Colin Mclarty
Biographic Data
| ID | 1127380 |
|---|---|
| NAME | Colin Mclarty |
| GIVEN NAMES | Colin |
| FAMILY NAME | Mclarty |
| SIGNATURE | MCLARTY C |
| AFFILIATIONS | Case Western Reserve University |
| ORCID | 0000-0002-3181-7537 |
| VERIFIED | Yes |
| TOTAL WORKS | 8 |
| TOTAL CITATIONS | 3 |
| AUTHOR COUNT | 8 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1990 |
| LATEST PUBLICATION YEAR | 2024 |
| H-INDEX | 1 |
Structuralism in differential equations
Structuralism in philosophy of mathematics has largely focused on arithmetic, algebra, and basic analysis. Some have doubted whether distinctively structural working methods have any impact in other fields such as differential equations. We show narrowly construed structuralism as offered by Benacerraf has no practical role in differential equations. But Dedekind’s approach to the continuum already did not fit that narrow sense, and little of mat…
Como Grothendieck simplificou a geometria algébrica
Alexandre Grothendieck (1922-2014) foi um dos maiores matemáticos do século 20 e um dos mais atípicos. Nascido na Alemanha a um pai anarquista de origem russa, sua infância foi marcada pela militância política dos seus pais, assim passando por revoluções, guerras e sobrevivência. Descoberto por sua precocidade matemática por Henri Cartan, Grothendieck fez seu doutorado sob orientação de Laurent Schwartz e Jean Dieudonné. As principais contribuiçõ…
Hilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics
This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the cha…
What Structuralism Achieves
The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics
While Saunders Mac Lane studied for his D.Phil in Göttingen, he heard David Hilbert's weekly lectures on philosophy, talked philosophy with Hermann Weyl, and studied it with Moritz Geiger. Their philosophies and Emmy Noether's algebra all influenced his conception of category theory, which has become the working structure theory of mathematics. His practice has constantly affirmed that a proper large-scale organization for mathematics is the most…
Poor Taste as a Bright Character Trait: Emmy Noether and the Independent Social Democratic Party
The creation of algebraic topology required “all the energy and the temperament of Emmy Noether” according to topologists Paul Alexandroff and Heinz Hopf. Alexandroff stressed Noether's radical pro-Russian politics, which her colleagues found in “poor taste”; yet he found “a bright trait of character.” She joined the Independent Social Democrats (USPD) in 1919. They were tiny in Göttingen until that year when their vote soared as they called for …
La notion de nombre chez Dedekind, Cantor, Frege: Theories, conceptions, et philosophie. Jean-Pierre Belna
The Uses and Abuses of the History of Topos Theory
The view that toposes originated as generalized set theory is a figment of set theoretically educated common sense. This false history obstructs understanding of category theory and especially of categorical foundations for mathematics. Problems in geometry, topology, and related algebra led to categories and toposes. Elementary toposes arose when Lawvere's interest in the foundations of physics and Tierney's in the foundations of topology led bo…
The Uses and Abuses of the History of Topos Theory
The view that toposes originated as generalized set theory is a figment of set theoretically educated common sense. This false history obstructs understanding of category theory and especially of categorical foundations for mathematics. Problems in geometry, topology, and related algebra led to categories and toposes. Elementary toposes arose when Lawvere's interest in the foundations of physics and Tierney's in the foundations of topology led bo…
The Uses and Abuses of the History of Topos Theory
The view that toposes originated as generalized set theory is a figment of set theoretically educated common sense. This false history obstructs understanding of category theory and especially of categorical foundations for mathematics. Problems in geometry, topology, and related algebra led to categories and toposes. Elementary toposes arose when Lawvere's interest in the foundations of physics and Tierney's in the foundations of topology led bo…
La notion de nombre chez Dedekind, Cantor, Frege: Theories, conceptions, et philosophie. Jean-Pierre Belna
Poor Taste as a Bright Character Trait: Emmy Noether and the Independent Social Democratic Party
The creation of algebraic topology required “all the energy and the temperament of Emmy Noether” according to topologists Paul Alexandroff and Heinz Hopf. Alexandroff stressed Noether's radical pro-Russian politics, which her colleagues found in “poor taste”; yet he found “a bright trait of character.” She joined the Independent Social Democrats (USPD) in 1919. They were tiny in Göttingen until that year when their vote soared as they called for …
The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics
While Saunders Mac Lane studied for his D.Phil in Göttingen, he heard David Hilbert's weekly lectures on philosophy, talked philosophy with Hermann Weyl, and studied it with Moritz Geiger. Their philosophies and Emmy Noether's algebra all influenced his conception of category theory, which has become the working structure theory of mathematics. His practice has constantly affirmed that a proper large-scale organization for mathematics is the most…
What Structuralism Achieves
Hilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics
This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the cha…
Como Grothendieck simplificou a geometria algébrica
Alexandre Grothendieck (1922-2014) foi um dos maiores matemáticos do século 20 e um dos mais atípicos. Nascido na Alemanha a um pai anarquista de origem russa, sua infância foi marcada pela militância política dos seus pais, assim passando por revoluções, guerras e sobrevivência. Descoberto por sua precocidade matemática por Henri Cartan, Grothendieck fez seu doutorado sob orientação de Laurent Schwartz e Jean Dieudonné. As principais contribuiçõ…
Structuralism in differential equations
Structuralism in philosophy of mathematics has largely focused on arithmetic, algebra, and basic analysis. Some have doubted whether distinctively structural working methods have any impact in other fields such as differential equations. We show narrowly construed structuralism as offered by Benacerraf has no practical role in differential equations. But Dedekind’s approach to the continuum already did not fit that narrow sense, and little of mat…
Mathematics (6 works) · Philosophy (6 works) · Epistemology (5 works) · History and Theory of Mathematics (5 works) · Philosophy, Science, and History (3 works) · Art (2 works) · Humanities (2 works) · Philosophy (2 works) · Philosophy and History of Science (2 works) · Physics (2 works)