David Isaac Spivak is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and senior scientist at the Topos Institute. He has worked on applications of

category theory Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...

, in particular ologs and operadic compositionality of

dynamical systems In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

. He authored and coauthored the introductory texts on category theory and its applications, ''Category Theory for the Sciences'' and ''An Invitation to Applied Category Theory''.

Early life and education

Spivak received his

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in mathematics from

UC Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a public land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkele ...

in 2007 under the supervision of Peter Teichner and

Jacob Lurie Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the Institute for Advanced Study. In 2014, Lurie received a MacArthur Fellowship. Lurie's research interests are algebraic geometry, topology, and ...

. His thesis was on derived manifolds, Spivak worked as a

postdoc A postdoctoral fellow, postdoctoral researcher, or simply postdoc, is a person professionally conducting research after the completion of their doctoral studies (typically a PhD). Postdocs most commonly, but not always, have a temporary academ ...

at the

University of Oregon The University of Oregon (UO, U of O or Oregon) is a Public university, public research university in Eugene, Oregon, United States. Founded in 1876, the university is organized into nine colleges and schools and offers 420 undergraduate and gra ...

and

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

Work

Spivak and Robert Kent developed a human-readable categorical system of knowledge representation called ologs. These were applied, in a series of collaborations with the materials scientist Markus Buehler, to different problems in that materials science. Ologs have been also used by researchers at

NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...

. The goal of ologs, and of Spivak's book, was to show that category theory can be made relatively easy and thus be understood by a wider audience.

Piet Hut Piet Hut (born September 26, 1952) is a Dutch astrophysicist and interdisciplinary researcher known for his contributions to both scientific research and cross-disciplinary scholarship. He served as the head of the interdisciplinary studies pro ...

endorsed the book saying, "This is the first, and so far the only, book to make category theory accessible to non-mathematicians." Spivak has also studied dynamical systems and

operads In mathematics, an operad is a structure that consists of abstract Operation (mathematics), operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given ...

, originating the operadic approach to wiring diagram syntax. His unpublished wor
"Metric realization of fuzzy simplicial sets"
wa
cited
by the authors of UMAP as inspirational for that work. Spivak and Brendan Fong wrote a book that summarizes the developments in applied category theory for a wide audience, and started a nonprofit

applied category theory Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer science, physics (in particular quantum mechanics), natural language processing, control th ...

research institute called Topos Institute, located in Berkeley, California. The two, together with Rémy Tuyeras, wrote the first article using category theory to understand the structure of

deep learning Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience a ...

, called "Backprop as functor". Spivak is an editor of a

diamond open access Diamond open access refers to academic texts (such as monographs, edited collections, and journal articles) published/distributed/preserved with no fees to either reader or author. Alternative labels include platinum open access, non-commercial o ...

journal, ''Compositionality''.Editorial Board
''Compositionality''. Accessed August 16, 2019.

Bibliography

* Spivak
''Category Theory for the Sciences''
MIT Press, 2014 * Schultz & Spivak. ''Temporal Type Theory: a Topos-Theoretic Approach to Systems and Behavior'', Springer-Verlag, 2019, * Fong & Spivak. ''An Invitation to Applied Category Theory: Seven Sketches in Compositionality'', Cambridge University Press, 2019,

References

External links

Spivak's former MIT Homepage
{{DEFAULTSORT:Spivak, David Living people American textbook writers American male non-fiction writers 21st-century American mathematicians Category theorists Massachusetts Institute of Technology people Year of birth missing (living people)