Science and math

Gottlob Frege

Friedrich Ludwig Gottlob Frege (/ˈfreɪɡə/; German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.

His contributions include the development of modern logic in the Begriffsschrift and work in the foundations of mathematics. His book the Foundations of Arithmetic is the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical papers “On Sense and Reference” and “The Thought” are also widely cited. The former argues for two different types of meaning and descriptivism. In Foundations and “The Thought”, Frege argues for Platonism against psychologism or formalism, concerning numbers and propositions respectively. Russell’s paradox undermined the logicist project by showing Frege’s Basic Law V in the Foundations to be false.

https://en.wikipedia.org/wiki/Gottlob_Frege

Gottlob Frege was last modified: August 20th, 2023 by Jovan Stosic

Hippasus

Hippasus of Metapontum (/ˈhɪpəsəs/; Greek: Ἵππασος ὁ Μεταποντῖνος, Híppasos; c. 530 – c. 450 BC) was a Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this. However, the few ancient sources which describe this story either do not mention Hippasus by name (e.g. Pappus) or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere.[citation needed] The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer.

https://en.wikipedia.org/wiki/Hippasus

Hippasus was last modified: August 20th, 2023 by Jovan Stosic

Leopold Kronecker

Leopold Kronecker (German: [ˈkʁoːnɛkɐ]; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic. He criticized Georg Cantor’s work on set theory, and was quoted by Weber (1893) as having said, “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk” (“God made the integers, all else is the work of man”). Kronecker was a student and lifelong friend of Ernst Kummer.

https://en.wikipedia.org/wiki/Leopold_Kronecker

Leopold Kronecker was last modified: August 20th, 2023 by Jovan Stosic

Alonzo Church

Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematiciancomputer scientistlogician, and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem (“decision problem”), the Frege–Church ontology, and the Church–Rosser theorem. He also worked on philosophy of language (see e.g. Church 1970). Alongside his doctoral student Alan Turing, Church is considered one of the founders of computer science

https://en.wikipedia.org/wiki/Alonzo_Church

Alonzo Church was last modified: August 19th, 2023 by Jovan Stosic

Herman Goldstine

Herman Heine Goldstine (September 13, 1913 – June 16, 2004) was a mathematician and computer scientist, who worked as the director of the IAS machine at Princeton University‘s Institute for Advanced Study and helped to develop ENIAC, the first of the modern electronic digital computers. He subsequently worked for many years at IBM as an IBM Fellow, the company’s most prestigious technical position.

https://en.wikipedia.org/wiki/Herman_Goldstine

Herman Goldstine was last modified: August 19th, 2023 by Jovan Stosic

What is Russell’s paradox?

Russell’s paradox is based on examples like this: Consider a group of barbers who shave only those men who do not shave themselves. Suppose there is a barber in this collection who does not shave himself; then by the definition of the collection, he must shave himself. But no barber in the collection can shave himself. (If so, he would be a man who does shave men who shave themselves.)

https://www.scientificamerican.com/article/what-is-russells-paradox/

What is Russell’s paradox? was last modified: August 19th, 2023 by Jovan Stosic