Alex Kontorovich

Born in the former Soviet Union, Kontorovich moved to the United States with his family at age 8; his mother is a mathematician. He has played saxophone since eighth grade and was introduced to klezmer at PrincetonPrinceton UniversityPrinceton University is a private university and Ivy League member in Princeton, New Jersey. Chartered on October 22, 1746 as the College of New Jersey, it moved to Princeton in 1756 and adopted its present name in 1896. Undergraduate education leads to A.B. and B.S.E. degrees and emphasizes small-group discussion, independent research and residential college life. Graduate education spans the humanities, social sciences, natural sciences and engineering. As of October 2026, Christopher L. Eisgruber was president. Its 2026–27 operating budget was $3.407 billion, including $342 million for undergraduate aid.Open the full entry.⁠[1]

He recalled on X that his first paper, with Yakov Sinai in 2002, proved that 3x+1 paths are asymptotically a geometric Brownian motion.⁠[2]

On January 25, 2006, he and Yakov G. Sinai submitted “Structure Theorem for (d,g,h)-Maps” to arXiv, extending an earlier structure theorem for the 3x+1 map to a family of maps determined by coprime integers d and g and a periodic function h.⁠[3]

In 2007 he received a PhD in mathematics from Columbia UniversityColumbia UniversityColumbia University, formally Columbia University in the City of New York, is a private research university in New York City and a member of the Ivy League. Founded in 1754 by royal charter from King George II as King's College, it is the oldest institution of higher education in New York State and the fifth oldest in the United States. It was renamed Columbia College in 1784 and adopted the university name and moved to Manhattan's Morningside Heights in 1896. It has 17 schools and four affiliated colleges, with 35,978 students enrolled in fall 2025. Legal scholar Jennifer L. Mnookin became president on July 1, 2026.Open the full entry and then taught at Brown UniversityBrown UniversityBrown University is a private nonprofit research university in Providence, Rhode Island, and a member of the Ivy League. Chartered by Rhode Island's colonial legislature in 1764, it is known for its undergraduate Open Curriculum, which has no common required core. Christina H. Paxson, president since July 2012, announced on August 3, 2026, that the 2026–27 academic year would be her last in office. As of October 1, 2026, the search for Brown's 20th president remained underway.Open the full entry as an assistant professor until 2010.⁠[4]

That year he released the solo album Deep Minor; he has toured with the Grammy-winning Klezmatics and co-founded the Klez Dispensers.⁠[1]

His music site lists performances from September 2008 to March 2009 with bands including The Klezmatics and The Klez Dispensers in New York, Boston, Krakow and several Spanish cities.⁠[5]

On November 14, 2008, he and Hee Oh, both then at Brown University, submitted a paper to arXiv giving an asymptotic formula for the number of circles of curvature at most T in any bounded Apollonian circle packing and upper bounds for circles of prime curvature in integral packings; it later appeared in the Journal of the AMS.⁠[6]

On July 19, 2011, he and Jean Bourgain submitted “On Zaremba’s Conjecture” to arXiv. Zaremba’s 1971 conjecture predicts that every integer is the denominator of a finite continued fraction with partial quotients bounded by an absolute constant; they confirmed it for a set of density one.⁠[7]

The paper was published in the Annals of Mathematics, volume 180, issue 1 (2014), pages 137–196.⁠[8]

On May 20, 2012, he and Bourgain submitted a paper to arXiv proving that, for a fixed integral primitive Apollonian gasket, almost every admissible integer (in the sense of density) is the curvature of some circle in the gasket.⁠[9]

On August 27, 2012, he submitted the survey “From Apollonius To Zaremba: Local-Global Phenomena in Thin Orbits” to arXiv, explaining how seemingly unrelated arithmetic problems such as the local-global problem for Apollonian gaskets and Zaremba’s conjecture share a common formulation in terms of “thin” orbits.⁠[10]

Published in volume 50 of the Bulletin of the American Mathematical Society, it won him the American Mathematical Society’s 2014 Levi L. Conant Prize; the citation said the article introduces a new field of number theory that has proven extremely fruitful.⁠[11]

He taught at Yale UniversityYale UniversityYale University is a research university in New Haven, Connecticut. Its predecessor, the Collegiate School, received a charter in 1701. Trustees chose New Haven in 1716; the institution became Yale College in 1718 and Yale University in 1887. Yale provides undergraduate, graduate and professional education and has 14 undergraduate residential colleges. As of October 2026, its president was Maurie McInnis, who took office in July 2024. In 2026, Yale expanded aid for incoming undergraduates and celebrated its 325th anniversary.Open the full entry from 2011 and moved to Rutgers University in 2014 as an associate professor, becoming professor in 2017 and Distinguished Professor in 2023.⁠[4]

In 2017 he was elected a Fellow of the American Mathematical Society and became a Kavli Fellow of the National Academy of Sciences; his research has also been recognized with an Alfred P. Sloan Research Fellowship, a Simons Foundation Fellowship, an NSF CAREER award and a von Neumann Fellowship at the Institute for Advanced Study.⁠[12]

In the January 8, 2019, issue of PNAS he and Kei Nakamura introduced the notion of a “crystallographic sphere packing,” exhibited an infinite family of conformally inequivalent such packings with all radii reciprocals of integers, and proved that “superintegral” ones exist only in finitely many commensurability classes, all in at most 20 dimensions.⁠[13]

He was MoMath’s 2020–2021 Distinguished Professor for the Public Dissemination of Mathematics.⁠[12]

On September 1, 2020, he began a one-year term as Distinguished Visiting Professor for the Public Dissemination of Mathematics at the National Museum of Mathematics (MoMath) in New York, succeeding Peter Winkler; already the museum’s dean of academic content, he taught courses including “The Arc of Math, Ancient to Modern.”⁠[14]

He said the structure, harmony and rhythm of music use the same part of his brain that helps him find creative ideas in mathematics.⁠[14]

Outreach videos he has taken part in have over 100 million views, including Quanta Magazine’s January 2021 video on the Riemann hypothesis and Veritasium’s July 2021 video on the 3x+1 problem (42M+ views).⁠[2]

The Journal of the Association for Mathematical Research (JAMR), a diamond open access journal that charges neither authors nor readers, was founded in 2022 by the Association for Mathematical Research and its initial editorial board; Kontorovich has been its founding managing editor since 2023.⁠[15]

In January 2026 he posted “Diamond Open Access: The AMR Experiment” to arXiv, documenting the infrastructure, costs and editorial practices of the AMR’s diamond open access journals.⁠[16]

Since 2024 he and Terence TaoTerence TaoTerence Tao is an Australian-American mathematician and UCLA professor of mathematics whose research spans harmonic analysis, partial differential equations, combinatorics, and analytic number theory; a winner of the Fields Medal and the Breakthrough Prize in Mathematics, he has in recent years promoted AI-assisted mathematical research and formal proofs in Lean.Open the full entry have run the “Prime Number Theorem +” project.⁠[17]

The project aims to formalize in Lean the Prime Number Theorem with classical error term and related results such as the Prime Number Theorem in Arithmetic Progressions, with the Chebotarev density theorem as a stretch goal.⁠[18]

He recalls getting into Lean after hearing Kevin Buzzard’s talks; he said analytic number theory papers can run 100 pages with a thousand constants that must line up, and he used to work in his office from 10 p.m. to 5 a.m. after putting his kids and wife to bed just to hold the details in mind, so Lean was exactly the tool he needed.⁠[19]

In 2024 he founded Rutgers Math Corps.⁠[4]

He brought the Detroit-born Math Corps program to Rutgers University–New Brunswick, running a four-week camp in Scott Hall for about 40 seventh and eighth graders and 20 high school students serving as mentors; he said, “Math is just the vessel through which we try to impart values and good decision making.”⁠[20]

He was on leave in the 2024–2025 academic year, visiting Princeton University in the fall and the Institute for Advanced Study in the spring.⁠[21]

On October 3, 2025, he posted “The Shape of Math To Come” to arXiv, discussing what research mathematics may look like in the age of AI and formal verification; he wrote that he became involved in formalization about five years earlier because of the long, parameter-heavy arguments of analytic number theory.⁠[22]

The paper appears in the proceedings of the 2026 International Congress of Mathematicians in Philadelphia, where he gave a special plenary lecture.⁠[17]

He is chair of the Rutgers mathematics department for 2026–2029, a director and 2026–27 president of the Association for Mathematical Research, and a member of the Strategic Advisory Board of the Lean Focused Research Organization.⁠[21]

He and a Princeton computer science team hold a $3.7 million DARPA expMath award for 2026–2029.⁠[4]

He appeared with Steven BruntonSteven BruntonSteven Brunton is a professor of mechanical engineering at the University of Washington whose research combines machine learning with dynamical systems to model and control complex systems such as fluid flows; with collaborators he introduced the SINDy method for sparse identification of nonlinear dynamics, and he teaches engineering mathematics on YouTube as “eigensteve.”Open the full entry and Ankur MoitraAnkur MoitraAnkur Moitra is an American theoretical computer scientist and mathematician and a professor of mathematics at the Massachusetts Institute of Technology who develops algorithms with provable guarantees for machine learning and statistical inference; he co-authored a paper that won the 2026 Gödel Prize and received the 2026 IEEE Computer Society W. Wallace McDowell Award.Open the full entry on episode 503 of the Lex FridmanLex FridmanLex Fridman is a Soviet-born, US-raised computer scientist and podcast host who works as an MIT research scientist on human-AI interaction and autonomous driving. His Lex Fridman Podcast is known for hours-long conversations with guests including heads of state and technology leaders.Open the full entry Podcast.⁠[23]

Personal website: Public link: https://sites.math.rutgers.edu/~alexk/ (opens in a new window)⁠[21]

X: Public account: https://x.com/AlexKontorovich (opens in a new window)⁠[2]

Brown University: Official website: https://www.brown.edu/ (opens in a new window)⁠[6]

Yale University: Official website: https://www.yale.edu/ (opens in a new window)⁠[8]

Rutgers University: Official website: https://www.rutgers.edu/ (opens in a new window)⁠[20]

Association for Mathematical Research: Official website: https://amathr.org/ (opens in a new window)⁠[15]