1.1. The Stampacchia Prize.

The variational inequality came out of two papers, Formes bilinéaires coercitives sur les ensembles convexes (1964) by G Stampacchia and Variational inequalities (1967) by J L Lions and G Stampacchia. In order to honour its founder, the Stampacchia Prize was established by the Scuola Normale Superiore in Pisa, Italy with financial support from the National Research Council. The first Prizes were awarded in 1982 to six mathematical scientists with outstanding contributions to the problem of inequality and related problems.

1.1 Barry Simon wins the Stampacchia Prize.

The Stampacchia Prize was first awarded in 1982 for works devoted to the following subject:

New problems on differential equalities or inequalities, or the calculus of variations in presence of unilateral constraints.

The subject was chosen for the competition because, on the one hand, it links up with research carried out by Guido Stampacchia at the end of his life, and, on the other, it offers great scope for development both because of the variety of problems still unsolved in this connection (for instance, elliptic problems with thin irregular obstacles, penalisation and stability in relation to obstacles, the movement of a mechanical system in the presence of unilateral constraints, ... ) and because of the methods for solving them. Monographs or substantial papers, if published during 1980 or 1981 or unpublished, were eligible for consideration in the competition.

Edoardo Vesentini, director of the Scuola Normale Superiore in Pisa, announced the winners of the first Guido Stampacchia Prize of five million lira. The selection committee had considered thirty-seven papers submitted by twenty-two authors for the competition. The Committee noted that its decision was difficult because of the high quality of the papers which had been submitted.

The Committee decided unanimously to award the prize to

Michael Aizenman, Hans Wilhelm Alt, Luis A Caffarelli, Giannidal Maso, Avner Friedman and Barry Simon.

Barry Simon received his award as a result of his joint paper with Michael Aizenman, Brownian Motion and Harnack inequality for Schrödinger operators, Communications on Pure and Applied Mathematics 35 (1982), 209-273.

2.1. The Henri Poincaré Prize.

The Henri Poincaré Prize is sponsored by the Daniel Iagolnitzer Foundation and awarded by the International Association of Mathematical Physics. The Prize was created in 1997 to recognise outstanding contributions in mathematical physics, and contributions which lay the groundwork for novel developments in this broad field. The Prize is also created to recognise and support young people of exceptional promise who have already made outstanding contributions to the field of mathematical physics.

The prize is awarded every three years at the International Mathematical Physics Congress and in each case, is an award to three individuals (to be exact, the rules say approximately three allowing for exceptional circumstances, at the discretion of the prize committee).

2.2. Barry Simon's Henri Poincaré Prize Citation.

Barry Simon is honoured for his impact on many areas of mathematical physics including, in particular, the spectral theory of Schrödinger operators, for his mentoring of generations of young scientists, and for his lucid and inspirational books.

2.3. Laudatio for Barry Simon's Henri Poincaré Prize.

Laudatio for Barry Simon by Percy Deift, New York City, August, 2012.

I am very pleased and honoured to give the laudatio for Barry Simon, my former advisor, on his winning the Henri Poincare Prize for 2012.

Barry grew up in Brooklyn, New York, went to school there at James Madison High, obtained his bachelor degree at Harvard, and then his PhD in Physics at Princeton under Arthur Wightman in 1970. He was a faculty member at Princeton for 12 years, and since 1981 he has been the IBM Professor of Mathematics and Theoretical Physics at Caltech.

The 1970's were a very special time for mathematical physics at Princeton. One can read a lively account of those days, written by Barry himself, in the current edition of the Bulletin of the IAMP. The main thrust of the activity was in statistical mechanics, quantum field theory and non-relativistic quantum mechanics. The list of people who participated in Math-Phys at Princeton University in those years, for shorter or longer periods of time, as students, post-docs, junior faculty or senior faculty, or just visitors for a day, reads like a Who's Who of Mathematical Physics. Leading the charge were Arthur Wightman, Elliot Lieb and Barry. But there were also Eugene Wigner, Valentine Bargmann, Ed Nelson and many others, some of whom I see here in the audience today. And across the way at the Institute there was Freeman Dyson, doing wonderful things. Barry was a dynamo, challenging us with open problems, understanding every lecture instantaneously, writing paper after paper, often at the seminars themselves, and all the while supervising 7 or 8 PhD students.

In the early years of his career Barry divided his efforts more or less equally between statistical mechanics, quantum field theory and non-relativistic quantum mechanics, but in the 1980's he started to concentrate on questions of exotic spectra for Schrödinger operators, both continuous and discrete, which then led him to his current focus on orthogonal polynomials, both on the circle and on the line.

Here are just some of Barry's outstanding research accomplishments:

- After more than 30 years, Barry's work with Frohlich and Spencer, and Dyson and Lieb, still provides the only rigorous proofs of non-abelian classical and quantum continuous symmetry breaking

- Simon was the first to give a mathematically precise definition of resonance. He created the rigorous framework for the complex scaling method, which is not only a theoretical tool, but is also used by many computational quantum chemists. He used the method to provide the first rigorous proofs of the convergence of time dependent perturbation theory, and, with Harrell, of the Oppenheimer and Bender-Wu tunnelling formulae

- Simon pioneered the use of differential geometric invariants in understanding quantum phenomena. In 1983 he pointed out that the phase found by Berry was the holonomy of a connection on an associated manifold. Berry's phase, which Barry named and which won Berry the Wolff prize, might have remained obscure if not for Simon's influential paper

- Together with Perry and Sigal, Simon gave the first proof of the absence of singular continuous spectrum for general N-body quantum systems

- Together with Lieb, Simon gave the first rigorous interpretation/proof of Thomas-Fermi theory and Hartree-Fock theory

- Simon established the foundations of the theory of ergodic Schrödinger operators, including Last-Simon results on absolutely continuous spectrum, and discrete Kotani theory

- Together with Tom Wolff, Simon developed the Simon - Wolff criteria for localisation in quantum mechanics

- Together with Killip, and Damanik-Killip, Simon characterised $L^{2}$ perturbations of free and periodic problems

… and the list goes on!

Barry is also famous for his many books. Their influence is quite extraordinary. On Google Scholar, one sees that, as of 2 August, Barry's series with Mike Reed on Methods in Modern Mathematical Physics has 12,313 citations, and 3 of his other books have over 1,000 citations! It's a common refrain amongst mathematical physicists that they learned the subject from Barry's books. Barry has an uncanny, and famous, ability to extract the key elements of a proof. This ability is expressed in his books as a signature combination of economy and clarity, which accounts, I believe, for their usefulness and great popularity.

Another way Barry has influenced mathematical physics is through his knack in naming things in a way which sticks, e.g., hypercontractive semi-groups, Birman-Schwinger bounds, the CLR (Cwickel-Lieb-Rosenblum) inequality, infrared bounds, the almost Mathieu equation, checkerboard estimates, Verblunsky coefficients, CMV matrices, ..., and the Wonderland Theorem, which was proved by Simon, and which says roughly the following: If the operators with purely absolutely continuous spectrum form a dense set in a metric space $X$, and if the operators with purely point spectrum are also dense in $X$, then generically operators in $X$ have only singular continuous spectrum. Quite a wonder!

There are many Barry-stories and you can find a list of them on Barry's Wiki page. I would like to tell a personal story that goes back to the time when Barry was still living in Edison, New Jersey. One day a number of us went to visit Barry at his home to discuss a joint project on the decay of $L^{2}$ eigenfunctions. We spent the afternoon discussing various questions and came up with a long list of problems that should be addressed. We left in the late afternoon thinking about the challenging task that lay ahead of us. The next morning Barry came into the office. Not only had he solved all the problems on our list, but he had in his hand the first draft of the paper! We were overwhelmed. For a young person like myself, this was most discouraging. And I was doubly discouraged: Barry was younger than me!

All of us, his many students, his post-docs, his collaborators, and his colleagues, owe Barry a great debt for the extraordinary service he has provided to mathematical physics. I offer Barry my congratulations on his outstanding achievement in winning the Henri Poincare Prize for 2012!

3.1. The János Bolyai International Mathematics Award.

In honour of the 100th anniversary of the birth of world-famous Hungarian mathematician János Bolyai, the Hungarian Academy of Sciences established an international award of ten-thousand crowns for outstanding mathematical works in 1902. The first laureate in 1905 was Henri Poincaré of France, one of the most versatile mathematicians of the 19th century, and in 1910 David Hilbert of Germany received the award. The awarding of the medal was interrupted after the outbreak of the First World War. The Hungarian Academy of Sciences re-founded the award in 1994, calling it the János Bolyai International Mathematics Award. The award provides the winner USD 25,000 and a gold-plated bronze medallion made using the original designs. The Bolyai Prize is awarded every fifth year by the Hungarian Academy of Sciences to the author of the most outstanding, ground-breaking mathematical monograph presenting his/her own new results and methods published anywhere and in any language in the preceding fifteen (previously ten) years, taking into account the author's previous scientific work.

3.2. Barry Simon wins the János Bolyai Award.

In 2015 the János Bolyai International Mathematical Prize of the Hungarian Academy of Sciences was awarded to Barry Simon for Orthogonal Polynomials on the Unit Circle, American Mathematical Society, 2005.

This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analogue of the spectral theory of one-dimensional Schrödinger operators.

Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.

3.3. Extract from Barry Simon's acceptance speech.

Winning the 2015 Bolyai Prize is a great honour, in part, because of the distinguished company I join. I'd like to thank the Hungarian Academy and especially the members of the Prize Committee. But there is a special thrill in the Prize being from the Hungarian Academy because as I've learned in the past twenty years, the theory of orthogonal polynomials (OPs) is definitely a Hungarian sport. I have in mind not only the leaders of the current generation including Paul Nevai and Vilmos Totik but the previous generation (Erdős, Turán and Freud), and of course, the founder of the modern theory, Gábor Szegő.

Orthogonal Polynomials on the Real Line (OPRL) have roots in the work of French mathematicians in the late 18th century with key developments by Jacobi, Hermite and the Russian school in the 19th. But Orthogonal Polynomials on the Unit Circle (OPUC) are the invention of Szegő, especially in a two part paper of 1920-21. The books cited for the prize, published in 2005, are two volumes totalling 1050 pages on OPUC. They have at least had the impact of introducing the abbreviations/names OPRL, OPUC, CMV Matrix and Verblunsky coefficients. In early 2001, I'd not even heard of OPUC, so I thought, an appropriate acceptance talk would explain how I went from a novice to something of an "expert" and how I managed to find a cornucopia of new results.

3.4. MTA International Bolyai Prize goes to Barry Simon.

The Hungarian Academy of Sciences made the following announcement:

US mathematician Barry Simon has been awarded the International János Bolyai Prize of Mathematics this year. Founded in 1902 and awarded every five years, the Prize is received by the author of the best monograph in mathematics in the previous 15 years and it is the only international award issued by MTA. Simon, a member of the American Mathematical Society, is the sixth medallist of this prestigious award.

To commemorate the centenary birthday of János Bolyai, a world famous Hungarian mathematician, the Hungarian Academy of Sciences founded a prize worth ten thousand Koronas (old Hungarian currency) to be distributed every five years in recognition of some internationally outstanding mathematical work. In addition to the list of the original motives such as to honour the memory of Bolyai the prize founded was also meant to make up for a Nobel Prize non-existent for mathematicians at the time.

In 1905 the first prize winner was a Frenchman Henri Poincaré, one of the most resourceful mathematicians in the 19th century. Following World War I the awarding of the prize was discontinued. MTA decided to reintroduce the Prize in 1994 with the new name of International János Bolyai Prize of Mathematics. The gilt bronze medal remodelled from the original moulds and complete with a check for USD 25.000 was given in 2000 to Shaharon Selah, a mathematician from Israel, in 2005 to Mihail Gromov, a Russian scientist, and in 2010 to Jurij Manyin an author of Russian origin living in Germany.

Thus Barry Simon is the sixth in the winners' list. An international panel of jurors consisting of five Hungarian and five international mathematicians has decided to honour him for his book entitled Orthogonal polynomials on the unit circle published in 2005.

Aged 69, the scientist is an IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology, USA. He has written numerous books on mathematics and theoretical physics that have had a big impact on various disciplines.

His award winning book entitled "Orthogonal polynomials on the unit circle" is a monumental treatise that connects two important fields of mathematics: the theory of orthogonal polynomials and operator theory. This connected view has turned out to be extremely fertile in both areas leading to applications in various directions from stochastic processes to theoretical physics. Barry Simon's monograph contains the classical theory, all the new developments, as well as many of their applications. The book became an instant success - a worthy successor of the Hungarian mathematician Gábor Szegő's classic treatise on orthogonal polynomials written in 1939.

The International János Bolyai Prize of Mathematics was delivered in the second half of the year 2012 by MTA President László Lovász at a public session of the MTA's Section of Mathematics and was followed by a luncheon ceremony to congratulate the award-winner.

4.1. The Steele Prize.

The Leroy P Steele Prize was established by the American Mathematical Society in 1970 in honour of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein. It was endowed under the terms of a bequest from Leroy P Steele. From 1970 to 1976 one or more prizes were awarded each year for outstanding published mathematical research; most favourable consideration was given to papers distinguished for their exposition and covering broad areas of mathematics. In 1977 the Council of the American Mathematical Society modified the terms under which the prizes were awarded. In 1993, the Council formalised three categories of the prize by naming each of them: (1) The Leroy P Steele Prize for Lifetime Achievement; (2) The Leroy P Steele Prize for Mathematical Exposition; and (3) The Leroy P Steele Prize for Seminal Contribution to Research.

4.2. Barry Simon wins the Steele Prize for Lifetime achievement.

Barry Simon of the California Institute of Technology received the 2016 AMS Leroy P Steele Prize for Lifetime Achievement for:-

... his impact on the education and research of a generation of mathematical scientists through his significant research achievements, his highly influential books, and his mentoring of graduate students and postdocs.

The prize was awarded on Thursday, 7 January 2016, at the Joint Mathematics Meetings in Seattle.

4.3. Barry Simon's contributions leading to the award.

Simon's mathematical talent showed early in life. In 1962, at the age of 16, he was the subject of a short article in The New York Times, which recounted the story of Simon's participation in an exam contest sponsored by the Mathematical Association of America and the Society of Actuaries. After missing one question, he argued that the wording of the question had been ambiguous. The contest sponsors agreed, and Simon was awarded a perfect score.

An alumnus of Harvard University, Simon received his PhD from Princeton University in 1970 and was immediately appointed as an assistant professor. In the decade that followed, as Simon rose to the rank of full professor in 1981, Princeton became a thriving centre for mathematical physics, particularly in statistical mechanics, quantum field theory, and non-relativistic quantum mechanics. One of Simon's PhD students from that time, Percy Deift, described the atmosphere this way: "Barry was a dynamo, challenging us with open problems, understanding every lecture instantaneously, writing paper after paper, often at the seminars themselves, and all the while supervising 7 or 8 PhD students." Deift made these remarks in the laudatio for the Poincaré Prize, awarded to Simon in 2012.

Simon's prodigious productivity continued after he moved to Caltech in 1981 to take his present position as the IBM Professor of Mathematics and Theoretical Physics. Today his list of research publications includes over 400 items. His secret? He needs "only five percent of the time ordinary mortals need" to write a research paper, quipped his collaborator Jürg Frölich, in a reminiscence prepared for a conference celebrating Simon's 60th birthday. Simon has had 31 graduate students, many of whom have gone to become leaders in mathematical physics and other areas, and he has mentored about 50 postdoctoral researchers.

Simon's own research contributions range over several areas of pure mathematics and mathematical physics. One of his most important contributions still stands as a landmark today: After nearly 40 years, work done by Simon and 4 co-authors (Fröhlich, Thomas Spencer, Freeman Dyson, and Elliott Lieb) still stands as the only rigorous proof of symmetry breaking in certain regimes fundamental to physics.

Simon was the first to give a mathematically precise definition of resonance that allowed linking of time-independent and time-dependent perturbation theory and the first to use differential-geometric invariants to understand Berry's phase and some other quantum phenomena. In work with Lieb, Simon produced the first rigorous proofs and interpretations of theories central to quantum mechanics. A leading contributor to the construction of quantum fields in two space-time dimensions, Simon (together with Francesco Guerra and Lon Rosen) established an analogy with classical statistical mechanics that led to deep new insights. Simon also proved several definitive results in the general theory of Schrödinger operators.

In addition to his outstanding contributions at the forefront of research, Simon is known for several books that have had a major influence on generations of students entering the field of mathematical physics. His 4-volume work Methods of Modern Mathematical Physics, written with Michael Reed during the 1970s, is where many of today's top researchers first learned this subject. Simon's uncanny ability to extract the key elements in a proof "is expressed in his books as a signature combination of economy and clarity, which accounts, I believe, for their usefulness and great popularity," remarked Deift in the Poincaré laudatio. Simon's two-volume set Orthogonal Polynomials on the Unit Circle, published by the AMS in 2005, became instant classics, connecting the theory of orthogonal polynomials with the spectral theory of Schrödinger operators and other topics in mathematical physics.

On top of all of his other contributions, Simon is also the co-author of two highly popular manuals for Windows computers: The Mother of All Windows Books and The Mother of All PC Books, which appeared in the 1990s. Written with Woody Leonhard, the books provided clear and practical advice in a witty and irreverent style, making them highly popular with computer users struggling to make sense of their costly machines.

In addition to the aforementioned Poincaré Prize (2012), Simon's previous awards include several honorary degrees and the Bolyai Prize of the Hungarian Academy of Sciences (2015). He was named a Fellow of the AMS in 2013.

4.4. Caltech Press Release.

Kathy Svitil issued the following Caltech Press Release.

In conferring the award, the AMS noted Simon's "career of exceptional achievement," which includes the publication of 333 papers and 16 books. Simon was specifically recognised for proving a number of fundamental results in statistical mechanics and for contributing to the construction of quantum fields in two space‐time dimensions - topics that, the AMS notes, have "grown into major industries" - as well as for his "definitive results" on the general theory of Schrödinger operators, work that is crucial to an understanding of quantum mechanics and that has led to diverse applications, from probability theory to theoretical physics. He has also made fundamental contributions to the theory of orthogonal polynomials and their asymptotics.

"Barry Simon is a powerhouse in mathematical physics and has had an outstanding career which this award attests to," says Vladimir Markovic, the John D. MacArthur Professor of Mathematics. "Caltech is lucky to have him."

"Barry is a driving force in mathematics at Caltech and has had enormous influence as a scholar, a teacher, and a mentor," says Fiona Harrison, the Benjamin M. Rosen Professor of Physics and holder of the Kent and Joyce Kresa Leadership Chair for the Division of Physics, Mathematics and Astronomy.

Simon spoke at the International Congress of Mathematics in 1974 and has since given almost every prestigious lecture available in mathematics and physics. He was named a fellow of the American Academy of Arts and Sciences in 2005, and was among the inaugural class of AMS fellows in 2012. In 2015, Simon was awarded the International János Bolyai Prize of Mathematics by the Hungarian Academy of Sciences, given every five years to honour internationally outstanding works in mathematics, and in 2012, he was given the Henri Poincaré Prize by the International Association of Mathematical Physics. The prize is awarded every three years in recognition of outstanding contributions in mathematical physics and accomplishments leading to novel developments in the field.

Simon received his AB from Harvard College in 1966 and his doctorate in physics from Princeton University in 1970. He held a joint appointment in the mathematics and physics departments at Princeton for the next decade. He first arrived at Caltech as a Sherman Fairchild Distinguished Visiting Scholar in 1980 and joined the faculty permanently in 1981. He became the IBM Professor in 1984.

4.5. Biographical sketch of Barry Simon.

Barry Simon is the IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology. He was born in Brooklyn, New York, in 1946, received a BA from Harvard University (where he was a top-five Putnam winner) in 1966, and a PhD in physics from Princeton University in 1970. He started as an instructor in mathematics at Princeton in 1969-70, but since then all his appointments at Princeton and Caltech have been joint. He received tenure in 1972, two years after Charlie Fefferman, who was in the same graduate class. Since 1981, he has been at Caltech, where he served as executive officer (chair) for ten years. Simon has published just under 400 papers and twenty-one math books (plus several end-user-oriented computer books). His most recent books are the five-volume (3,200 pages) Comprehensive Course in Analysis published by the AMS in December 2015. At Google Scholar his citation number is about 60,000, and his h-index is 102 (i.e., 102 publications with at least 102 citations). His research has been in many aspects of mathematical physics and in the analytic theory of orthogonal polynomials.

He has been recognised with honorary degrees from Technion, the University of Wales-Swansea, and LMU-Munich. He was awarded the Poincaré Prize of the IAMP in 2012 and the Bolyai Prize of the Hungarian Academy of Science in 2015. He is a fellow of the American Physical Society (1981), the American Academy of Arts and Sciences (2005), and the AMS (2013). He has served as vice president of the AMS and of IAMP.

4.6. Barry Simon's response.

I should like to thank the American Mathematical Society and especially the Leroy P Steele Prize Committee for this noteworthy recognition. It is a great honour to join the distinguished list of former winners. I'd also like to acknowledge my mentors Arthur Wightman and Ed Nelson, who have passed away in the past few years. They not only taught me mathematics but how to be a mathematician.

I am especially pleased by this prize since it recognizes not only my research but my greater impacts. At the perhaps silly level this includes a listing of terms which appeared first in my papers, including hypercontractive and ultracontractive semigroups, Birman-Schwinger principle, diamagnetic inequality, Kato's inequality, CLR bound, Berry's phase, almost Mathieu equation, wonderland theorem, OPUC/OPRL, Verblunsky coefficients, CMV matrix, and clock behaviour.

More importantly, it recognizes the impact of my books. It is always a little thrill when I get into an email discussion with someone who then mentions that it was Reed and Simon that first turned them on to functional analysis. I take pleasure in the invigoration of the analytic theory of OPUC that was caused in part by those books. And I hope that my most recent five-volume opus will have impact.

Most directly, I cherish the impact on thesis students, postdocs, and others I've mentored. Mathematics is a communal enterprise, and I've taken great joy in my interaction with coauthors and those I've taught.

5.1. The Dannie Heineman Prize.

The Heineman Prize is named after Dannie N Heineman, an engineer, business executive and philanthropic sponsor of the sciences. The Dannie Heineman Prize is sponsored by the American Physical Society, the American Institute of Physics and The Heineman Foundation. The prize was established in 1959 by the Heineman Foundation for Research, Educational, Charitable, and Scientific Purposes, Inc., and is administered jointly by the American Physical Society and the American Institute of Physics. The prize recognises outstanding publications in the field of mathematical physics. The prize consists of $10,000 and a certificate citing the contributions made by the recipient plus travel expenses to attend the meeting at which the prize is awarded. It is presented annually. The prize is awarded solely for valuable published contributions made in the field of mathematical physics with no restrictions placed on a candidate's citizenship or country of residence. "Publication" is defined as either a single paper, a series of papers, a book, or any other communication which can be considered a publication. The prize may be awarded to more than one person on a shared basis when all recipients have contributed to the same accomplishments.

5.2. About the American Institute of Physics and the American Physical Society.

The American Institute of Physics is a federation of scientific societies in the physical sciences, representing scientists, engineers, educators, and students. AIP offers authoritative information, services, and expertise in physics education and student programs, science communication, government relations, career services, statistical research in physics employment and education, industrial outreach, and history of the physical sciences. AIP publishes Physics Today, the most closely followed magazine of the physical sciences community, and is also home to the Society of Physics Students and the Niels Bohr Library and Archives. AIP owns AIP Publishing LLC, a scholarly publisher in the physical and related sciences.

The American Physical Society is a non-profit membership organization working to advance and diffuse the knowledge of physics through its outstanding research journals, scientific meetings, and education, outreach, advocacy and international activities. APS represents over 53,000 members, including physicists in academia, national laboratories and industry in the United States and throughout the world. Society offices are located in College Park, MD (Headquarters), Ridge, NY, and Washington, DC.

5.2. Barry Simon wins the Dannie Heineman Prize.

Barry Simon was awarded the 2018 Dannie Heineman Prize:-

... for his fundamental contributions to the mathematical physics of quantum mechanics, quantum field theory, and statistical mechanics, including spectral theory, phase transitions, and geometric phases, and his many books and monographs that have deeply influenced generations of researchers.

The Prize was presented by the American Institute of Physics and the American Physical Society on behalf of the Heineman Foundation at the American Physical Society March 2018 Meeting in Los Angeles, California. A special Ceremonial Session was held at the meeting where Barry Simon received the $10,000 prize.

5.3. 2018 Dannie Heineman Prize News Release.

Barry Simon wins the 2018 Dannie Heineman Prize for Mathematical Physics. The American Institute of Physics and the American Physical Society awarded the prize to the mathematical and theoretical physicist for his seminal contributions to the field in a broad spectrum of topics.

The American Institute of Physics (AIP) and the American Physical Society (APS) announced that Barry Simon of Caltech is the recipient of the 2018 Dannie Heineman Prize for Mathematical Physics, which is awarded annually to honour significant contributions to the field.

In recognising Barry Simon, the two organisations cited him "For his fundamental contributions to the mathematical physics of quantum mechanics, quantum field theory, and statistical mechanics, including spectral theory, phase transitions, and geometric phases, and his many books and monographs that have deeply influenced generations of researchers."

"Dr Simon has impacted so many fundamental aspects of physics over multiple decades with his mathematical insights. His multiple text books, including the classic 'Methods of Modern Mathematical Physics,' which he co-authored with M Reed, continue to help students develop fundamental skills in modelling physical systems," said Catherine O'Riordan, interim co-CEO and COO at AIP. "We offer sincere congratulations to Dr Simon who is joining eight of his co-authors and collaborators who have previously won the Heineman award."

The accomplishments of Barry Simon's work form a collection of theoretical understandings ranging from anharmonic oscillators to phase transitions, accounting for a citation that he describes as somewhat of a "kitchen sink." His mathematical models have deep and fundamental applications to almost all fields of physics from condensed matter to atomic and molecular physics. "I like to describe myself as having the heart of a physicist, but the head of a mathematician," he said.

Simon applied his mathematical inclinations to physics theory early on, in time to declare the focus as his major while an undergraduate at Harvard University. "One of the reasons I'm not just a pure mathematician is I had an absolutely amazing high school physics teacher named Sam Marantz," Simon said. "It was because of his influence that I majored in physics in college and I have a physics Ph.D."

A year after earning his doctorate from Princeton University in mathematical physics, he co-authored the first volume of what would eventually be a four-volume text book: "Methods of Modern Mathematical Physics" is considered in the field to be a standard and significant reference for theoretical physics modelling.

Even a trimmed list of the physics topics Simon's mathematical findings impacted would be lengthy. Among them is his work describing Berry's phase, applying geometric insights to the relationship between classical and quantum phases. Simon met Michael Berry in the early 1980s when their paths crossed in Australia, and quickly applied the findings he'd recently made in a separate body of his work to the work Berry was in the process of publishing.

"He told me about his work and in a few days, I figured out its geometric contents," said Simon. "So, he just had formulae and I figured out a way of understanding it geometrically, which is the way everyone now talks about it."

Simon's accomplishments aren't simply numerous, but reach across an incredibly wide range of fundamental physics systems and phenomena. He credits his mentors and colleagues for this kind of approach, the breadth of which seems to be a key to many of Simon's most notable discoveries.

"What sometimes happens is a mathematical technique that's very natural in one setting turns out to be very useful in another setting and you might not have even thought of using it if you haven't already thinking about it," said Simon. "It happened that I was doing some work in quantum field theory models and some technique was invented. It turned out to be the key for understanding something in the models for nonrelativistic quantum mechanics, and if I were just thinking about the nonrelativistic quantum mechanics, I never would have found this result."

Simon continues to publish while in his role as professor emeritus at Caltech, adding to his list of over 20 published books. He published a five-volume graduate course in analysis less than two years ago and is currently working on another book in addition to numerous reviews.

5.4. About Barry Simon.

Barry Simon is IBM Professor of Mathematics and Theoretical Physics, Emeritus at the California Institute of Technology. He is also an author of several texts, including Methods of Modern Mathematical Physics Vol I-IV, which were voted most significant mathematical physics book of the 20th century at 2000 ICMP. Simon received his bachelor's degree from Harvard University in 1966 and his doctorate from Princeton University in 1970. He received the Steele prize for lifetime achievement from the American Mathematical Society.

5.5. Caltech Press Release.

Lorinda Dajose issued the following Caltech Press Release.

Barry M Simon, the International Business Machines (IBM) Professor of Mathematics and Theoretical Physics, Emeritus, has been awarded the 2018 Dannie Heineman Prize for Mathematical Physics. The prize is administered jointly by the American Physical Society and the American Institute of Physics, and recognises outstanding publications in the field of mathematical physics.

Simon was recognised for "his fundamental contributions to the mathematical physics of quantum mechanics, quantum field theory, and statistical mechanics, including spectral theory, phase transitions, and geometric phases, and his many books and monographs that have deeply influenced generations of researchers," according to the award citation.

"It is a pleasure and honour to get this award, which my advisor - and eight of my co-authors - previously received," Simon says. "As someone who works between mathematics and physics, it is nice to feel validated by the physics community."

Simon spoke at the International Congress of Mathematics in 1974 and has since given almost every prestigious lecture available in mathematics and physics. He was named a fellow of the American Academy of Arts and Sciences in 2005 and was among the inaugural class of American Mathematical Society fellows in 2012. He has been a fellow of the American Physical Society since 1981. Most recently, Simon received the 2016 Leroy Steele Prize for Lifetime Achievement of the American Mathematical Society. In 2015, Simon was awarded the International János Bolyai Prize of Mathematics by the Hungarian Academy of Sciences, given every five years to honour internationally outstanding works in mathematics, and in 2012, he was given the Henri Poincaré Prize by the International Association of Mathematical Physics. The prize is awarded every three years in recognition of outstanding contributions in mathematical physics and accomplishments leading to novel developments in the field.

Simon received his AB from Harvard College in 1966 and his doctorate in physics from Princeton University in 1970. He held a joint appointment in the mathematics and physics departments at Princeton for the next decade. He first arrived at Caltech as a Sherman Fairchild Distinguished Visiting Scholar in 1980 and joined the faculty permanently in 1981. He became the IBM Professor in 1984 and IBM Professor, Emeritus, in 2016.