Ralph Saul Phillips (23 June 1913 – 23 November 1998) was an American mathematician and academic known for his contributions to

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

scattering theory In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiat ...

, and

servomechanism In mechanical and control engineering, a servomechanism (also called servo system, or simply servo) is a control system for the position and its time derivatives, such as velocity, of a mechanical system. It often includes a servomotor, and ...

s. He served as a Professor of mathematics at

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

. He made major contributions to acoustical scattering theory in collaboration with

Peter Lax Peter David Lax (1 May 1926 – 16 May 2025) was a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics. Lax made important contributions to integrable systems, fluid dynamics an ...

, proving remarkable results on local energy decay and the connections between poles of the

scattering matrix In physics, the ''S''-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory ...

and the analytic properties of the resolvent. With Lax, he coauthored the widely referred book on

titled ''Scattering Theory for Automorphic Functions''. Phillips received the 1997

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for Lifetime Achievement.

Education and career

Phillips was born in

Oakland Oakland is a city in the East Bay region of the San Francisco Bay Area in the U.S. state of California. It is the county seat and most populous city in Alameda County, with a population of 440,646 in 2020. A major West Coast port, Oakland is ...

on 23 June 1913. He received his bachelor's degree from the

University of California The University of California (UC) is a public university, public Land-grant university, land-grant research university, research university system in the U.S. state of California. Headquartered in Oakland, California, Oakland, the system is co ...

Los Angeles Los Angeles, often referred to by its initials L.A., is the List of municipalities in California, most populous city in the U.S. state of California, and the commercial, Financial District, Los Angeles, financial, and Culture of Los Angeles, ...

(UCLA) in 1935 and his Ph.D. from the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

in 1939 under the direction of Theophil H. Hildebrandt. From 1939 until 1942 he was a member of the Institute for Advanced Study in

Princeton Princeton University is a private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the Unit ...

, an instructor at the

University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...

, and an instructor at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

. It was at the University of Washington he met his future wife, Jean. During the war he led a research group at the Radiation Laboratory at the

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 ...

, the facility where much of the theoretical and practical work on radar technology was done. This work led to his book Theory of Servomechanisms, which for many years was the standard text in the subject. After the war he returned to mathematics, joining as an assistant professor at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

. He moved to the

University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...

the next year and returned to UCLA in 1958. In 1960 he joined

and remained there until his death in 1998. He was the Robert Grimmett Professor of Mathematics at Stanford. Philips's work (with A. Lubotzky and P. Sarnak) on

Ramanujan graphs In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent spectral expanders. As Murty's survey paper notes ...

had a huge impact on

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and

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, ...

Books

*''Scattering Theory for Automorphic Functions'', with P. D. Lax.

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...

(1977).

Education and career

Books

References

Further reading