__NOTOC__ Jacob Theodore "Jack" Schwartz (January 9, 1930 – March 2, 2009) was 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 ...

computer scientist A computer scientist is a scientist who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation. Although computer scientists can also focus their work and research on ...

, and professor of

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

at the

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

Courant Institute of Mathematical Sciences. He was the designer of the SETL

programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...

and started the NYU Ultracomputer project. He founded the New York University Department of Computer Science, chairing it from 1964 to 1980.

Early life

Schwartz was born in

The Bronx The Bronx ( ) is the northernmost of the five Boroughs of New York City, boroughs of New York City, coextensive with Bronx County, in the U.S. state of New York (state), New York. It shares a land border with Westchester County, New York, West ...

, New York on January 9, 1930, to Ignatz and Hedwig Schwartz. He attended

Stuyvesant High School Stuyvesant High School ( ) is a co-ed, State school, public, college-preparatory, Specialized high schools in New York City, specialized high school in Manhattan, New York City. The school, commonly called "Stuy" ( ) by its students, faculty, a ...

and went on to City College of New York.Anastasio, Sal
"In Memory of Jacob Schwartz"
''

Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume was published in 1953. Each issue of the magazine ...

'', v.62, n.5, May 2015

Education

Schwartz received his B.S. (1949) from the

City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a Public university, public research university within the City University of New York (CUNY) system in New York ...

and his M.A. (1949) and Ph.D. in mathematics (1952) from

Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...

. His doctoral thesis was entitled ''Linear Elliptic Differential Operators'' and his thesis advisor was

Nelson Dunford Nelson James Dunford (December 12, 1906 – September 7, 1986) was an American mathematician, known for his work in functional analysis, namely vector measure, integration of vector valued functions, ergodic theory, and linear operators. The Dunf ...

Career

Schwartz's research interests included the theory of

linear operator In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pr ...

von Neumann algebra In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann al ...

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

time-sharing In computing, time-sharing is the Concurrency (computer science), concurrent sharing of a computing resource among many tasks or users by giving each Process (computing), task or User (computing), user a small slice of CPU time, processing time. ...

parallel computing Parallel computing is a type of computing, computation in which many calculations or Process (computing), processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. ...

design and implementation,

robotics Robotics is the interdisciplinary study and practice of the design, construction, operation, and use of robots. Within mechanical engineering, robotics is the design and construction of the physical structures of robots, while in computer s ...

set-theoretic Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly ...

approaches in computational logic,

proof Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a co ...

and

program verification In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal ver ...

systems; multimedia authoring tools; experimental studies of visual perception; multimedia and other high-level software techniques for analysis and visualization of bioinformatic data. Schwartz authored 18 books and more than 100 papers and technical reports. He wrote the three-volume textbook ''

Linear Operators In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pr ...

'' with

. He was also the inventor of the Artspeak programming language, which historically ran on mainframes and produced graphical output using a single-color graphical plotter. Schwartz served as chairman of the Computer Science Department (which he founded) at the Courant Institute of Mathematical Sciences,

, from 1969 to 1977. He also served as chairman of the Computer Science Board of the National Research Council and was the former chairman of the

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

Advisory Committee for Information, Robotics and Intelligent Systems. From 1986 to 1989, he was the director of

DARPA The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Adva ...

's Information Science and Technology Office (DARPA/ISTO) in

Arlington, Virginia Arlington County, or simply Arlington, is a County (United States), county in the U.S. state of Virginia. The county is located in Northern Virginia on the southwestern bank of the Potomac River directly across from Washington, D.C., the nati ...

Personal life

Schwartz was previously married to computer scientist Frances E. Allen from 1972 to 1982. He died of liver cancer in 2009 at age 79.

Publications

*Nelson Dunford, Jacob T. Schwartz ''Linear Operators'', Part I General Theory , Part II Spectral Theory, Self Adjoint Operators in Hilbert Space , Part III Spectral Operators * *Jacob T. Schwartz, ''Introduction to Matrices and Vectors'', McGraw-Hill (1961), Dover Reprint (2001) *Jacob T. Schwartz, ''Lectures on the Mathematical Method in Analytical Economics'', Gordon and Breach (1961), Dover Reprint (2018) *Jacob T. Schwartz, ''Relativity In Illustrations'', New York University Press (1962), Dover Reprint (1989) *Jacob T. Schwartz, ''Theory of money (Mathematics and its applications)'', Gordon and Breach (1965) *Jacob T. Schwartz, ''W-* algebras (Notes on mathematics and its applications)'', Gordon and Breach (1967), *Jacob T. Schwartz (ed.)
''Mathematical Aspects of Computer Science''
American Mathematical Society (1967) *Jacob T. Schwartz, ''Nonlinear Functional Analysis'', Gordon and Breach (1968) *Jacob T. Schwartz, ''Differential Geometry and Topology'', Gordon and Breach (1969) * Schwartz, J.T.; Cocke, John
''PROGRAMMING LANGUAGES AND THEIR COMPILERS : Preliminary Notes''
Courant Institute of Mathematical Sciences, New York University, Second Revised Version, April 1970 * * *Jacob T. Schwartz, Robert B. K. Dewar, ''Programming With Sets: An Introduction to Setl'', Springer (November 1986), *Jacob T. Schwartz, ''The Limits of Artificial Intelligence'', found in the ''Encyclopedia of Artificial Intelligence'', 2 vols., John Wiley and Songs, 1987 *Jacob T. Schwartz, Mark Kac, and Gian-Carlo Rota, ''Discrete Thoughts: Essays on Mathematics, Science, and Philosophy'', Birkhäuser Boston; 2nd edition (January 11, 2008), *Jacob T. Schwartz, Domenico Cantone, and Eugenio G. Omodeo, ''Computational logic and set theory: Applying formalized logic to analysis'', Springer-Verlag, 2011. Foreword by Martin D. Davis.

Awards and honors

*Recipient Wilbur Cross Medal,

*Townsend Harris Medal, City University of New York *Mayor's Medal for Contributions to Science and Technology, New York City, 1986 * Leroy P. Steele Prize,

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, ...

, August 1981 (shared with N. Dunford) *Sloan Fellow, 1961–1962 *Distinguished Lecturer at the following Universities: University of California, Santa Barbara; Harvard University; MIT; Cornell University; University of Washington; University of Southern California; Trinity College, Dublin * Elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

in 1976, and to the

National Academy of Engineering The National Academy of Engineering (NAE) is an American Nonprofit organization, nonprofit, NGO, non-governmental organization. It is part of the National Academies of Sciences, Engineering, and Medicine (NASEM), along with the National Academ ...

in 2000.

References

External links

A Symposium to Honor the Scientific Career of Jacob T. Schwartz
(2004). *

*
Jacob SchwartzNAE pageJacob T. Schwartz's personal web siteMartin Davis and Edmond Schonberg, "Jacob Theodore Schwartz", Biographical Memoirs of the National Academy of Sciences (2011)
{{DEFAULTSORT:Schwartz, Jack 1930 births 2009 deaths 20th-century American mathematicians 21st-century American mathematicians Programming language designers City College of New York alumni Yale University alumni Yale University faculty Courant Institute of Mathematical Sciences faculty Donegall Lecturers of Mathematics at Trinity College Dublin Harvard University staff Deaths from liver cancer in New York (state) Members of the United States National Academy of Sciences Operator theorists Mathematicians from New York (state) Scientists from the Bronx