David Hilbert

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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The Beautiful Mind of John Forbes Nash

The Beautiful Mind of John Forbes Nash

On June 13, 1928, American mathematician John Forbes Nash Jr. was born. Nash made fundamental contributions to game theory, differential geometry, and the study of partial differential equations. His work has provided insight into the factors that govern chance and decision-making inside complex systems found in everyday life. John Nash is the only person to be awarded both the Nobel Memorial Prize in Economic Sciences and the Abel Prize. “You don’t have…
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It’s Computable – thanks to Alonzo Church

It’s Computable – thanks to Alonzo Church

You know, the fact that you can read your email on a cell phone as well as on your desktop computer or almost any other computer connected to the internet, in principle is possible thanks to mathematician Alonzo Church, who gave the proof (together with Alan Turing) that everything that is computable on the simple model of a Turing Machine, also is computable with any other ‘computer model’.[8] Academic Career Alonzo Church…
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Churchill’s Best Horse in the Barn – Alan Turing, Codebreaker and AI Pioneer

Churchill’s Best Horse in the Barn – Alan Turing, Codebreaker and AI Pioneer

On June 23, 1912, English computer scientist, mathematician, logician, and cryptanalyst,Alan Mathison Turing was born. Outside the world of computer science or mathematics the name of probably the most influential figure and in some sense the father of all computing technology Alan Turing is hardly known. But it was him, who laid the foundations of the theory of computing. Already in the 1930s, when no digital electronic computer had ever been built,…
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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 mind…
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Kolmogorov and the Foundations of Probability Theory

Kolmogorov and the Foundations of Probability Theory

On April 25, 1903, Soviet mathematician Andrey Nikolaevich Kolmogorov was born. He was one of the most important mathematicians of the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity. “The epistemological value of probability theory is based on the fact that chance phenomena, considered collectively and on a grand scale, create non-random regularity.” – Andrey Kolmogorov, Limit Distributions…
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