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Colin McLarty (born July 12, 1951) is an American
Grothendieck Circle
which provides on-line and open access to many writings about the mathematician Alexandre Grothendieck, who revolutionized Banach-space theory and algebraic geometry and whose life has fascinated many biographers and mathematical scientists. McLarty has also written about the German
'Emmy Noether’s ‘Set Theoretic’ Topology: From Dedekind to the rise of functors'
in ''The Architecture of Modern Mathematics: Essays in history and philosophy'' (edited by
Saunders Mac Lane (1909–2005): His Mathematical Life and Philosophical Works
" ''Philosophia Mathematica 13'': 237–51. With selected bibliography emphasizing Mac Lane's philosophical writings. * --------, 2007,
The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics
", ''British Journal for the Philosophy of Science 58(1)'': 77–112.
Personal website of Colin McLarty
Grothendieck Circle
which lists McLarty as a member. (A collection of mathematical and biographical information, photos, links about Alexander Grothendieck.) * {{DEFAULTSORT:McLarty, Colin Category theorists Mathematical logicians American logicians Philosophers of mathematics American historians of mathematics Philosophers of science Historians of science Intellectual historians Algebraists Algebraic geometers 20th-century American mathematicians 21st-century American mathematicians 20th-century American philosophers Living people 21st-century American philosophers 1951 births
Colin McLarty (born July 12, 1951) is an American logician
Logic is the study of correct reasoning. It includes both Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...
whose publications have ranged widely in philosophy and the foundations of mathematics, as well as in the history of science
The history of science covers the development of science from ancient times to the present. It encompasses all three major branches of science: natural, social, and formal.
Science's earliest roots can be traced to Ancient Egypt and Meso ...
and of mathematics.
Research
Category theory
He has written papers aboutSaunders Mac Lane
Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.
Early life and education
Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftvill ...
, one of the founders of category theory.
McLarty's ''Elementary Categories and Elementary Toposes'' describes category theory and topos theory
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion ...
at an elementary level.
McLarty worked on establishing that Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have bee ...
can be proven in a setting with much weaker assumptions than the ones used in Wiles' proof, which makes use of involved category theoretical constructions.
History of Mathematics
He is a member of thGrothendieck Circle
which provides on-line and open access to many writings about the mathematician Alexandre Grothendieck, who revolutionized Banach-space theory and algebraic geometry and whose life has fascinated many biographers and mathematical scientists. McLarty has also written about the German
algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
ist Emmy Noether
Amalie Emmy Noether Emmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noeth ...
and her involvement with German political history.
Positions
AtCase Western Reserve University
Case Western Reserve University (CWRU) is a private research university in Cleveland, Ohio. Case Western Reserve was established in 1967, when Western Reserve University, founded in 1826 and named for its location in the Connecticut Western Res ...
(CWRU), Colin McLarty is the Truman P. Handy Professor of Philosophy and the current Chair of the Philosophy Department.
At CWRU, he is also a professor of mathematics.
Bibliography
* * Colin McLarty, ''The Uses and Abuses of the History of Topos Theory'', ''Br. J. Philos. Sci'', 41 (1990) p 355. * Colin McLarty'Emmy Noether’s ‘Set Theoretic’ Topology: From Dedekind to the rise of functors'
in ''The Architecture of Modern Mathematics: Essays in history and philosophy'' (edited by
Jeremy Gray
Jeremy John Gray (born 25 April 1947) is an English mathematician primarily interested in the history of mathematics.
Biography
Gray studied mathematics at Oxford University from 1966 to 1969, and then at Warwick University, obtaining his P ...
and José Ferreirós), Oxford University Press (2006) p. 187–208.
* McLarty, Colin, 2005,Saunders Mac Lane (1909–2005): His Mathematical Life and Philosophical Works
" ''Philosophia Mathematica 13'': 237–51. With selected bibliography emphasizing Mac Lane's philosophical writings. * --------, 2007,
The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics
", ''British Journal for the Philosophy of Science 58(1)'': 77–112.
See also
* "Abstract nonsense In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra. More generally, "abs ...
", a (usually ironic) term for category theory and category-theoretic arguments in homological algebra
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology ...
* " Generalized abstract nonsense", an ironic and affectionate term for topos theory
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion ...
* Other topos theorists (besides Saunders Mac Lane
Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.
Early life and education
Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftvill ...
):
** Martin Hyland
(John) Martin Elliott Hyland is professor of mathematical logic at the University of Cambridge and a fellow of King's College, Cambridge. His interests include mathematical logic, category theory, and theoretical computer science.
Education
H ...
** Peter Johnstone
** William Lawvere
Francis William Lawvere (; born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
Biography
Lawvere studied continuum mechanics as an undergraduate with Clifford Truesdell ...
References
External links
Personal website of Colin McLarty
Grothendieck Circle
which lists McLarty as a member. (A collection of mathematical and biographical information, photos, links about Alexander Grothendieck.) * {{DEFAULTSORT:McLarty, Colin Category theorists Mathematical logicians American logicians Philosophers of mathematics American historians of mathematics Philosophers of science Historians of science Intellectual historians Algebraists Algebraic geometers 20th-century American mathematicians 21st-century American mathematicians 20th-century American philosophers Living people 21st-century American philosophers 1951 births