Anil Nerode

{{short description|American mathematician}}

File:Anil Nerode June 2007.jpg

Anil Nerode (born 1932) is an American mathematician, known for his work in mathematical logic and for his many-decades tenure as a professor at Cornell University.

He received his undergraduate education and a Ph.D. in mathematics from the University of Chicago, the latter under the directions of Saunders Mac Lane. He enrolled in the Hutchins College at the University of Chicago in 1947 at the age of 15, and received his Ph.D. in 1956. His Ph.D. thesis was on an algebraic abstract formulation of substitution in many-sorted free algebras and its relation to equational definitions of the partial recursive functions.For a description of Nerode's mathematical work until 1992, see "The Work of Anil Nerode: A Retrospective" co-authored by Nerode's former student J. B. Remmel and J.N. Crossley, which appears in the 1992 Festschrift volume [https://books.google.com/books?id=5kX6A5eFxZ8C Logical Methods: In Honor of Anil Nerode's Sixtieth Birthday] (J. N. Crossley, Jeffrey B. Remmel, Richard A. Shore, and Moss E. Sweedler, eds., Birkhäuser, 1993, {{ISBN|0-8176-3690-0}}).

While in graduate school, beginning in 1954, he worked at Professor Walter Bartky's Institute for Air Weapons Research, which did classified work for the US Air Force. He continued to work there following the completion of his Ph.D., from 1956 to 1957. In the summer of 1957 he attended the Cornell NSF Summer 1957 Institute in Logic. In 1958 to 1959 he went to the Institute for Advanced Study in Princeton, New Jersey, where he worked with Kurt Gödel. He also did post-graduate work at University of California, Berkeley.

When in 1959 he got an unsolicited offer of a faculty position at Cornell University, he accepted, in part because on his previous visit to the campus he had thought "it was the prettiest place I'd ever seen". Nerode is a distinguished professor of arts and sciences in mathematics at Cornell.{{Cite web |title=Anil Nerode |url=https://math.cornell.edu/anil-nerode |access-date=2025-02-27 |website=Cornell University Department of Mathematics}} He was formerly Goldwin Smith Professor of Mathematics at Cornell, having been named to that chair in 1991. His interests are in mathematical logic, the theory of automata, computability and complexity theory, the calculus of variations, and distributed systems. With John Myhill, Nerode proved the Myhill–Nerode theorem specifying necessary and sufficient conditions for a formal language to be regular.Martin Davis, Elaine J. Weyuker, [https://books.google.com/books?id=GRWOqKwZGRAC&dq=myhill-nerode+theorem&pg=PA263 Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science.] Elsevier, 1994, {{ISBN|978-0-12-206382-4}}; Ch. 7. Myhill-Nerode theorem.{{cite report | author=John Myhill | contribution=Finite automata and the representation of events | pages=112–137 | url=https://books.google.com/books?id=QjZwISLU4rAC | editor1=Anil Nerode |editor2= Burton P. Sauer | title=Fundamental Concepts in the Theory of Systems | institution=Wright Air Development Center | type=WADC Technical Report | number=57–624 | date=Nov 1957 }} ASTIA Document No. AD 155741{{cite journal | jstor=2033204 | doi=10.1090/S0002-9939-1958-0135681-9 | author=Anil Nerode | title=Linear Automaton Transformations | journal=Proceedings of the American Mathematical Society | volume=9 | number=4 | pages=541–544 | year=1958 | doi-access=free }} With Bakhadyr Khoussainov, Nerode founded the theory of automatic structures, an extension of the theory of automatic groups.

The academic year 2019–20 saw Nerode's 60th year as an active faculty member at Cornell, which the university said was its longest such tenure ever.{{cite news | url=http://news.cornell.edu/stories/2019/09/after-years-wandering-longest-serving-professor-finds-home-cornell | title=After years of wandering, longest-serving professor finds a home at Cornell | author-first=Melanie | author-last=Lefkowitz | work=Cornell Chronicle | publisher=Cornell University | date= September 11, 2019}} Also published in Math Matters newsletter, Cornell University Department of Mathematics, January 2020, p. 2. In 2022, the Nerode-90 conference was held online to celebrate his contributions to the field.Math Matters newsletter, Cornell University Department of Mathematics, Winter 2022–2023, p. 10.

Nerode is an Editorial Board member of the journals Annals of Mathematics and Artificial Intelligence,[https://www.springer.com/computer/artificial/journal/10472?detailsPage=editorialBoard Editorial Board], Annals of Mathematics and Artificial Intelligence, Springer-Verlag. Accessed January 21, 2010 Mathematical and Computer Modelling,[http://www.elsevier.com/wps/find/journaleditorialboard.cws_home/623/editorialboard Editorial Board], Mathematical and Computer Modelling, Elsevier. Accessed January 21, 2010. Documenta Mathematica[http://www.math.uiuc.edu/documenta/stab.html Editorial Board] {{webarchive|url=https://web.archive.org/web/20130121003220/http://www.math.uiuc.edu/documenta/stab.html |date=2013-01-21 }}, Documenta Mathematica, University of Illinois. Accessed January 21, 2010 and others.

In 2012 he became a fellow of the American Mathematical Society.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-02-24.