**Saunders Mac Lane** (4 August 1909, Taftville, Connecticut - 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. August 4 is the 216th day of the year in the Gregorian Calendar (217th in leap years), with 149 days remaining. ...
1909 (MCMIX) was a common year starting on Friday (see link for calendar). ...
A recent aerial photo shows the original mill building, river and dam at the top and some of the the company owned houses in a rectangular grid pattern. ...
Official language(s) English Capital Hartford Largest city Bridgeport Area - Total - Width - Length - % water - Latitude - Longitude Ranked 48th 14,371 kmÂ² 113 km 177 km 12. ...
April 14 is the 104th day of the year in the Gregorian calendar (105th in leap years). ...
2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...
This article is in need of attention from an expert on the subject. ...
Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ...
Samuel Eilenberg (September 30, 1913-January 30, 1998) was a Polish mathematician. ...
## Career
Mac Lane earned a BA from Yale University in 1930, and an MA from the University of Chicago in 1931. During this period, he published his first scientific paper, in physics and co-authored with Irving Langmuir. He attended the University of Göttingen, 1931-33, studying logic and mathematics under Paul Bernays, Emmy Noether, and Hermann Weyl. Göttingen's Mathematisches Institut awarded him the Ph.D. in 1934. While he was at Göttingen, Hitler came to power and implemented the anti-Semitic policies that destroyed Göttingen's excellence in mathematics, science, and philosophy. Yale University is a private university in New Haven, Connecticut. ...
The University of Chicago is a private research university located primarily in the Hyde Park neigborhood of Chicago, Illinois. ...
A black hole concept drawing by NASA. Physics (from the Greek, Ï†Ï…ÏƒÎ¹ÎºÏŒÏ‚ (physikos), natural, and Ï†ÏÏƒÎ¹Ï‚ (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ...
Irving Langmuir -- chemist and physicist Irving Langmuir (January 31, 1881 in Brooklyn, New York - August 16, 1957 in Woods Hole, Massachusetts) was an American chemist and physicist. ...
The Georg-August University of GÃ¶ttingen (Georg-August-UniversitÃ¤t GÃ¶ttingen, often called the Georgia Augusta) was founded in 1734 by George II, King of Great Britain and Elector of Hanover, and opened in 1737. ...
Paul Bernays (17 Oct 1888 - 18 Sept 1977) was a Swiss mathematician who played a crucial role in the development of mathematical logic in the 20th century. ...
Emmy Noether (born NÃ¶ther) (March 23, 1882 â€“ April 14, 1935) was one of the most talented mathematicians of the early 20th century, with penetrating insights that she used to develop elegant abstractions which she formalized beautifully. ...
Hermann Weyl Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ...
1934-38, Mac Lane held short term appointments at Harvard University, Cornell University, and the University of Chicago. He then held a tenure track appointment at Harvard, 1938-47, before spending the rest of his career at the University of Chicago. In 1944 and 1945, he also directed Columbia University's Applied Mathematics Group, which was involved in the war effort. Harvard University, incorporated as The President and Fellows of Harvard College, is a private university in Cambridge, Massachusetts, USA and a member of the Ivy League. ...
Cornell University is a research university whose main campus is located on the East Hill of Ithaca, New York, and whose two medical campuses are located in New York City and in Education City, Qatar, near Doha. ...
The University of Chicago is a private research university located primarily in the Hyde Park neigborhood of Chicago, Illinois. ...
Mac Lane served as vice president of the National Academy of Sciences and the American Philosophical Society, and as president of the American Mathematical Society. While presiding over the Mathematical Association of America in the 1950s, he initiated its activities aimed at improving the teaching of modern mathematics. He was a member of the National Science Board, 1974-80, advising the American government. In 1976, he led a delegation of mathematicians to China to study the conditions affecting mathematics there. Mac Lane was elected to the National Academy of Sciences in 1949, and received the National Medal of Science in 1989. President Harding and the National Academy of Sciences at the White House, Washington, DC, April 1921 The National Academy of Sciences (NAS) is a corporation in the United States whose members serve pro bono as advisers to the nation on science, engineering, and medicine. ...
The American Philosophical Society, founded in 1743 by founding father Benjamin Franklin, continues to operate to this day. ...
The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...
The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. ...
The logo of the National Science Foundation The National Science Foundation (NSF) is an independent United States government agency responsible for supporting basic science research mainly by providing research funding. ...
President Harding and the National Academy of Sciences at the White House, Washington, DC, April 1921 The National Academy of Sciences (NAS) is a corporation in the United States whose members serve pro bono as advisers to the nation on science, engineering, and medicine. ...
National Medal of Science The National Medal of Science, also called the Presidential Medal of Science, is an honor given by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social...
## Contributions After a thesis in mathematical logic, his early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. He started writing on group extensions in 1942, and began his epochal collaboration with Samuel Eilenberg in 1943, on what are now called Eilenberg–Mac Lane spaces K(*G*,*n*), having a single non-trivial homotopy group *G* in dimension *n*. This work opened the way to group cohomology in general. Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
Field theory is a branch of mathematics which studies the properties of fields. ...
Model Theory In logic and model theory, a valuation is a map from the set of variables of a first-order language to the universe of some interpretation of that language. ...
In abstract algebra, local rings are certain rings that are comparatively simple and serve to describe the local behavior of functions defined on varieties or manifolds. ...
In abstract algebra, an extension of a field K is a field L which contains K as a subfield. ...
In mathematics, for G a group or algebra over a field, or other algebraic structure, G′ is an extension of G if there is an exact sequence . See also central extension, extension problem, field extension. ...
This article is about the year. ...
Samuel Eilenberg (September 30, 1913-January 30, 1998) was a Polish mathematician. ...
1943 (MCMXLIII) is a common year starting on Friday. ...
In mathematics, an Eilenberg-MacLane space is a special kind of topological space that is important in many contexts in algebraic topology, including stage-by-stage constructions of spaces, computations of homotopy groups of spheres, and definition of cohomological operations. ...
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. ...
In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. ...
After introducing, via the Eilenberg–Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945. He is especially known for his work on coherence theorems. In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. ...
Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ...
Mac Lane had an exemplary devotion to writing approachable texts, starting with his very influential *A Survey of Modern Algebra*, coauthored in 1941 with Garrett Birkhoff. From then on, it was possible to teach elementary modern algebra to undergraduates using an English text. His *Categories for the Working Mathematician* remains the definitive introduction to category theory. Garrett Birkhoff (January 19, 1911 - November 22, 1996) was an American mathematician who was born in Princeton, New Jersey, USA and died on November 22,1996 inWater Mill, New York, USA. He is the son of the mathematician George David Birkhoff. ...
Categories for the Working Mathematician is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg. ...
He supervised the Ph.Ds of, among others, David Eisenbud, Irving Kaplanski, Anil Nerode, Robert Solovay, and John Thompson. David Eisenbud (born 8 April 1947) is an American mathematician. ...
Anil Nerode is a U.S. mathematician. ...
Robert M. Solovay is a set theorist who spent many years as a professor at UC Berkeley. ...
John Thompson is the name of: John Thompson (banker) (1802-1891), American banker John Thompson (politician) (1809-1890), US Congressman from New York [1] John Burton Thompson (1810-1874), Whig politician from Kentucky John A. Snowshoe Thompson (1827-1876), mail carrier across the Sierras John McCandless Thompson (1829-1903), US...
## Books by Mac Lane - 1997 (1941).
*A Survey of Modern Algebra* (with Garrett Birkhoff). A K Peters. - 1963.
*Homology*. - 1979 (1967).
*Algebra* (with Garrett Birkhoff). - 1998 (1972).
*Categories for the Working Mathematician*. - 1986.
*Mathematics, Form and Function*. An excellent survey of undergraduate mathematics, with a fair bit of philosophical material. - 1992.
*Sheaves in Geometry and Logic: A First Introduction to Topos Theory* ( with Ieke Moerdijk). - 2005. Autobiography.
Garrett Birkhoff (January 19, 1911 - November 22, 1996) was an American mathematician who was born in Princeton, New Jersey, USA and died on November 22,1996 inWater Mill, New York, USA. He is the son of the mathematician George David Birkhoff. ...
Garrett Birkhoff (January 19, 1911 - November 22, 1996) was an American mathematician who was born in Princeton, New Jersey, USA and died on November 22,1996 inWater Mill, New York, USA. He is the son of the mathematician George David Birkhoff. ...
Categories for the Working Mathematician is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg. ...
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