1. Francis William Lawvere was an American mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
23 Facts About William Lawvere
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William Lawvere studied continuum mechanics and kinetic theory as an undergraduate with Clifford Truesdell.
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William Lawvere learned of category theory while teaching a course on functional analysis for Truesdell, specifically from a problem in John L Kelley's textbook General Topology.
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William Lawvere found it a promising framework for simple rigorous axioms for the physical ideas of Truesdell and Walter Noll.
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William Lawvere spent a year in Berkeley as an informal student of model theory and set theory, following lectures by Alfred Tarski and Dana Scott.
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William Lawvere tried to use the then current axiomatic set theory but found it unworkable for undergraduates, so he instead developed the first axioms for the more relevant composition of mappings of sets.
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William Lawvere later streamlined those axioms into the Elementary Theory of the Category of Sets, which became an ingredient of elementary topos theory.
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William Lawvere's dissertation introduced the category of categories as a framework for the semantics of algebraic theories.
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William Lawvere then taught at the University of Chicago, working with Mac Lane, and at the City University of New York Graduate Center, working with Alex Heller.
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William Lawvere had pointed out that a Grothendieck topology can be entirely described as an endomorphism of the subobject representor, and Tierney showed that the conditions it needs to satisfy are just idempotence and the preservation of finite intersections.
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William Lawvere was controversial for his political opinions, for example, his opposition to the 1970 use of the War Measures Act, and for teaching the history of mathematics without permission.
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William Lawvere ran a seminar in Perugia, Italy and especially worked on various kinds of enriched category.
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William Lawvere continued to work on his 50-year quest for a rigorous flexible base for physical ideas, free of unnecessary analytic complications.
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William Lawvere was professor emeritus of mathematics and adjunct professor emeritus of philosophy at Buffalo.
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William Lawvere explains that he began applying Grothendieck topos theory, learned from Gabriel, to simplify the foundations of continuum mechanics, inspired by Truesdell's teachings, Noll's axiomatizations, and his own efforts in 1958 to categorize topological dynamics.
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William Lawvere acknowledges the skepticism around this idea but emphasizes its fruitful outcomes over the past 300 years.
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William Lawvere believes that recent developments have positioned mathematicians to make this program more explicit, focusing on how continuum physics can be mathematically constructed from "simple ingredients".
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William Lawvere explains that his interest stemmed from his earlier studies in physics, particularly the foundations of continuum physics as inspired by Truesdell, Noll, and others.
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William Lawvere realized that further work on the notion of topos was necessary to achieve his goals.
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William Lawvere has proposed formalizations in category theory, categorical logic and topos theory of concepts which are motivated from philosophy, notably in Georg Hegel's Science of Logic.
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William Lawvere argues that these advancements will provide precise mathematical models for age-old philosophical distinctions, such as general versus particular, objective versus subjective, and being versus becoming.
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William Lawvere emphasizes that mathematicians need to engage with these philosophical questions to make mathematics and other sciences more accessible and useful.
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William Lawvere saw his political commitments as related to his mathematical work in sometimes surprising and unexpected ways: for instance, here's a passage from Quantifiers and Sheaves :.