Colin McLarty
{{Short description|American logician (born 1951)}}
Colin McLarty (born July 12, 1951) is an American logician whose publications have ranged widely in philosophy and the foundations of mathematics, as well as in the history of science and of mathematics.
Research
= Category theory =
He has written papers about Saunders Mac Lane, one of the founders of category theory.
McLarty's Elementary Categories and Elementary Toposes describes category theory and topos theory at an elementary level.*Elementary Categories, Elementary Toposes.
McLarty worked on establishing that Fermat's Last Theorem can be proven in a setting with much weaker assumptions than the ones used in Wiles's proof of Fermat's Last Theorem, which makes use of involved category theoretical constructions.{{citation|title=Andrew Wiles' Proof of Fermat's Last Theorem, As Expected, Does Not Require a Large Cardinal Axiom: A Discussion of Colin McLarty's "The Large Structures of Grothendieck Founded on Finite-Order Arithmetic"|first=William H.|last=Wheeler|year=2023|arxiv=2309.07151}}
= History of Mathematics =
He is a member of the [http://www.grothendieckcircle.org/ 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.[https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/index.php website of the Grothendieck Circle].
McLarty has also written about the German algebraist Emmy Noether and her involvement with German political history.Journal History of Mathematics.
Positions
At Case Western Reserve University (CWRU), Colin McLarty is the Truman P. Handy Professor of Philosophy and the current Chair of the Philosophy Department.{{Cite web | url=https://philosophy.case.edu/about-us/letter-from-the-chair/ |title = Letter from the Chair – Department of Philosophy}}
At CWRU, he is also a professor of mathematics.
Bibliography
- {{cite book
| last = McLarty
| first = Colin
| title = Elementary Categories, Elementary Toposes
| publisher = Oxford University Press
| location = Oxford
| year = 1992
| url = https://books.google.com/books?id=V8cON1x39bIC
| isbn = 0-19-853392-6}}
- Colin McLarty, The Uses and Abuses of the History of Topos Theory, Br. J. Philos. Sci, 41 (1990) p 355. {{doi|10.1093/bjps/41.3.351}}
- Colin McLarty, [https://books.google.com/books?id=GywTDAAAQBAJ&pg=PA187 '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 and José Ferreirós), Oxford University Press (2006) p. 187–208.
- McLarty, Colin, 2005, "[https://archive.today/20130113090248/http://philmat.oxfordjournals.org/cgi/content/full/13/3/237 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, "[https://web.archive.org/web/20130704192551/http://www.cwru.edu/artsci/phil/BJPSMacLane.pdf 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.
- {{citation
| last = McLarty | first = Colin
| doi = 10.1017/s1755020319000340
| issue = 2
| journal = The Review of Symbolic Logic
| mr = 4092251
| pages = 296–325
| title = The large structures of Grothendieck founded on finite-order arithmetic
| volume = 13
| year = 2020
| zbl = 1484.03106| arxiv = 1102.1773
}}
See also
- "Abstract nonsense", a (usually ironic) term for category theory and category-theoretic arguments in homological algebra
- "Generalized abstract nonsense", an ironic and affectionate term for topos theory
- Other topos theorists (besides Saunders Mac Lane):
- Martin Hyland
- Peter Johnstone
- William Lawvere
References
External links
- [http://www.colinmclarty.com Personal website of Colin McLarty]
- [http://www.case.edu/artsci/phil/mclarty.html CWRU website of Colin McLarty]
- [http://www.grothendieckcircle.org/ Grothendieck Circle], which lists McLarty as a member. (A collection of mathematical and biographical information, photos, links about Alexander Grothendieck.)
- {{MathGenealogy|id=151858}}
{{authority control}}
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Category:Mathematical logicians
Category:American philosophers of mathematics
Category:American historians of mathematics
Category:American philosophers of science
Category:American historians of science
Category:20th-century American mathematicians
Category:21st-century American mathematicians
Category:20th-century American philosophers