Terence Tao

Terence Tao
Born	Terence Chi-Shen Tao 17 7, 1975
Birthplace	Adelaide, South Australia, Australia
Nationality	Australian, American
Occupation	Mathematician, professor
Title	James and Carol Collins Chair in the College of Letters and Sciences
Employer	University of California, Los Angeles
Known for	Partial differential equations, analytic number theory, random matrices, compressed sensing, combinatorics, harmonic analysis
Education	Princeton University (Ph.D., 1996)
Spouse(s)	Laura Tao
Children	2
Awards	Fields Medal (2006), MacArthur Fellowship (2006), Breakthrough Prize in Mathematics (2014)
Website	[https://www.math.ucla.edu/~tao/ Official site]

Terence Chi-Shen Tao (born 17 July 1975) is an Australian-American mathematician who holds the James and Carol Collins Chair in the College of Letters and Sciences at the University of California, Los Angeles (UCLA). Born in Adelaide, South Australia, to Chinese immigrant parents, Tao displayed extraordinary mathematical ability from a remarkably young age, competing in the International Mathematical Olympiad as a child and earning his Ph.D. from Princeton University at the age of twenty. His research spans an unusually broad range of mathematical fields, including harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, and analytic number theory. Tao was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory. He has also received the MacArthur Fellowship (2006), the Royal Medal (2014), and the Breakthrough Prize in Mathematics (2014). The author or co-author of over three hundred research papers, Tao has more recently become a prominent public voice on the applications of artificial intelligence in mathematics.

Early Life

Terence Chi-Shen Tao was born on 17 July 1975 in Adelaide, South Australia, to Billy and Grace Tao, who had emigrated from Hong Kong to Australia. His father, Billy Tao, was a pediatrician, and his mother, Grace, had a background in mathematics and physics. Tao grew up in Adelaide alongside his two younger brothers, Trevor and Nigel, both of whom also demonstrated high academic ability.

Tao's mathematical precocity became apparent at an exceptionally early age. By the age of two, he was reportedly teaching other children to count using number blocks. He began studying university-level mathematics courses while still in primary school, attracting the attention of educators and researchers studying gifted children. His extraordinary abilities drew public attention and media coverage during his childhood, including profiles while he was still in single digits of age.

Tao's participation in the International Mathematical Olympiad (IMO) remains one of the most notable aspects of his youth. He first competed at the IMO in 1986, at the age of ten, making him one of the youngest participants in the competition's history. Over three appearances, he won a bronze medal in 1986, a silver medal in 1987, and a gold medal in 1988, at the age of thirteen — at the time the youngest gold medalist in the history of the competition. This record stood for several decades and illustrated the depth of his mathematical talent even as a child.

His parents, particularly his father, took an active role in managing his education, seeking out mentors and resources to ensure that his abilities were nurtured without the social costs sometimes associated with extreme academic acceleration. Studies of Tao's development as a gifted child have been cited in educational research on talent identification and support.

Education

Tao attended Flinders University in Adelaide, where he earned his bachelor's and master's degrees in mathematics at an early age. He subsequently moved to the United States to pursue doctoral studies at Princeton University, working under the supervision of Elias M. Stein, a distinguished mathematician known for his contributions to harmonic analysis and related fields.

Tao completed his Ph.D. in 1996 at the age of twenty, with a dissertation titled Three Regularity Results in Harmonic Analysis. The dissertation addressed problems in the regularity theory of operators in harmonic analysis, a field that would remain central to Tao's research throughout his career. Following the completion of his doctorate, Tao joined the faculty at UCLA, where he has remained for the entirety of his academic career.

In February 2026, Princeton University honored Tao at its Alumni Day celebration, recognizing him as one of its most distinguished alumni alongside Smithsonian executive Kevin Gover.

Career

Early Academic Career at UCLA

Tao joined the Department of Mathematics at the University of California, Los Angeles shortly after completing his Ph.D. at Princeton in 1996. He was appointed a full professor at UCLA in 1999, at the age of twenty-four, making him one of the youngest individuals to hold such a position at a major American research university. He has held the James and Carol Collins Chair in the College of Letters and Sciences at UCLA, a named professorship reflecting his standing within the university.

Throughout his career at UCLA, Tao has produced an extraordinarily large and diverse body of mathematical research. He has authored or co-authored over three hundred research papers, spanning a range of mathematical disciplines that is unusual in its breadth for a single mathematician. His research areas include harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, analytic number theory, and, more recently, the applications of artificial intelligence in mathematics.

Harmonic Analysis and Partial Differential Equations

Tao's earliest and perhaps most foundational research contributions lie in the fields of harmonic analysis and partial differential equations, the subjects of his doctoral dissertation. His work on the regularity properties of solutions to various classes of partial differential equations has been influential in shaping modern research directions in these areas. He has made significant contributions to the study of dispersive equations, including the Korteweg–de Vries equation and the nonlinear Schrödinger equation, advancing the understanding of the existence, uniqueness, and regularity of solutions to these equations.

The Fields Medal citation in 2006 specifically recognized Tao's contributions to partial differential equations as one of his major areas of achievement. The American Mathematical Society noted the breadth and depth of his work in these areas, describing his contributions as having had a transformative impact on the field.

Additive Combinatorics and Number Theory

One of Tao's most celebrated results came through his collaboration with British mathematician Ben Green. In 2004, Green and Tao proved the Green–Tao theorem, which states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. This result resolved a longstanding conjecture and represented a major advance in additive number theory and combinatorics. The theorem drew upon techniques from harmonic analysis, ergodic theory, and combinatorics, and its proof exemplified the cross-disciplinary approach that characterizes much of Tao's work.

The Fields Medal committee cited this work as one of the primary reasons for Tao's award. The Green–Tao theorem has since stimulated extensive further research in additive combinatorics and analytic number theory, and its techniques have found applications in a variety of other mathematical problems.

Tao's work in combinatorics extends beyond the Green–Tao theorem. He has made contributions to algebraic combinatorics, arithmetic combinatorics, and geometric combinatorics, often applying techniques from one area to resolve problems in another. His collaborative approach — Tao has worked with a large number of co-authors over his career — has been a notable feature of his research output.

Compressed Sensing

In collaboration with Emmanuel Candès, Tao made foundational contributions to the field of compressed sensing, a technique for efficiently acquiring and reconstructing signals. Their work demonstrated that sparse signals can be recovered from far fewer measurements than traditional sampling theory would require, provided certain mathematical conditions are met. This result has had broad applications in signal processing, medical imaging (particularly magnetic resonance imaging), and data science. The Tao–Candès work on compressed sensing is considered one of the most impactful applications of pure mathematical research to practical problems in engineering and science in the early twenty-first century.

Erdős Discrepancy Problem and Other Results

Tao resolved the Erdős discrepancy problem in 2015, a conjecture posed by the Hungarian mathematician Paul Erdős in the 1930s. The problem asked whether, for any sequence of +1s and −1s, the partial sums along homogeneous arithmetic progressions can be made arbitrarily large. Tao's proof confirmed that this is indeed the case, settling a question that had resisted solution for decades. This result further demonstrated Tao's ability to resolve deep, long-standing open problems across different areas of mathematics.

More recently, Tao has been engaged in the intersection of mathematics and artificial intelligence. In early 2026, he noted that OpenAI's GPT-5.2 Pro had solved an open Erdős problem largely on its own, calling it a milestone while cautioning that the result says more about the speed of AI computation than the difficulty of the problem itself.

Artificial Intelligence and Mathematics

In addition to his pure mathematical research, Tao has become a prominent commentator on the role of artificial intelligence and generative AI in mathematical research. As of 2025–2026, he has discussed both the promise and the limitations of AI tools in advancing mathematical discovery. UCLA has highlighted Tao's engagement with these topics, noting his role as an adjudicator of AI-written proofs and his efforts to explain the implications of AI for the future of the discipline. In a February 2026 interview with The Atlantic, Tao discussed the frontier of mathematics and the role that generative AI may play in extending human mathematical capabilities.

Tao's interest in AI in mathematics is part of a broader pattern in his career of engaging with computational and applied aspects of the discipline, including his earlier work on compressed sensing and his use of collaborative online platforms for mathematical research.

Mentorship and Doctoral Students

Throughout his career at UCLA, Tao has supervised a number of doctoral students, several of whom have gone on to prominent academic careers. His doctoral students include Monica Vișan and Tim Austin, both of whom have made significant contributions to their respective areas of mathematics. Tao has also been influential as a mathematical communicator, maintaining an active research blog and publishing expository works aimed at both professional mathematicians and broader audiences.

In December 2025, the Simons Foundation announced that Quanta Books would publish a popular mathematics title by Tao, alongside a popular physics title by David Tong.

Public Engagement and Advocacy

Tao has spoken publicly about science funding and the importance of stable support for mathematical and scientific research. In a September 2025 feature published by UCLA, Tao discussed the impact of funding suspensions on the future of mathematics and science, arguing for the necessity of sustained investment in basic research. He has been described in media coverage as the "Mozart of Math," a moniker reflecting both his prodigious early talent and the breadth of his mature mathematical contributions.

Personal Life

Tao is married to Laura Tao, an engineer. The couple has two children. The family resides in Los Angeles, California, where Tao has been based throughout his academic career at UCLA.

Tao holds both Australian and American citizenship. He has maintained connections to his Australian roots and has been recognized in both countries for his contributions to mathematics.

Tao is known within the mathematical community for his accessibility, collaborative spirit, and prolific output. His research blog, which he has maintained for many years, serves as a platform for mathematical exposition, open problems, and public discussion of research topics. The blog has become a notable resource in the mathematical community, attracting both professional mathematicians and students.

Recognition

Tao has received numerous awards and honors throughout his career. His most significant recognitions include:

• Fields Medal (2006): Awarded at the International Congress of Mathematicians in Madrid "for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory."
• MacArthur Fellowship (2006): Also known as the "genius grant," this award recognized Tao's exceptional creativity and potential for future contributions to mathematics.
• Breakthrough Prize in Mathematics (2014): One of the most lucrative academic prizes in the world, awarded for Tao's cumulative contributions to multiple areas of mathematics.
• Royal Medal (2014): Awarded by the Royal Society for his outstanding contributions to mathematics.
• Crafoord Prize in Mathematics: Tao was among the recipients of this prize, awarded by the Royal Swedish Academy of Sciences for mathematics and related fields.
• Simons Investigator: Tao was named a Simons Investigator by the Simons Foundation, a designation supporting outstanding researchers in mathematics and the sciences.
• Fellow of the American Mathematical Society (AMS): Listed among the inaugural class of AMS Fellows.
• Fellow of the Australian Academy of Science (FAA) and Fellow of the Royal Society (FRS).

In February 2026, Princeton University honored Tao at its Alumni Day, recognizing him as one of its most distinguished graduates.

Legacy

Tao's influence on contemporary mathematics is extensive. His body of work, spanning over three hundred research papers across a dozen or more subfields, has reshaped research directions in harmonic analysis, combinatorics, number theory, and partial differential equations. The Green–Tao theorem, establishing the existence of arbitrarily long arithmetic progressions in the primes, stands as one of the landmark results of early twenty-first-century mathematics. His foundational work with Emmanuel Candès on compressed sensing has had a lasting impact not only within mathematics but also in engineering and applied science.

Tao's career has also served as a case study in the development and support of mathematical talent. His trajectory from child prodigy in Adelaide to Fields Medalist has been the subject of research in gifted education, and his parents' approach to nurturing his abilities has been discussed in educational literature.

As a mathematical communicator, Tao has set a standard for openness and accessibility in modern research mathematics. His blog and expository writings have made advanced mathematical ideas available to a broader audience, and his engagement with artificial intelligence in mathematics has positioned him as a leading voice on the future of the discipline.

The American Mathematical Society's 2009 survey of Tao's work described the breadth and depth of his contributions, noting the range of techniques he has brought to bear on problems across mathematics. His continued productivity and his engagement with emerging technologies suggest that his influence on the field will continue to grow.