Sloan Fellowships for Basic Research for 1983-1984 have been awarded to eighty-eight outstanding scientists, including twenty mathematicians. The recipients were selected on the basis of their exceptional potential to make creative contributions to scientific knowledge. The fellowships, granted by the Alfred P Sloan Foundation, run for two years and are in the amount of $25,000. Candidates for fellowships are nominated by senior scientists familiar with their talents. Fellows need not pursue a specified research project and are free to shift the direction of their research at any time. The grants are administered by the Fellows' institutions.

S S Chern of the University of California, Berkeley, Peter D Lax of New York University, Courant Institute of Mathematical Sciences, and David Mumford of Harvard University are the mathematicians on the fifteen-member selection committee.

The mathematicians awarded Sloan Fellowships for 1983, with their affiliations, are: ... Peter Sarnak (New York University, Courant Institute of Mathematical Sciences) ...

The National Science Foundation recently announced the selection of 200 engineers and scientists to receive the Presidential Young Investigator Awards for 1985. This is the second year in a program begun in 1984. It is expected that 100 new investigators will be selected to receive the five year awards in future years. The awards, which fund research by faculty near the beginning of their academic careers, are intended to help universities attract and retain outstanding young Ph.D.'s who might otherwise pursue non-teaching careers. The awards carry an annual base grant from NSF of $25,000. In addition, NSF will provide up to $37,500 per year to match contributions from non-university sources, bringing the possible total support to $100,000 per year and $500,000 for the five-year term of the award.

Names of 1985 recipients of Presidential Young Investigator Awards in the mathematical sciences, their institutional affiliations and research interest follow: ... Peter Sarnak (Stanford University), Analysis, Number Theory and Geometry ...

3.1. The 1998 George Pólya Prize in Mathematics.

The George Pólya Prize in Mathematics, established by the Society for Industrial and Applied Mathematics, is awarded every four years for a significant contribution, as evidenced by a refereed publication, in an area of mathematics of interest to George Pólya not covered by the George Pólya Prize in Applied Combinatorics or the George Pólya Prize for Mathematical Exposition. Such areas may include approximation theory, complex analysis, number theory, orthogonal polynomials, probability theory, and mathematical discovery and learning. The prize is broadly intended to recognise specific recent work.

The 1998 George Pólya Prize in Mathematics was awarded at the annual meeting in July to Percy Deift, Xin Zhou, and Peter Sarnak for their:-

... pathbreaking extension of steepest descent methods for the asymptotic analysis of oscillatory Riemann-Hilbert problems.

They had introduced a new tool in the theory of orthogonal polynomials which connected the asymptotic behaviour of orthogonal polynomials with a Riemann-Hilbert problem. This was a very successful new tool and several interesting papers using this approach had soon been published.

3.2. SIAM Awards 1998 Pólya Prize.

The George Pólya Prize for 1998 was awarded by the Society for Industrial and Applied Mathematics at its annual meeting in July to Percy Deift of New York University-Courant Institute, Xin Zhou of Duke University, and Peter Sarnak of Princeton University.

The Pólya Prize is awarded every two years for notable contributions in an area of mathematics that was of interest to George Pólya. The prize is awarded alternately for a notable application of combinatorial theory or for a contribution in any of the following areas: approximation theory, complex analysis, number theory, orthogonal polynomials, probability theory, or mathematical discovery and learning. The prize is intended to recognise specific recent work. The prize carries a total cash award of $20,000, which is divided equally among the recipients.

4.1. Iwaniec, Sarnak, and Taylor Receive Ostrowski Prize.

The seventh Ostrowski Prize recognising outstanding mathematical achievement has been awarded to Henryk Iwaniec of Rutgers University; Peter Sarnak of Princeton University, the Institute for Advanced Study in Princeton, and Courant Institute at New York University; and Richard L Taylor of Harvard University.

The prize carries a monetary award of 150,000 Swiss francs (approximately US$87,000) and three fellowships of 30,000 Swiss francs. The jury, consisting of representatives from the universities of Basel, Jerusalem, and Waterloo and from the academies of Denmark and the Netherlands decided to divide the Ostrowski Prize into three equal parts.

4.2. Peter Sarnak wins the 2001 Ostrowski Prize.

Sarnak's work is characterised by an extraordinary span of interests and by great originality. His contributions to number theory and to questions of analysis often motivated by number theory have been very influential in mathematics. Particularly significant are: his work (with N Katz) about universality in spacing of zeros of general $L$-functions over function fields; his work (with collaborators) on the determination of which integers in a totally real number field are representable by a given positive ternary definite quadratic form, a problem previously viewed as out of reach; and his work on quantum chaos, which indicates that the Laplacian eigenvalues of arithmetic congruence modular curves behave differently from physicists' expectations.

4.3. About the Ostrowski Prize.

The Ostrowski Foundation was created by Alexander Ostrowski, for many years a professor at the University of Basel. He left his entire estate to the foundation and stipulated that the income should provide a prize for outstanding recent achievements in pure mathematics and the foundations of numerical mathematics. The prize is awarded every other year. Previous recipients of the Ostrowski Prize are Louis de Branges (1990), Jean Bourgain (1992), Miklos Laczkovich (1994), Marina Ratner (1994), Andrew Wiles (1996), Yuri Nesterenko (1998), Gilles Pisier (1998), Alexander Beilinson (2000), and Helmut Hofer (2000).

5.1. The 2003 Levi L Conant Prize.

The 2003 Levi L Conant Prize was awarded at the 109th Annual Meeting of the American Mathematical Society in Baltimore in January 2003.

The Conant Prize is awarded annually to recognise an outstanding expository paper published in either the Notices of the American Mathematical Society or the Bulletin of the American Mathematical Society in the preceding five years. Established in 2000, the prize honours the memory of Levi L Conant (1857-1916), who was a mathematician at Worcester Polytechnic University. The prize carries a cash award of $1,000.

The Conant Prize is awarded by the American Mathematical Society Council acting on the recommendation of a selection committee. For the 2003 prize the members of the selection committee were: Brian J Parshall, Anthony V Phillips, and Joseph H Silverman.

Previous recipients of the Conant Prize are: Carl Pomerance (2001), and Elliott Lieb and Jakob Yngvason (2002).

The 2003 Conant Prize was awarded to Nicholas Katz and Peter Sarnak. The text that follows presents the committee's citation, brief biographical sketches, and the awardees' response upon receiving the prize.

5.2. The 2003 Levi L Conant Prize Citation.

The Levi L Conant Award in 2003 is granted to Nicholas Katz and Peter Sarnak for their expository paper "Zeroes of zeta functions and symmetry", Bulletin of the American Mathematical Society 36 (1999), 1-26. "Zeroes of zeta functions and symmetry" is a model of high-level exposition. Katz and Sarnak do justice to their beautiful topic, a rich mix of intensive numerical exploration, conjectures, and theorems. The theorems take us deep into Weil-Deligne territory, but the authors manage, with well-chosen, concrete examples, to keep the general mathematical reader on the trail. In this paper, obviously a labour of love, the authors' enthusiasm and wonderment are inescapable and contagious.

5.3. Biographical Sketch: Peter Sarnak.

Peter Sarnak was born on December 18, 1953, in Johannesburg, South Africa. He received his Ph.D. from Stanford University (1980).

Sarnak began his academic career at the Courant Institute of Mathematical Sciences, advancing from assistant professor (1980-83) to associate professor (1983). He moved to Stanford University as a professor of mathematics (1987-91). Since 1991 he has been a professor of mathematics at Princeton University. At Princeton he has also served as the H. Fine Professor (1995-96) and as department chair (1996-99). He was a professor at the Courant Institute (2001-02).

Sarnak was a Sloan Fellow (1983-85) and a Presidential Young Investigator (1985-90). He was a fellow at Hebrew University's Institute of Advanced Studies (1987-88), the Sherman Fairchild Distinguished Scholar at the California Institute of Technology (1989), and a member at the Institute for Advanced Study (1999-2002).

He has published extensively in his areas of research interest, which include number theory and cusp forms.

5.4. Response from Sarnak and Katz.

It is both a great honour and a great pleasure for us to receive the Levi L Conant Award in 2003 for our article "Zeroes of zeta functions and symmetry". We are very pleased to be complimented on our exposition. We are also particularly gratified that our article and the ideas put forth in it have stimulated some very interesting work by others. Some of this work provides partial evidence for our conjectures, which we find reassuring. Even more exciting to us is that much of this work, both analytical and numerical, goes way beyond what we had envisioned and establishes the use of random matrix models as a powerful predictor of what should be true in some very classical questions concerning Dirichlet $L$-functions and the Riemann zeta function.

6.1. The 2005 Frank Nelson Cole Prize in Number Theory.

The 2005 Frank Nelson Cole Prize in Number Theory was awarded at the 111th Annual Meeting of the American Mathematical Society in Atlanta in January 2005.

The Cole Prize in Number Theory is awarded every three years for a notable research memoir in number theory that has appeared during the previous five years (until 2001, the prize was usually awarded every five years). The awarding of this prize alternates with the awarding of the Cole Prize in Algebra, also given every three years. These prizes were established in 1928 to honour Frank Nelson Cole (1861-1926) on the occasion of his retirement as secretary of the American Mathematical Society after twenty-five years of service and as editor-in-chief of the Bulletin for twenty-one years. The endowment was made by Cole, contributions from Society members, and his son, Charles A Cole. The Cole Prize carries a cash award of $5,000.

The Cole Prize in Number Theory is awarded by the American Mathematical Society Council acting on the recommendation of a selection committee. For the 2005 prize the members of the selection committee were: Andrew J Granville, Richard L Taylor (chair), and Marie France Vigneras.

Previous recipients of the Cole Prize in Number Theory are: H S Vandiver (1931), Claude Chevalley (1941), H B Mann (1946), Paul Erdös (1951), John T Tate (1956), Kenkichi Iwasawa (1962), Bernard M Dwork (1962), James B Ax and Simon B Kochen (1967), Wolfgang M Schmidt (1972), Goro Shimura (1977), Robert P Langlands (1982), Barry Mazur (1982), Dorian M Goldfeld (1987), Benedict H Gross and Don B Zagier (1987), Karl Rubin (1992), Paul Vojta (1992), Andrew J Wiles (1997), Henryk Iwaniec (2002), and Richard Taylor (2002).

The 2005 Cole Prize in Number Theory was awarded to Peter Sarnak. The text that follows presents the selection committee's citation, a brief biographical sketch, and the awardee's response upon receiving the prize.

6.2. Citation for Peter Sarnak.

The Frank Nelson Cole Prize in Number Theory is awarded to Peter Sarnak of New York University and Princeton University for his work relating the distribution of zeros of $L$-functions in certain families to the distribution of eigenvalues in a large compact linear group of a type that depends on the family of $L$-functions one is considering. In particular it is awarded for the book Random Matrices, Frobenius Eigenvalues, and Monodromy (with N Katz) in which this Katz-Sarnak philosophy is introduced and in which it is extensively verified in the function field case. This philosophy has had a major impact on the direction of work in analytic number theory. In addition the prize is awarded for the papers "The non-vanishing of central values of automorphic $L$-functions and Landau-Siegel zeros" (with H Iwaniec) and "Low lying zeros of families of $L$-functions" (with H Iwaniec and W Luo) in which this philosophy is tested in the much harder number field case. For example, the second paper shows, subject to suitable Riemann hypotheses, that the low lying zeros of the $L$-functions of modular forms with root number 1 (resp. -1) are distributed like the low lying eigenvalues of a random matrix in $SO(2N)$ (resp. $SO(2N + 1)$) as $N$ gets large.

6.3. Peter Sarnak: Biographical Sketch.

Peter Sarnak was born on December 18, 1953, in Johannesburg, South Africa. He received his Ph.D. from Stanford University in 1980. Sarnak began his academic career at the Courant Institute of Mathematical Sciences, advancing from assistant professor (1980-83) to associate professor (1983). He moved to Stanford University as a professor of mathematics (1987-91). Sarnak has been a professor of mathematics at Princeton University since 1991 and at the Courant Institute since 2001. Since 2002, Sarnak has held the position of Eugene Higgins Professor of Mathematics at Princeton, having served as the H Fine Professor (1995-96) and as department chair (1996-99).

Sarnak was a Sloan Fellow (1983-85) and a Presidential Young Investigator (1985-90). In 1991 he was elected to the American Academy of Arts and Sciences. With P Deift and X Zhou, he received the Pólya Prize of the Society for Industrial and Applied Mathematics in 1998. Sarnak was elected to membership in the National Academy of Sciences (2002), won the AMS's Levi L Conant Prize (jointly with N Katz) in 2003, and held the Rothschild Chair of the Isaac Newton Institute in Cambridge, UK, and the Aisenstadt Chair of the Centre de Recherches Mathématiques in Montreal in 2004. He has sat on numerous editorial boards, oversight committees, and advisory committees, and he has published extensively in the areas of number theory and automorphic forms.

6.4. Response by Peter Sarnak.

It is a great honour for me to receive this prize. I have mostly worked in collaboration with others. Not only has this allowed me to achieve things I could never have done by myself, but it is also more fun (especially when you are stuck, which, of course, is most of the time). This recognition belongs as much to my co-workers as to me.

In my work with Nick Katz cited above, our original aim was to determine if there was a function field analogue of the phenomenon (due to Montgomery and Odlyzko) that the local fluctuations of the distribution of the zeros of the Riemann zeta function are governed by the distributions of the eigenvalues for the Gaussian Unitary Ensemble in random matrix theory. After a lot of false starts and misunderstandings, we found such an analogue. Its source lay in the analysis of the large n limit of monodromy groups associated with families of such zeta functions. This led naturally to the possibility that the distribution of low lying zeros of a family of automorphic $L$-functions might also be governed in a decisive way by a symmetry type associated with the family. The extensive numerical computations of zeros of such $L$-functions by Mike Rubinstein, who was a graduate student at Princeton at that time, gave us valuable evidence for this belief.

The paper with Henryk Iwaniec and Wenzhi Luo, cited above, developed methods to study these questions for $L$-functions of automorphic forms. The paper with Iwaniec does the same for the related problem of the quantitative study of non-vanishing of such $L$-functions at special points on the critical line and its arithmetical applications. This allowed for the verification of aspects of the conjectured distribution of zeros as dictated by the symmetry.

One of my greatest pleasures in connection with these works has been to see how others have picked up on these ideas and run with them, far beyond what I had anticipated. Let me mention in particular the remarkable conjectures for the moments of central values of families of $L$-functions (Keating, Snaith, Conrey, Farmer, and Rubinstein) and the determination of some of these moments as well as far-reaching quantitative non-vanishing results for such central values (Kowalski, Michel, Soundararajan, and VanderKam).

Finally, it was Paul Cohen who many years ago, when I was a student at Stanford, pointed me to Montgomery's work on the pair-correlation of the zeros of zeta and its connection to random matrix theory and asked, why is it so?

My efforts to try to answer that question began with a paper with Zeev Rudnick on the higher correlations for zeros of the zeta function and led eventually to the works cited above.

7.1. The Paul R Halmos-Lester R Ford Awards.

The Paul R Halmos-Lester R Ford Awards recognise authors of articles of expository excellence published in The American Mathematical Monthly. This award is $1,000 and up to four awards may be awarded each year. The awards were established in 1964 as the Ford awards, named for Lester R Ford, Sr., a distinguished mathematician, editor of The American Mathematical Monthly, 1942-1946, and President of the Mathematical Association of America, 1947-1948. In 2012, the Board of Governors designated these awards as the Paul R Halmos-Lester R Ford Awards to recognise the support for the awards provided by the Halmos family and to recognise Paul R Halmos, a distinguished mathematician and editor of The Monthly, 1982-1986.

7.2. The 2012 Paul R Halmos-Lester R Ford Prize.

The 2012 Paul R Halmos-Lester R Ford Prize was awarded to: David A Cox for the paper Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First; Ravi Vakil for the paper The Mathematics of Doodling; Peter Sarnak for the paper Integral Apollonian Packings; Graham Everest and Tom Ward for their paper A Repulsion Motif in Diophantine Equations.

7.3. Abstract of Integral Apollonian Packings.

We review the construction of integral Apollonian circle packings. There are a number of Diophantine problems that arise in the context of such packings. We discuss some of them and describe some recent advances.

8.1. Sarnak Awarded 2014 Wolf Prize in Mathematics.

The 2014 Wolf Prize in Mathematics was awarded to Peter Sarnak of Princeton University and the Institute for Advanced Study:-

... for his deep contributions to analysis, number theory, geometry, and combinatorics.

8.2. Description of the Prizewinner's Work.

Following is the citation from the Wolf Foundation.

Peter Sarnak is a mathematician covering an extremely broad spectrum with a far-reaching vision. He has influenced the development of several mathematical fields, often by uncovering deep and unsuspected connections. In analysis, he investigated eigenfunctions of quantum mechanical Hamiltonians which correspond to chaotic classical dynamical systems in a series of fundamental papers. He formulated and supported the "Quantum Unique Ergodicity Conjecture," asserting that all eigenfunctions of the Laplacian on negatively curved manifolds are uniformly distributed in phase space. Sarnak's introduction of tools from number theory into this domain allowed him to obtain results which had seemed out of reach and paved the way for much further progress, in particular the recent works of E Lindenstrauss and N Anantharaman. In his work on $L$-functions (jointly with Z Rudnick) the relationship of contemporary research on automorphic forms to random matrix theory and the Riemann hypothesis is brought to a new level by the computation of higher correlation functions of the Riemann zeros. This is a major step forward in the exploration of the link between random matrix theory and the statistical properties of zeros of the Riemann zeta function going back to H Montgomery and A Odlyzko. In 1999 it culminated in the fundamental work, jointly with N Katz, on the statistical properties of low-lying zeros of families of $L$-functions. Sarnak's work (with A Lubotzky and R Philips) on Ramanujan graphs had a huge impact on combinatorics and computer science. Here again he used deep results in number theory to make surprising and important advances in another discipline.

By his insights and his readiness to share ideas he has inspired the work of students and fellow researchers in many areas of mathematics.

8.3. Biographical Sketch of Peter Sarnak.

Peter Sarnak was born in Johannesburg, South Africa, in 1953. He received his Ph.D. from Stanford University in 1980 under the direction of Paul Cohen. He has held positions at the Courant Institute of Mathematical Sciences, New York University (1980-1983 and 2001-2005); Stanford University (1984-1991); Princeton University (1991-1999 and 2002-present); and the Institute for Advanced Study (member, 1999-2002, 2005-2007; professor, 2007-present). He is currently the Eugene Higgins Professor of Mathematics at Princeton University, as well as a professor at the Institute for Advanced Study in Princeton.

Sarnak held an Alfred P Sloan Foundation Fellowship from 1983 to 1985. He was chosen as a Presidential Young Investigator (1985-1990). He was awarded the Polya Prize of the Society of Industrial and Applied Mathematics (SIAM) in 1998 and the Ostrowski Prize in 2001. In 2003, Sarnak and his coauthor Nicholas Katz received the AMS Conant Prize for their article "Zeroes of zeta functions and symmetry", which appeared in the Bulletin of the American Mathematical Society 36 (1999), 1-26. Sarnak also received the American Mathematical Society Cole Prize in Number Theory in 2005 for his fundamental contributions to number theory and, in particular, his book Random Matrices, Frobenius Eigenvalues and Monodromy, written jointly with Katz. He was awarded the Lester Ford Prize of the Mathematical Association of America (MAA) in 2012. He has been elected to the American Academy of Arts and Sciences (1991), the National Academy of Sciences (2002), and the American Philosophical Society (2008). He was elected a fellow of the Royal Society of London in 2002.

8.4. About the Wolf Prize.

The Wolf Prize carries a cash award of US$100,000. The science prizes are given annually in the areas of agriculture, chemistry, mathematics, medicine, and physics. Laureates receive their awards from the president of the State of Israel in a special ceremony at the Knesset building (Israel's parliament) in Jerusalem.

8.5. NJ academics collect top prizes in Israel.

In June 2014, two New Jerseyans travelled to Israel to collect their Wolf Prizes, academic honours that in various fields rival or anticipate the Nobel Prizes. The awards highlight achievements in science, medicine, mathematics, agriculture, and the arts.

Recently, New Jersey Jewish News had a chance to talk with both local winners. Dr Joachim Messing, director of Rutgers University's Waksman Institute of Microbiology, won the 2013 Wolf Prize in Agriculture, and Prof Peter Sarnak, of the Institute for Advanced Study and Princeton University, who won the 2014 prize in mathematics.

Sarnak, a graduate of the University of Witwatersrand in Johannesburg, South Africa, and Stanford University in California, is the Eugene Higgins Professor of Mathematics at Princeton, and also serves on the permanent faculty at the School of Mathematics of the Institute for Advanced Study. The foundation said of him, "By his insights and his readiness to share ideas he has inspired the work of students and fellow researchers in many areas of mathematics."

He received the award for his achievements in number theory, "uncovering deep and unsuspected connections" among various mathematical fields, according to the prize committee.

"Given the modern digital world, this classical topic, which was considered to be theoretical and pure, is today quite central in many applications," Sarnak said.

"Being added to this list is very humbling for me," he said. That the award is based in Israel was significant as well, he said; the country is one of the "leading centres" in mathematics.

"They have fantastic talent at every level," said Sarnak. "This has been the case for some time and especially after the influx to Israel of many Russians in the last 30 years."

One condition of receiving the award, Sarnak pointed out, is a willingness to come to Israel to receive it. The ceremony took place at the Knesset.

"Some people have used the opportunity to express criticism of Israel, and the Wolf people place no restriction on that," said Sarnak, who is the grandson of one of Johannesburg's leading rabbis and lived in Israel for three years as a child. In accepting the award, he said, "... recipients are making it clear that they are not among those boycotting the country."

9.1. Royal Society Sylvester Medal awarded to Peter Sarnak.

The Sylvester Medal is awarded annually by the Royal Society of London for outstanding contributions in the field of mathematics. The award was created in memory of the mathematician James Joseph Sylvester FRS, who was Savilian Professor of Geometry at the University of Oxford in the 1880s. It was first awarded in 1901. The medal is of bronze, is now awarded annually and is accompanied by a gift of £2,000.

The Royal Society of London awarded Peter Sarnak its Sylvester Medal in 2019:-

... for transformational contributions across number theory, combinatorics, analysis and geometry.

When awarded the Medal in 2019, Sarnak became the 10th non-British citizen to be awarded the Sylvester Medal of the Royal Society.

9.2. Peter Sarnak's Royal Society biography.

Peter Sarnak has made major contributions to analysis and number theory. He is widely recognised internationally as one of the leading analytic number theorists of his generation. His early work on the existence of cusp forms led to the disproof of a conjecture of Selberg. He has obtained the strongest known bounds towards the Ramanujan conjectures for sparse graphs, and he was one of the first to exploit connections between certain questions of theoretical physics and analytic number theory. There are fundamental contributions to arithmetical quantum chaos, a term which he introduced, and to the relationship between random matrix theory and the zeros of $L$-functions. His work on subconvexity for Rankin-Selberg $L$-functions led to the resolution of Hilbert's eleventh problem.

9.3. Princeton University announcement.

The Royal Society has announced that Peter Sarnak is one of 24 winners of its annual medals and awards for "scientists who have done exceptional, ground-breaking work," said Venki Ramakrishnan, president of the Royal Society.

The Sylvester Medal is awarded annually to an outstanding researcher in the field of mathematics. Sarnak, the Eugene Higgins Professor of Mathematics at Princeton and a professor of mathematics at the Institute for Advanced Study, was recognized for his "transformational contributions across number theory, combinatorics, analysis and geometry." Sarnak has been a member of the American Academy of Arts & Sciences since 1991, and he was elected to both the (US) National Academy of Sciences and the (UK) Royal Society in 2002.

He will receive the medal and a gift of £2,000 at the Royal Society's Anniversary Day meeting on 29 November. Recent winners of the Sylvester Medal include Timothy Gowers, a visiting professor at Princeton from 2000 to 2002, and Ben Green, a visiting graduate student during the 2000-2001 school year.