People

Al-Khwarizmi

  • محمد بن موسى خوارزمی

  • Muhammad ibn Musa al-Khwarizmi (c.780–850), Persia

  • Al-Khwarizmi is latinized as Algorithmi

  • founder of algebra

  • godfather of algorithm, "math as calculations"

  • mathematics, astronomy, geography

  • "completing the square" approach to linear and quadratic equations

  • "algorithm" and "algorism" derived from his name

  • the word "algebra" comes from the title of his book, specifically from the the word al-jabr meaning "completion" or "rejoining"

  • In the 12th century, Latin translations of his textbook on arithmetic, Algorithmo de Numero Indorum which codified the various Indian numerals, introduced the decimal positional number system to the Western world.

  • "The Compendious Book on Calculation by Completion and Balancing", translated into Latin by Robert of Chester in 1145, was used until the XVI century as the principal mathematical textbook of European universities.

  • revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities.

  • produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial.

  • made important contributions to trigonometry, producing accurate sine and cosine tables, and the first table of tangents.

Aristotle

  • Aristotle (384—322 BCE), (Stagira, Chalkidiki, North of) Greece

  • father of Western Philosophy, contributed to its lexicon, including problems and methods of inquiry thereby influencing almost all forms of knowledge

  • roots of formalized logic

Cantor

Georg Cantor, Germany

Church

Alonzo Church, USA https://en.wikipedia.org/wiki/Alonzo_Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, proving the undecidability of the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem. He also worked on philosophy of language.

Dedekind

Dedekind

Euclid

Euclid of Alexandria (325–265 BCE), Egypt. For Euclid, mathematics consists of proofs and constructions.

Frege

  • Friedrich Ludwig Gottlob Frege (1848-1925), Germany.

  • philosophy, logic, math

  • father of analytic philosophy, philosophy of language and math

  • widely ignored during his lifetime (re-intro by Peano and Russell)

  • contributions to development of modern logic with "Begriffsschrift"

  • foundations of mathematics with "Foundations of Arithmetic"

  • 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.

  • Frege invented a universal characteristic in 1879; he called it "Begriffsschrift". With it, Frege introduced propositional and predicate calculus.

Gauss

Carl Friedrich Gauß (1777-1855)

Gentzen

Gerhard Gentzen (1909–1945), Germany. Gentzen's system of natural deduction allows us to write proofs in a way that is mathematically natural. (he didn't went crazy but Nazi).

Godel

Godel incomp th

Hankel

Hermann Hankel (1839-1873), a student of Riemann

Riemann

Bernhard Riemann (1826-1866)

Klein

Felix Klein (1849-1925)

Grassmann

  • Hermann Günther Graßmann (1809-1877), German

  • challenged aritmetic prompting Peano's work

  • from the early 1830s, working on math foundations, discovered Linear Algebra

  • The Ausdehnungslehre (Theory of Extension) in 1844. "I realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to those that in geometry seem bound to space. I soon realized that I had come upon the domain of a new science of which geometry itself is only a special application."

  • His entirely abstract approach allowed him to consider new mathematical ideas such as n-dimensional spaces and noncommutative multiplication

  • "Every displacement of a system of m-th order can be represented as a sum of m displacements belonging to m given independent methods of evolution of the system, the sum being unique for each such set".

David Hilbert

David Hilbert (1862 - 1943) was a famous German mathematician, recognized as one of the most influential and universal mathematicians in his time.

Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spetral theory of operators and its application to integral equations, mathematical physics, and foundations of mathematics (particularly proof theory).

Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.

https://www.wikiwand.com/en/Hilbert%27s_problems

Christiaan Huygens

Christiaan Huygens (1629-1695) was a Dutch mathematician, astronomer, physicist. He exchanged correspondence with Leibniz.

Leibniz

Gotfried Wilhelm Leibniz (1646-1716), was a german polymath that invented calculus (independently from Newton). His stance of the mathematical proof was that arguing is futile and that all that needs to be done is to calculate it, embodied in his Calculemus! motto. The part of his "let's calculate it" motion was the idea of constructing a suitable universal language for writing math proofs.

In 1679, Leibniz wrote to Huygens (published in 1833): "I am still not satisfied with algebra. I believe that, so far as geometry is concerned, we still need another analysis which is distinctly geometrical or linear and which will express situation directly as algebra expresses magnitude. I believe that by this method one could treat mechanics almost like geometry, and one could even test the qualities of materials. I have no hope that we can get very far in physics until we have found such a method". Leibniz never managed to invent the method he envisioned that later became linear algebra.

Łukasiewicz

Jan Łukasiewicz (1878-1956), Poland Logician and philosopher born in Lemberg, a city in the Galician kingdom of Austria-Hungary (now Lviv, Ukraine). His work centred on philosophical logic, mathematical logic, and history of logic. He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Łukasiewicz of a revolutionary paradigm. The Łukasiewicz approach was reinvigorated in the early 1970s in a series of papers by John Corcoran and Timothy Smiley - which inform modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009. Łukasiewicz is regarded as one of the most important historians of logic. https://en.wikipedia.org/wiki/Jan_%C5%81ukasiewicz

Kleene

Stephen Cole Kleene https://en.wikipedia.org/wiki/Stephen_Cole_Kleene (January 5, 1909 – January 25, 1994) was an American mathematician.

One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science.

Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixpoint theorem. He also invented regular expressions, and made significant contributions to the foundations of mathematical intuitionism.

Newton

Isaac Newton. English. Calculus

Peano

  • Giuseppe Peano (1858–1932), Italian

  • published 200+ math papers and books

  • a founder of mathematical logic

  • contributed a lot to mathematical notation

  • key contributions to the rigorous and systematic treatment of induction

  • Peano axioms - standard axiomatization of naturals named in his honor

  • tought math at the University of Turin

Poincaré

Jules Henri Poincaré Jules Henri Poincaré (1854-1912), French mathematician, physicist, engineer, philosopher. "The Last Universalist" for he excelled in all fields of math as it existed during his lifetime. The Poincaré conjecture, the Poincaré group, three-body problem, chaos theory, topology, gravitational waves.

Post

Emil Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory.

Russell

Bertrand Russell (1872–1970), English. Phylosophy, Logic, Logicism. With Whitehead "Principia". Russell's paradox.

Turing

Alan Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general purpose computer. Turing is widely considered to be the father of theoretical computer science and artificial intelligence.

Whitehead

  • Alfred North Whitehead (1861-1947)

  • investigated systems of symbolic reasoning in his "Universal Algebra, Volume 1" of 1898

  • There never was never a second volume - after the International Congress in 1900, Whitehead and his student Russel started working on "Principia Mathematica" (1902-1913)

Möbius

August Ferdinand Möbius (1790-1868), German mathematician and astronomer

Minkowski

Hermann Minkowski (1864-1909)

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