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Bertrand Russel

mathematics
G. H. Hardy and the aesthetics of Mathematics

G. H. Hardy and the aesthetics of Mathematics

Harald Sack
On December 1, 1947, English mathematician G. H. Hardy passed away. Hardy is known for his achievements in number theory and mathematical analysis, but also for his 1940 essay on the aesthetics of mathematics, A Mathematician’s Apology, and for mentoring the brilliant Indian mathematician Srinivasa Ramanujan. “A mathematician … has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time…
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philosophy
The Philosophy of Ludwig Wittgenstein

The Philosophy of Ludwig Wittgenstein

Harald Sack
On April 26, 1889, Austrian-British philosopher Ludwig Wittgenstein was born. He worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considered one of the world‘s most famous philosophers. Wittgenstein‘s influence has been felt in nearly every field of the humanities and social sciences. “My work consists of two parts: of the one which is here, and of everything which I have not…
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mathematics
Gottlob Frege and the Formula Language of Pure Thinking

Gottlob Frege and the Formula Language of Pure Thinking

Harald Sack
On November 8, 1848, German mathematician, logician and philosopher Gottlob Frege was born. He is considered as one of the fathers of modern mathematical logic and has developed the Begriffsschrift, an approach to put classical philosophical logic into a formal mathematical language. While he was mainly ignored by the intellectual world when he published his writings, Giuseppe Peano [7] and Bertrand Russell [8] introduced his work to later generations of logicians and philosophers. Unless…
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philosophy
Reality according to Alexius Meinong

Reality according to Alexius Meinong

Harald Sack
On July 17, 1853 Austrian philosopher Alexius Meinong was born. He is best known for his contributions to ontology as well as to the philosophy of mind and theory of value. Famous is also his his belief in nonexistent objects. Meinong distinguished several levels of reality among objects and facts about them. The object theory of Alexius Meinong states fundamentally that every experienced act of perception is intentional. The experience is directed to the object…
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philosophy
Rudolf Carnap and the Logical Structure of the World

Rudolf Carnap and the Logical Structure of the World

Harald Sack
On May 18, 1891, German-born philosopher Rudolf Carnap was born. He was a major member of the Vienna Circle and an advocate of logical positivism and made significant contributions to logic and the philosophy of science. To avoid the ambiguities resulting from the use of ordinary language, he made a logical analysis of language. He believed in studying philosophical issues in artificial languages constructed under the rules of logic and mathematics, which…
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computer science
Norbert Wiener and the Science of Cybernetics

Norbert Wiener and the Science of Cybernetics

Harald Sack
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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mathematics
Giuseppe Peano and the Axiomatization of Mathematics

Giuseppe Peano and the Axiomatization of Mathematics

Harald Sack
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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mathematics
Frank P. Ramsey and the Ramsey Theory

Frank P. Ramsey and the Ramsey Theory

Harald Sack
On February 22, 1903, precocious British philosopher, mathematician and economist Frank Plumpton Ramsey was born. Although he died already at age 26, he had made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. “The first problem I…
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mathematics
David Hilbert’s 23 Fundamental Problems

David Hilbert’s 23 Fundamental Problems

Harald Sack
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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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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