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, structure, space, models, and change. History On ...

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 that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

, in particular

olog The theory of ologs is an attempt to provide a rigorous mathematical framework for knowledge representation, construction of scientific models and data storage using category theory, linguistic and graphical tools. Ologs were introduced in 2010 ...

s and operadic compositionality of

dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a p ...

. 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 in mathematics from

UC Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public university, public land-grant university, land-grant research university in Berkeley, California. Established in 1868 as the University of Californi ...

in 2007 under the supervision of

Peter Teichner Peter Teichner (born June 30, 1963 in Bratislava, Czechoslovakia) is a German mathematician and one of the directors of the Max Planck Institute for Mathematics in Bonn. His main areas of work are topology and geometry. Life In 1988, Peter Tei ...

and

Jacob Lurie Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the Institute for Advanced Study. Lurie is a 2014 MacArthur Fellow. Life When he was a student in the Science, Mathematics, and Computer Science ...

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

University of Oregon The University of Oregon (UO, U of O or Oregon) is a public research university in Eugene, Oregon. Founded in 1876, the institution is well known for its strong ties to the sports apparel and marketing firm Nike, Inc, and its co-founder, billion ...

and

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

Work

Spivak and Robert Kent developed a human-readable categorical system of knowledge representation called

s. 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 sci ...

. 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-American astrophysicist, who divides his time between research in computer simulations of dense stellar systems and broadly interdisciplinary collaborations, ranging from other fields in natural scien ...

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 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 an operad O, one defin ...

. 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 Discipline (academia), academic discipline in which methods from category theory are used to study other fields including but not limited to computer science, physics (in particular Categorical quantum mechanics, quant ...

research institute called Topos Institute, located in Berkeley, California. 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 op ...

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)