Sextus Empiricus's three known works are the Outlines of Pyrrhonism ( Πυῤῥώνειοι ὑποτύπωσεις or Pyrrhōneioi hypotypōseis, thus commonly abbreviated PH ), and two distinct works preserved under the same title, Against the Mathematicians ( Adversus Mathematicos ), one of which is probably incomplete.

Through Bugaev's star student, Dmitri Egorov, many famous Russian mathematicians, such as Andrei Kolmogorov and Nikolai Luzin, directly " descend " from Bugaev — and thus from the Prince of Mathematicians, Carl Friedrich Gauss.

Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique ( EGA ) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time.

He went on to plan and execute a major foundational programme for rebuilding the foundations of algebraic geometry, which were then in a state of flux and under discussion in Claude Chevalley's seminar ; he outlined his programme in his talk at the 1958 International Congress of Mathematicians.

Mathematicians do research in fields such as logic, set theory, category theory, abstract algebra, number theory, analysis, geometry, topology, dynamical systems, combinatorics, game theory, information theory, numerical analysis, optimization, computation, probability and statistics.

Mathematicians now know of many types of projective geometry such as complex Minkowski space that might describe the layout of things in perception ( see Peters ( 2000 )) and it has also emerged that parts of the brain contain patterns of electrical activity that correspond closely to the layout of the retinal image ( this is known as retinotopy ).

He was the president of the geometry section at the International Congress of Mathematicians in Toronto ( 1924 ), Zürich ( 1932 ), and Oslo ( 1936 ).

In an address to the 1994 International Congress of Mathematicians in Zurich, speculated that mirror symmetry for a pair of Calabi – Yau manifolds X and Y could be explained as an equivalence of a triangulated category constructed from the algebraic geometry of X ( the derived category of coherent sheaves on X ) and another triangulated category constructed from the symplectic geometry of Y ( the derived Fukaya category ).

The Clifford algebra Cℓ ( V, Q ) is the " freest " algebra generated by V subject to the condition < ref > Mathematicians who work with real Clifford algebras and prefer positive definite quadratic forms ( especially those working in index theory ) sometimes use a different choice of sign in the fundamental Clifford identity.

The Jalali calendar was introduced by Omar Khayyám alongside other Mathematicians and Astronomers in Nishapur, today it is one of the oldest calendars in the world as well as the most accurate solar calendar in use today.

Mathematicians, scientists, and engineers continued to use infinitesimals to produce correct results.

Mathematicians and scientists use very large and small numbers to describe physical quantities, and have created even larger and smaller numbers for theoretical purposes.

In 2006, the International Mathematical Union decided at the 25th International Congress of Mathematicians in Madrid, Spain to use a new logo based on the Borromean rings.

Mathematicians typically use " polygon " to refer only to the shape made up by the line segments, not the enclosed region, however some may use " polygon " to refer to a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments ( i. e., by a closed polygonal chain )..

Mathematicians today tend to use script letters such as instead, and replace Green's modular arithmetic-style notation with the infix style used here.

Already in 1900, at the International Congress of Mathematicians at Paris in he said: " In mathematics there is no ignorabimus.

He did not abandon mathematics completely, however, lecturing on the paradoxes of set theory ( Burali-Forti paradox, Cantor's paradox, and Russell's paradox ) to a meeting of the Deutsche Mathematiker – Vereinigung in 1903, and attending the International Congress of Mathematicians at Heidelberg in 1904.

Rolf Nevanlinna served as President of the International Mathematical Union, IMU, in 1959 – 63 and as President of the International Congress of Mathematicians, ICM, in 1962.

In classical mechanics, he is best known for the Kolmogorov – Arnold – Moser theorem ( first presented in 1954 at the International Congress of Mathematicians ).

Mathematicians such as Karl Weierstrass ( 1815 – 1897 ) discovered pathological functions such as continuous, nowhere-differentiable functions.

* Sergei Lvovich Sobolev., in: Russian Mathematicians in the 20th Century ( Yakov Sinai, editor ), pp. 381 – 382.

He was Instructor of Mathematics at Harvard University, 1930 – 31, 1933 – 35 ; NRC Fellow, Mathematics, 1931 – 33 ; Assistant Professor, 1935 – 40 ; Associate Professor, 1940 – 46, Professor, 1946 – 52 ; Professor Instructor, Institute for Advanced Study, Princeton University, 1952 – 77 ; Professor Emeritus, 1977 – 89 ; Chairman of the Mathematics Panel, National Science Foundation, 1953 – 56 ; Exchange Professor, Collège de France, 1957 ; Memorial Committee, Support of Research in Mathematical Sciences, National Research Council, 1966 – 67 ; President, International Commission of Mathematical Instruction, 1979 – 82 ; Research Mathematicians, National Defense Research Committee, 1943 – 45 ; Construction of the School of Mathematics.

* Maurice Mashaal ( 2006 ), Bourbaki: A Secret Society of Mathematicians, American Mathematical Society, ISBN 0-8218-3967-5, Chapter 10: New Math in the Classroom, pp 134 – 45.

* Marian Rejewski, " How the Polish Mathematicians Broke Enigma ," Appendix D to Władysław Kozaczuk, Enigma, 1984, pp. 246 – 71.

* William Goldman, " Locally homogeneous geometric manifolds ", Proceedings of the 2010 International Congress of Mathematicians, Hyderabad, In-dia ( 2010 ), 717 – 744, Hindustan Book Agency, New Delhi, India

* Maurice Mashaal ( 2006 ), Bourbaki: A Secret Society of Mathematicians, American Mathematical Society, ISBN 0-8218-3967-5, see pages 140 – 1 for Lichnerowicz Commission.

* A. Padoa ( 1900 ) " Un Nouveau Système de Définitions pour la Géométrie Euclidienne ", Proceedings of the International Congress of Mathematicians, pages 353 – 63.

; Mathematical logic and foundations, including set theory: Mathematicians have always worked with logic and symbols, but for centuries the underlying laws of logic were taken for granted, and never expressed symbolically.

Dynkin's one hour talk at the 1962 International Congress of Mathematicians in Stockholm, was delivered by Kolmogorov, since prior to his emigration, Dynkin was never permitted to travel to the West.

Usually, their purpose is to promote students ' scientific achievements by organizing lecture sessions, science excursions, and international student conferences, such as the International Workshop for Young Mathematicians, which is organized by the Zaremba Association of Mathematicians.

Mathematicians, such as Edmond Halley, developed the life table as the basis for life insurance mathematics.

Mathematicians and philosophers, such as Bertrand Russell, Alfred North Whitehead, and Baruch Spinoza, have attempted to create their own foundational " Elements " for their respective disciplines, by adopting the axiomatized deductive structures that Euclid's work introduced.

He is highly respected among Indian Mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle ; rhombus ; circle and semicircle.

" Mathematicians, astronomers, chemical scientists continually disprove and reject the conclusions of the ancients ; nothing is fixed, nothing final ; everything is continually changing because human reason is progressing along new roads of investigation and arriving at new conclusions every day.

Mathematicians had vainly attempted to solve all of these problems since the time of the ancient Greeks.

Note that none of these titles except Against the Mathematicians and Outlines of Pyrrhonism, are found in the manuscripts.

His most recent book, Physics for Mathematicians: Mechanics I, which contains the material that these lectures stemmed from and more, was published on December 6, 2010.

Mathematicians, particularly those who were also astronomers, were looking for an easier way, and trigonometry was one of the most advanced and familiar fields to these people.

Mathematicians of this " school " met for long hours at the Scottish Café, where the problems they discussed were collected in the famous Scottish Book, which is a thick notebook provided by Banach's wife.

Tarski's lecture at the 1950 International Congress of Mathematicians in Cambridge ushered in a new period in which model-theoretic aspects were developed, mainly by Tarski himself, as well as C. C.

There were 23 problems on David Hilbert's famous list of unsolved mathematical problems, presented to the International Congress of Mathematicians in Paris in 1900.

To calculate derivatives, one needs to have local coordinate systems defined consistently in X. Mathematicians were surprised in 1956 when John Milnor showed that consistent coordinate systems could be set up on the 7-sphere in two different ways that were equivalent in the continuous sense, but not in the differentiable sense.

The ideas were also advanced by Alessandro Padoa at both that Congress and the International Congress of Mathematicians also held in Paris that year.