David Hilbert

Karl Schwarzschild and the Event Horizon

Karl Schwarzschild and the Event Horizon

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 the event horizon of a…
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Hermann Minkowski and the four-dimensional Space-Time

Hermann Minkowski and the four-dimensional Space-Time

On June 22, 1864, German mathematician Hermann Minkowski was born. Minkowski developed the geometry of numbers and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity. But he is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein’s special theory of relativity can be understood geometrically as a theory of four-dimensional space–time, since known as the “Minkowski…
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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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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. “Scientific discovery consists in the interpretation for our own convenience of a system of existence which has…
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Eugene Wigner and the Structure of the Atomic Nucleus

Eugene Wigner and the Structure of the Atomic Nucleus

On November 17, 1902, Hungarian American theoretical physicist and mathematician Eugene Paul Wigner was born. He is best known for for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles for which he shared the 1963 Nobel Prize in Physics with Maria Goeppert. [4] “A possible explanation of the physicist’s use of mathematics to formulate his laws of nature…
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Giuseppe Peano and the Axiomatization of Mathematics

Giuseppe Peano and the Axiomatization of Mathematics

On August 27, 1858, Italian mathematician and philosopher Giuseppe Peano was born. He is the 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 completeness of number…
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Statistical Mechanics with Paul Ehrenfest

Statistical Mechanics with Paul Ehrenfest

On January 18, 1881, Austrian and Dutch theoretical physicist Paul Ehrenfest was born. Ehrenfest made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. “Einstein, my upset stomach hates your theory — it almost hates you yourself ! How am I to provide for my students ? What am I to answer to the philosophers ?” –…
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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 Semantic Web Technologies lecture series I always introduce my students to model-theoretic semantics as means to enable a formal representation of meaning for languages. I…
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David Hilbert’s 23 Fundamental Problems

David Hilbert’s 23 Fundamental Problems

On August 8, 1900 David Hilbert, probably the greatest mathematician of his age,  gave a speech at the Paris conference of the International Congress of Mathematicians, at the Sorbonne, where he presented 10 mathematical Problems (out of a list of 23), all unsolved at the time, and several of them were very influential for 20th century mathematics. “Who of us would not be glad to lift the veil behind which the future…
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Every Set can be Well Ordered – Ernst Zermelo

Every Set can be Well Ordered – Ernst Zermelo

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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