil Artin was born in Vienna to parents Emma Maria Artin, a soubrette on the operetta…
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Felix Klein and the Klein-Bottle

Felix Klein and the Klein-Bottle

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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Alfred Tarski and the Undefinability of Truth

Alfred Tarski and the Undefinability of Truth

On January 14, 1902, Polish-American mathematician and logician Alfred Tarski was born. A prolific author he is best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy. For my annual Semantic Web Technologies lecture series I always introduce my students to model-theoretic semantics as a means to enable a formal representation of meaning…
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Norbert Wiener and the Science of Cybernetics

Norbert Wiener and the Science of Cybernetics

On November 26, 1894, American mathematician Norbert Wiener was born. Wiener established the science of cybernetics, a term he coined, which is concerned with the common factors of control and communication in living organisms, automatic machines, and organizations. He attained international renown by formulating some of the most important contributions to mathematics in the 20th century. Wiener was born in Columbia, Missouri, the first child of Leo Wiener and Bertha Kahn, Jews…
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Karl Schwarzschild and the Event Horizon

Karl Schwarzschild and the Event Horizon

Karl Schwarzschild (1873 – 1916) On October 9, 1873, German physicist and astronomer Karl Schwarzschild was born. He provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished in 1915, the same year that Albert Einstein first introduced general relativity. The Schwarzschild solution leads to a derivation of the Schwarzschild radius, which is the size of…
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Giuseppe Peano and the Axiomatization of Mathematics

Giuseppe Peano and the Axiomatization of Mathematics

Giuseppe Peano (1858-1932) On August 27, 1858, Italian mathematician and philosopher Giuseppe Peano was born. He is he author of over 200 books and papers, and is considered the founder of mathematical logic and set theory. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and…
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