Barry Martin Simon (born 16 April 1946) is an American

mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

and was the IBM professor of Mathematics and

Theoretical Physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

, known for his prolific contributions in

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result o ...

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 (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

, and

nonrelativistic The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

(particularly Schrödinger

operators Operator may refer to: Mathematics * A symbol indicating a mathematical operation * Logical operator or logical connective in mathematical logic * Operator (mathematics), mapping that acts on elements of a space to produce elements of another sp ...

), including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics. His work has focused on broad areas of mathematical physics and

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

covering:

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...

random matrix theory In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...

, general nonrelativistic quantum mechanics (including

N-body In physics and astronomy, an ''N''-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see ''n''-body problem for other applications). ''N''-body simulations ar ...

systems and

resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...

s), nonrelativistic quantum mechanics in

electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...

and

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

s, the semi-classical limit, the

singular Singular may refer to: * Singular, the grammatical number that denotes a unit quantity, as opposed to the plural and other forms * Singular homology * SINGULAR, an open source Computer Algebra System (CAS) * Singular or sounder, a group of boar, ...

continuous spectrum In physics, a continuous spectrum usually means a set of attainable values for some physical quantity (such as energy or wavelength) that is best described as an interval of real numbers, as opposed to a discrete spectrum, a set of attainable ...

, random and

ergodic In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies tha ...

Schrödinger operators,

orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonality, orthogonal to each other under some inner product. The most widely used orthogonal polynomial ...

, and non-

selfadjoint In mathematics, and more specifically in abstract algebra, an element ''x'' of a *-algebra is self-adjoint if x^*=x. A self-adjoint element is also Hermitian, though the reverse doesn't necessarily hold. A collection ''C'' of elements of a star ...

spectral theory.

Early life

Barry Simon's mother was a school teacher, his father was an accountant. Simon attended James Madison High School in

Brooklyn Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...

Career

During his high school years, Simon started attending college courses for highly gifted pupils at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

. In 1962, Simon won a MAA mathematics competition. ''

The New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...

'' reported that in order to receive full credits for a faultless test result he had to make a submission with MAA. In this submission he proved that one of the problems posed in the test was ambiguous. In 1962, Simon entered

Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

with a stipend. He became a

Putnam Fellow The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regard ...

in 1965 at 19 years old. He received his AB in 1966 from

Harvard College Harvard College is the undergraduate college of Harvard University, an Ivy League research university in Cambridge, Massachusetts. Founded in 1636, Harvard College is the original school of Harvard University, the oldest institution of higher lea ...

and his PhD in

Physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

in 1970, supervised by Arthur Strong Wightman. His dissertation dealt with ''Quantum mechanics for Hamiltonians defined as quadratic forms''. Following his doctoral studies, Simon took a professorship at Princeton for several years, often working with colleague

Elliott H. Lieb Elliott Hershel Lieb (born July 31, 1932) is an American mathematical physics#Mathematically rigorous physics, mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, Cond ...

on the

Thomas Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (disambiguation) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Ap ...

Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and ...

Theory and

Hartree The hartree (symbol: ''E''h or Ha), also known as the Hartree energy, is the unit of energy in the Hartree atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is = The hartree energy is approxima ...

- Fock Theory of

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

s in addition to

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

s and mentoring many of the same students as Lieb. He eventually was persuaded to take a post at

, from which he retired in the summer of 2016. His status is legendary in mathematical physics and he is renowned for his ability to write scientific manuscripts "in five percent of the time ordinary mortals need to write such papers." A former graduate student of Simon's, in a tale revealing of his brilliance, once stated:

Honors and awards

*1974: Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Vancouver *1981: Elected fellow of the

American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...

*1990: Elected correspondent member of the Austrian Academy of Sciences *2005: Elected fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

*2012: Elected 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, ...

*2012: Awarded the

Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. The prize is sponsored by the Daniel Iagolnitzer Foundat ...

*2015: Awarded the

Bolyai Prize The International János Bolyai Prize of Mathematics is an international prize founded by the Hungarian Academy of Sciences. The prize is named after János Bolyai and is awarded every five years to mathematicians for monographs with important new r ...

of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma ...

*2016: Awarded the

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 ...

for Lifetime achievements *2018:

Dannie Heineman Prize for Mathematical Physics Dannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman. As of 2010 ...

from the

*2019: Elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, 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 Nati ...

Selected publications

Articles

*Resonances in ''n''-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Annals of Mathematics 97 (1973), 247–274 (over 700 citations) *(with F. Guerra and L. Rosen) The P(φ)₂ quantum theory as classical statistical mechanics, Annals of Mathematics 101 (1975), 111–259 *(with E. Lieb) The Thomas-Fermi theory of atoms, molecules and solids,

Advances in Mathematics ''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed ...

23 (1977), 22–116 (over 700 citations) *(with J. Fröhlich and T. Spencer) Infrared bounds, phase transitions and continuous symmetry breaking, Commun. Math. Phys. 50 (1976), 79–85 *(with P. Perry and I. M. Sigal) Spectral analysis of multiparticle Schrödinger operators, Annals of Mathematics 114 (1981), 519–567 * Schrödinger semigroups, Bulletin of the American Mathematical Society 7 (1982), 447–526 (over 1500 citations) *(with M. Aizenman
Brownian motion and Harnack's inequality for Schrödinger operators
Commun. Pure Appl. Math. 35 (1982), 209–273 (over 600 citations) *Holonomy, the quantum adiabatic theorem and Berry's phase, Phys. Rev. Lett. 51 (1983), 2167–2170 (over 2050 citations) *(with Joseph E. Avron and Ruedi Seiler) Homotopy and quantization in condensed matter physics, Phys. Rev. Lett. 51 (1983) 51–53 (over 600 citations) *Semiclassical analysis of low lying eigenvalues, II. Tunneling, Annals of Mathematics 120 (1984), 89–118 *(with T. Wolff) Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math. 39 (1986), 75–90 *Operators with singular continuous spectrum: I. General operators, Annals of Mathematics 141 (1995), 131–145

Books

* ''Quantum mechanics for hamiltonians defined as quadratic forms.'' Princeton University Press, Princeton NJ 1971, . * with

Michael C. Reed Michael (Mike) Charles Reed is an American mathematician known for his contributions to mathematical physics and mathematical biology. Reed first attended Yale University, where he graduated with a bachelor's degree. In 1969 he earned a PhD fr ...

: ''Methods of Modern Mathematical Physics.'' 4 vols. Academic Press, New York, NY etc. 1972–1978; ** vol. 1: ''Functional Analysis.'' 1972, ; ** vol. 2: ''Fourier Analysis, Self-Adjointness.'' 1975, ; ** vol. 3: ''Scattering Theory.'' Academic Press, 1979, ; ** vol. 4: ''Analysis of Operators.'' Academic Press, 1978, . * ''The

\Phi^2

Euclidean (Quantum) Field Theory.'' Princeton University Press, Princeton NJ 1974, . * as editor with Elliott H. Lieb and Arthur S. Wightman: ''Studies in mathematical physics. Essays in Honor of Valentine Bargmann.'' Princeton University Press, Princeton NJ 1976, , contributions by Barry Simon: ** pp. 305–326: ''On the number of bound states of two body Schrödinger operators – a review.'
online PDF; 377 kB.
** pp. 327–349: ''Quantum dynamics: from automorphism to hamiltonian.'
online PDF; 573 kB.
* ''Functional integration and quantum physics'' (= ''Pure and Applied Mathematics.'' 86). Academic Press, New York NY etc. 1979, ISBN 0-12-644250-9 (2nd edition: American Mathematical Society, Providence RI 2005, ). * ''Trace Ideals and their applications'' (= ''London Mathematical Society. Lecture Note Series.'' 35). Cambridge University Press, Cambridge etc. 1979, (2nd edition: (= ''Mathematical Surveys and Monographs.'' 120). American Mathematical Society, Providence RI 2005, ). * with Hans L. Cycon, Richard G. Froese, and Werner Kirsch: ''Schrödinger Operators.'' Springer, Berlin etc. 1987, (corrected and extended 2nd printing: Springer 2008, ). * ''The Statistical mechanics of lattice gases.'' vol. 1. Princeton University Press, Princeton NJ 1993, . * ''Orthogonal polynomials on the unit circle'' (= ''American Mathematical Society Colloquium Publications.'' 54, 1–2). 2 vols. American Mathematical Society, Providence RI 2005; ** vol. 1: ''Classical theory.'' 2005, ; ** vol. 2: ''Spectral theory.'' 2005, . * ''Convexity. An analytic viewpoint'' (= ''Cambridge Tracts in Mathematics.'' 187). Cambridge University Press, Cambridge etc. 2011, . * ''Szegő´s theorem and its descendants. Spectral theory for

L^2

perturbations of orthogonal polynomials.'' Princeton University Press, Princeton NJ 2011, .
''A Comprehensive Course in Analysis''
4 vols. with vol. 2 published in 2 parts, American Mathematical Society, Providence RI 2015, . ** vol. 1: ''Real Analysis.'' ** vol. 2A: ''Basic Complex Analysis.'' ** vol. 2B: ''Advanced Complex Analysis.'' ** vol. 3: ''Harmonic Analysis.'' ** vol. 4: ''Operator Theory.''
''Loewner's theorem on monotone matrix functions''
Springer, 2019,

References

External links

* * ttps://scholar.google.com/citations?user=OM0D_3wAAAAJ&oi=ao Publications and citationsat

Google Scholar Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes p ...

* * (KBS Fest at ISI Bangalore) * * * * * * Caltech Heritage Project, interviews from 2021 & 2022 ** (interview Thursday Nov. 18, 2021) ** ** (interview Friday Nov. 26, 2021) ** ** (interview Thursday Dec. 2, 2021) ** ** (interview Thursday Dec. 9, 2021) ** ** (interview Wednesday Dec. 15, 2021) ** ** (interview Thursday Dec. 23, 2021) ** (interview March 7, 2022) {{DEFAULTSORT:Simon, Barry 1946 births Living people 20th-century American mathematicians 21st-century American mathematicians 21st-century American physicists Jewish American physicists Harvard University alumni Princeton University alumni Princeton University faculty California Institute of Technology faculty Putnam Fellows Fellows of the American Mathematical Society Mathematical physicists Operator theorists James Madison High School (Brooklyn) alumni Mathematicians from New York (state) Members of the United States National Academy of Sciences Fellows of the American Physical Society 21st-century American Jews