Anil Nerode (born 1932) 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 ...

. He received his undergraduate education and a Ph.D. in mathematics from the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

, the latter under the directions of

Saunders Mac Lane Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville ...

. 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 algebra In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the po ...

s and its relation to equational definitions of the

partial recursive function In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as i ...

s. While in graduate school, beginning in 1954, he worked at Professor

Walter Bartky Walter Bartky (1901–1958) was an American astronomer, applied mathematician, and educator, noteworthy for his role in the Manhattan Project. Education and career Walter Bartky received his B.S. from the University of Chicago in 1923 and his Ph.D ...

'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 NSF may stand for: Political organizations *National Socialist Front, a Swedish National Socialist party *NS-Frauenschaft, the women's wing of the former German Nazi party *National Students Federation, a leftist Pakistani students' political gr ...

Summer 1957 Institute in Logic. In 1958 to 1959 he went to the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

in Princeton, New Jersey, where he worked with Kurt Gödel. He also did post-graduate work at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. When in 1959 he got an unsolicited offer of a faculty position at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

, 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 Goldwin Smith Professor of Mathematics at Cornell, having been named to that chair in 1991. His interests are in

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

, the

theory of automata Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματο� ...

computability Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is clo ...

and complexity theory, the calculus of variations, and

distributed system A distributed system is a system whose components are located on different networked computers, which communicate and coordinate their actions by passing messages to one another from any system. Distributed computing is a field of computer sci ...

s. With

John Myhill John R. Myhill Sr. (11 August 1923 – 15 February 1987) was a British mathematician. Education Myhill received his Ph.D. from Harvard University under Willard Van Orman Quine in 1949. He was professor at SUNY Buffalo from 1966 until his death ...

, Nerode proved the

Myhill–Nerode theorem In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1958 . ...

specifying necessary and sufficient conditions for a

formal language In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of sy ...

to be regular. With

Bakhadyr Khoussainov Bakhadyr M. Khoussainov ( Cyrillic: Бахадыр Хусаинов) is a computer scientist and mathematician, who was born and educated in the Soviet Union, works in the fields of mathematical logic, computability theory, computable model theor ...

, Nerode founded the theory of automatic structures, an extension of the theory of

automatic group In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given word representation of a group element is in a ...

s. 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. Also published in ''Math Matters'' newsletter, Cornell University Department of Mathematics, January 2020, p. 2. Nerode is an Editorial Board member of the journals ''Annals of Mathematics and Artificial Intelligence'', ''Mathematical and Computer Modelling'', ''Documenta Mathematica'' and others. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-02-24.

Notes

References

John E. Hopcroft John Edward Hopcroft (born October 7, 1939) is an American theoretical computer scientist. His textbooks on theory of computation (also known as the Cinderella book) and data structures are regarded as standards in their fields. He is the IBM P ...

and

Jeffrey D. Ullman Jeffrey David Ullman (born November 22, 1942) is an American computer scientist and the Stanford W. Ascherman Professor of Engineering, Emeritus, at Stanford University. His textbooks on compilers (various editions are popularly known as the ...

, ''

Introduction to Automata Theory, Languages, and Computation ''Introduction to Automata Theory, Languages, and Computation'' is an influential computer science textbook by John Hopcroft and Jeffrey Ullman on formal languages and the theory of computation. Rajeev Motwani contributed to later editions beg ...

'', Addison-Wesley Publishing, Reading Massachusetts, 1979. . ''(See chapter 3 for Myhill-Nerode theorem)'' *

External links

Anil Nerode's homepage
{{DEFAULTSORT:Nerode, Anil 1932 births University of Chicago alumni 20th-century American mathematicians 21st-century American mathematicians American computer scientists Cornell University faculty Living people Fellows of the American Mathematical Society American academics of Indian descent Indian American