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Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the
University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school the ...
(UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences. His research includes topics in harmonic analysis,
partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics,
probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
, compressed sensing and analytic number theory. Tao was born to Chinese immigrant parents and raised in
Adelaide Adelaide ( , ; ) is the list of Australian capital cities, capital and most populous city of South Australia, as well as the list of cities in Australia by population, fifth-most populous city in Australia. The name "Adelaide" may refer to ei ...
. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014, and is a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers, and is widely regarded as one of the greatest living mathematicians.


Life and career


Family

Tao's parents are first generation immigrants from
Hong Kong Hong Kong)., Legally Hong Kong, China in international treaties and organizations. is a special administrative region of China. With 7.5 million residents in a territory, Hong Kong is the fourth most densely populated region in the wor ...
to
Australia Australia, officially the Commonwealth of Australia, is a country comprising mainland Australia, the mainland of the Australia (continent), Australian continent, the island of Tasmania and list of islands of Australia, numerous smaller isl ...
.'' Wen Wei Po'', Page A4, 24 August 2006. Tao's father, Billy Tao, was a Chinese paediatrician who was born in Shanghai and earned his
medical degree A medical degree is a professional degree admitted to those who have passed coursework in the fields of medicine and/or surgery from an accredited medical school. Obtaining a degree in medicine allows for the recipient to continue on into special ...
( MBBS) from the University of Hong Kong in 1969. Tao's mother, Grace Leong, was born in Hong Kong; she received a first-class honours degree in
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
and
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
at the University of Hong Kong.Terence Tao: the Mozart of maths
7 March 2015, Stephanie Wood,
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.
She was a secondary school teacher of mathematics and physics in Hong Kong. Billy and Grace met as students at the University of Hong Kong. They then emigrated from Hong Kong to Australia in 1972. Tao also has two brothers, Trevor and Nigel, who are currently living in Australia. Both formerly represented Australia at the International Mathematical Olympiad. Furthermore, Trevor Tao has been representing Australia internationally in chess and holds the title of Chess International Master. Tao speaks Cantonese but cannot write Chinese. Tao is married to Laura Tao, an electrical engineer at
NASA The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States ...
's Jet Propulsion Laboratory. They live in
Los Angeles Los Angeles, often referred to by its initials L.A., is the List of municipalities in California, most populous city in the U.S. state of California, and the commercial, Financial District, Los Angeles, financial, and Culture of Los Angeles, ...
, California, and have two children.


Childhood

A child prodigy, Terence Tao skipped 5 grades. Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He is one of only three children in the history of the Johns Hopkins Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just eight years old; Tao scored a 760. Julian Stanley, Director of the Study of Mathematically Precocious Youth, stated that Tao had the greatest mathematical reasoning ability he had found in years of intensive searching. Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten; in 1986, 1987, and 1988, he won a bronze, silver, and gold medal, respectively. Tao remains the youngest winner of each of the three medals in the Olympiad's history, having won the gold medal at the age of 13 in 1988.


Career

At age 14, Tao attended the Research Science Institute, a summer program for secondary students. In 1991, he received his bachelor's and master's degrees at the age of 16 from Flinders University under the direction of Garth Gaudry.It's prime time as numbers man Tao tops his Field
Stephen Cauchi, 23 August 2006. Retrieved 31 August 2006.
In 1992, he won a postgraduate Fulbright Scholarship to undertake research in mathematics at
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his PhD at the age of 21. In 1996, he joined the faculty of the
University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school the ...
. In 1999, when he was 24, he was promoted to full professor at UCLA and remains the youngest person ever appointed to that rank by the institution. He is known for his collaborative mindset; by 2006, Tao had worked with over 30 others in his discoveries, reaching 68 co-authors by October 2015. Tao has had a particularly extensive collaboration with British mathematician Ben J. Green; together they proved the Green–Tao theorem, which is well known among both amateur and professional mathematicians. This theorem states that there are arbitrarily long arithmetic progressions of
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
s. ''
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'' described it this way: Many other results of Tao have received mainstream attention in the scientific press, including: * his establishment of finite time blowup for a modification of the Navier–Stokes existence and smoothness Millennium Problem * his 2015 resolution of the Erdős discrepancy problem, which used entropy estimates within analytic number theory * his 2019 progress on the Collatz conjecture, in which he proved the probabilistic claim that almost all Collatz orbits attain almost bounded values. Tao has also resolved or made progress on a number of conjectures. In 2012, Green and Tao announced proofs of the conjectured " orchard-planting problem," which asks for the maximum number of lines through exactly 3 points in a set of n points in the plane, not all on a line. In 2018, with Brad Rodgers, Tao showed that the
de Bruijn–Newman constant The de Bruijn–Newman constant, denoted by \Lambda and named after Nicolaas Govert de Bruijn and Charles Michael Newman, is a mathematical constant defined via the zeros of a certain function H(\lambda,z), where \lambda is a real parameter ...
, the nonpositivity of which is equivalent to the Riemann hypothesis, is nonnegative. In 2020, Tao proved Sendov's conjecture, concerning the locations of the roots and critical points of a complex polynomial, in the special case of polynomials with sufficiently high degree.


Recognition

Tao has won numerous mathematician honours and awards over the years. He is a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
, the Australian Academy of Science (Corresponding Member), the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
(Foreign member), the American Academy of Arts and Sciences, the
American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...
, and the American Mathematical Society. In 2006 he received the Fields Medal; he was the first Australian, the first
UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...
faculty member, and one of the youngest mathematicians to receive the award. He was also awarded the MacArthur Fellowship. He has been featured in ''
The New York Times ''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of ...
'', CNN, ''
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'', '' Popular Science'', and many other media outlets. In 2014, Tao received a CTY Distinguished Alumni Honor from Johns Hopkins Center for Gifted and Talented Youth in front of 979 attendees in 8th and 9th grade that are in the same program from which Tao graduated. In 2021, President
Joe Biden Joseph Robinette Biden Jr. (born November 20, 1942) is an American politician who was the 46th president of the United States from 2021 to 2025. A member of the Democratic Party (United States), Democratic Party, he served as the 47th vice p ...
announced Tao had been selected as one of 30 members of his President's Council of Advisors on Science and Technology, a body bringing together America's most distinguished leaders in science and technology. In 2021, Tao was awarded the Riemann Prize Week as recipient of the inaugural Riemann Prize 2019 by the Riemann International School of Mathematics at the University of Insubria. Tao was a finalist to become Australian of the Year in 2007. As of 2022, Tao had published over three hundred articles, along with sixteen books. He has an Erdős number of 2. He is a highly cited researcher. An article by '' New Scientist'' writes of his ability: British mathematician and Fields medalist Timothy Gowers remarked on Tao's breadth of knowledge:


Research contributions


Dispersive partial differential equations

From 2001 to 2010, Tao was part of a collaboration with James Colliander, Markus Keel, Gigliola Staffilani, and Hideo Takaoka. They found a number of novel results, many to do with the well-posedness of weak solutions, for Schrödinger equations, KdV equations, and KdV-type equations. Michael Christ, Colliander, and Tao developed methods of Carlos Kenig, Gustavo Ponce, and Luis Vega to establish ill-posedness of certain Schrödinger and KdV equations for Sobolev data of sufficiently low exponents. In many cases these results were sharp enough to perfectly complement well-posedness results for sufficiently large exponents as due to Bourgain, Colliander−Keel−Staffilani−Takaoka−Tao, and others. Further such notable results for Schrödinger equations were found by Tao in collaboration with Ioan Bejenaru. A particularly notable result of the Colliander−Keel−Staffilani−Takaoka−Tao collaboration established the long-time existence and scattering theory of a power-law Schrödinger equation in three dimensions. Their methods, which made use of the scale-invariance of the simple power law, were extended by Tao in collaboration with Monica Vișan and Xiaoyi Zhang to deal with nonlinearities in which the scale-invariance is broken. Rowan Killip, Tao, and Vișan later made notable progress on the two-dimensional problem in radial symmetry. An article by Tao in 2001 considered the wave maps equation with two-dimensional domain and spherical range. He built upon earlier innovations of Daniel Tataru, who considered wave maps valued in Minkowski space. Tao proved the global well-posedness of solutions with sufficiently small initial data. The fundamental difficulty is that Tao considers smallness relative to the critical Sobolev norm, which typically requires sophisticated techniques. Tao later adapted some of his work on wave maps to the setting of the Benjamin–Ono equation; Alexandru Ionescu and Kenig later obtained improved results with Tao's methods. In 2016, Tao constructed a variant of the
Navier–Stokes equations The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician Georg ...
which possess solutions exhibiting irregular behavior in finite time. Due to structural similarities between Tao's system and the Navier–Stokes equations themselves, it follows that any positive resolution of the Navier–Stokes existence and smoothness problem must take into account the specific nonlinear structure of the equations. In particular, certain previously proposed resolutions of the problem could not be legitimate. Tao speculated that the Navier–Stokes equations might be able to simulate a Turing complete system, and that as a consequence it might be possible to (negatively) resolve the existence and smoothness problem using a modification of his results. However, such results remain (as of 2024) conjectural.


Harmonic analysis

Bent Fuglede introduced the Fuglede conjecture in the 1970s, positing a tile-based characterisation of those Euclidean domains for which a Fourier ensemble provides a basis of Tao resolved the conjecture in the negative for dimensions larger than 5, based upon the construction of an elementary counterexample to an analogous problem in the setting of finite groups. With Camil Muscalu and Christoph Thiele, Tao considered certain multilinear singular integral operators with the multiplier allowed to degenerate on a hyperplane, identifying conditions which ensure operator continuity relative to spaces. This unified and extended earlier notable results of Ronald Coifman, Carlos Kenig, Michael Lacey, Yves Meyer, Elias Stein, and Thiele, among others. Similar problems were analysed by Tao in 2001 in the context of Bourgain spaces, rather than the usual spaces. Such estimates are used in establishing well-posedness results for dispersive partial differential equations, following famous earlier work of Jean Bourgain, Kenig, Gustavo Ponce, and Luis Vega, among others. A number of Tao's results deal with "restriction" phenomena in Fourier analysis, which have been widely studied since the time of the articles of Charles Fefferman, Robert Strichartz, and Peter Tomas in the 1970s. Here one studies the operation which restricts input functions on Euclidean space to a submanifold and outputs the product of the Fourier transforms of the corresponding measures. It is of major interest to identify exponents such that this operation is continuous relative to spaces. Such multilinear problems originated in the 1990s, including in notable work of Jean Bourgain, Sergiu Klainerman, and Matei Machedon. In collaboration with Ana Vargas and Luis Vega, Tao made some foundational contributions to the study of the bilinear restriction problem, establishing new exponents and drawing connections to the linear restriction problem. They also found analogous results for the bilinear Kakeya problem which is based upon the X-ray transform instead of the Fourier transform. In 2003, Tao adapted ideas developed by Thomas Wolff for bilinear restriction to conical sets into the setting of restriction to quadratic hypersurfaces. The multilinear setting for these problems was further developed by Tao in collaboration with Jonathan Bennett and Anthony Carbery; their work was extensively used by Bourgain and Larry Guth in deriving estimates for general oscillatory integral operators.


Compressed sensing and statistics

In collaboration with Emmanuel Candes and Justin Romberg, Tao has made notable contributions to the field of compressed sensing. In mathematical terms, most of their results identify settings in which a convex optimisation problem correctly computes the solution of an optimisation problem which seems to lack a computationally tractable structure. These problems are of the nature of finding the solution of an underdetermined linear system with the minimal possible number of nonzero entries, referred to as "sparsity". Around the same time, David Donoho considered similar problems from the alternative perspective of high-dimensional geometry. Motivated by striking numerical experiments, Candes, Romberg, and Tao first studied the case where the matrix is given by the discrete Fourier transform. Candes and Tao abstracted the problem and introduced the notion of a "restricted linear isometry," which is a matrix that is quantitatively close to an isometry when restricted to certain subspaces. They showed that it is sufficient for either exact or optimally approximate recovery of sufficiently sparse solutions. Their proofs, which involved the theory of convex duality, were markedly simplified in collaboration with Romberg, to use only linear algebra and elementary ideas of harmonic analysis. These ideas and results were later improved by Candes. Candes and Tao also considered relaxations of the sparsity condition, such as power-law decay of coefficients. They complemented these results by drawing on a large corpus of past results in random matrix theory to show that, according to the Gaussian ensemble, a large number of matrices satisfy the restricted isometry property. In 2007, Candes and Tao introduced a novel statistical estimator for linear regression, which they called the "Dantzig selector." They proved a number of results on its success as an estimator and model selector, roughly in parallel to their earlier work on compressed sensing. A number of other authors have since studied the Dantzig selector, comparing it to similar objects such as the statistical lasso introduced in the 1990s. Trevor Hastie, Robert Tibshirani, and Jerome H. Friedman conclude that it is "somewhat unsatisfactory" in a number of cases. Nonetheless, it remains of significant interest in the statistical literature. In 2009, Candes and Benjamin Recht considered an analogous problem for recovering a matrix from knowledge of only a few of its entries and the information that the matrix is of low rank. They formulated the problem in terms of convex optimisation, studying minimisation of the nuclear norm. Candes and Tao, in 2010, developed further results and techniques for the same problem. Improved results were later found by Recht. Similar problems and results have also been considered by a number of other authors.


Random matrices

In the 1950s, Eugene Wigner initiated the study of random matrices and their eigenvalues. Wigner studied the case of hermitian and symmetric matrices, proving a "semicircle law" for their eigenvalues. In 2010, Tao and Van Vu made a major contribution to the study of non-symmetric random matrices. They showed that if is large and the entries of a matrix are selected randomly according to any fixed
probability distribution In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...
of expectation 0 and
standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
1, then the eigenvalues of will tend to be uniformly scattered across the disk of radius around the origin; this can be made precise using the language of
measure theory In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude (mathematics), magnitude, mass, and probability of events. These seemingl ...
. This gave a proof of the long-conjectured circular law, which had previously been proved in weaker formulations by many other authors. In Tao and Vu's formulation, the circular law becomes an immediate consequence of a "universality principle" stating that the distribution of the eigenvalues can depend only on the average and standard deviation of the given component-by-component probability distribution, thereby providing a reduction of the general circular law to a calculation for specially-chosen probability distributions. In 2011, Tao and Vu established a "four moment theorem", which applies to random hermitian matrices whose components are independently distributed, each with average 0 and standard deviation 1, and which are exponentially unlikely to be large (as for a
Gaussian distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real number, real-valued random variable. The general form of its probability density function is f(x ...
). If one considers two such random matrices which agree on the average value of any quadratic polynomial in the diagonal entries and on the average value of any quartic polynomial in the off-diagonal entries, then Tao and Vu show that the expected value of a large number of functions of the eigenvalues will also coincide, up to an error which is uniformly controllable by the size of the matrix and which becomes arbitrarily small as the size of the matrix increases. Similar results were obtained around the same time by László Erdös, Horng-Tzer Yau, and Jun Yin.


Analytic number theory and arithmetic combinatorics

In 2004, Tao, together with Jean Bourgain and Nets Katz, studied the additive and multiplicative structure of subsets of finite fields of prime order. It is well known that there are no nontrivial subrings of such a field. Bourgain, Katz, and Tao provided a quantitative formulation of this fact, showing that for any subset of such a field, the number of sums and products of elements of the subset must be quantitatively large, as compared to the size of the field and the size of the subset itself. Improvements of their result were later given by Bourgain, Alexey Glibichuk, and Sergei Konyagin. Tao and Ben Green proved the existence of arbitrarily long arithmetic progressions in the
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
s; this result is generally referred to as the Green–Tao theorem, and is among Tao's most well-known results. The source of Green and Tao's arithmetic progressions is Endre Szemerédi's 1975 theorem on existence of arithmetic progressions in certain sets of integers. Green and Tao showed that one can use a "transference principle" to extend the validity of Szemerédi's theorem to further sets of integers. The Green–Tao theorem then arises as a special case, although it is not trivial to show that the prime numbers satisfy the conditions of Green and Tao's extension of the Szemerédi theorem. In 2010, Green and Tao gave a multilinear extension of Dirichlet's celebrated theorem on arithmetic progressions. Given a matrix and a matrix whose components are all integers, Green and Tao give conditions on when there exist infinitely many matrices such that all components of are prime numbers. The proof of Green and Tao was incomplete, as it was conditioned upon unproven conjectures. Those conjectures were proved in later work of Green, Tao, and Tamar Ziegler.


Notable awards

Terence Tao has won numerous awards for his work. He won the Fields Medal, the highest award of mathematics, in 2006. * 1999 – Packard Fellowship * 2000 – Salem Prize for: ::"his work in harmonic analysis and on related questions in geometric measure theory and
partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s." * 2002 – Bôcher Memorial Prize for: ::''Global regularity of wave maps I. Small critical Sobolev norm in high dimensions.'' Internat. Math. Res. Notices (2001), no. 6, 299–328. ::''Global regularity of wave maps II. Small energy in two dimensions.'' Comm. Math. Phys. 2244 (2001), no. 2, 443–544. :in addition to "his remarkable series of papers, written in collaboration with J. Colliander, M. Keel, G. Staffilani, and H. Takaoka, on global regularity in optimal Sobolev spaces for KdV and other equations, as well as his many deep contributions to Strichartz and bilinear estimates." * 2003 – Clay Research Award for: ::his restriction theorems in Fourier analysis, his work on wave maps, his global existence theorems for KdV-type equations, and for his solution with Allen Knutson of Horn's conjecture * 2005 – Australian Mathematical Society Medal * 2005 – Ostrowski Prize (with Ben Green) for: ::"their exceptional achievements in the area of analytic and combinatorial number theory" * 2005 – Levi L.Conant Prize (with Allen Knutson) for: ::their expository article "Honeycombs and Sums of Hermitian Matrices" (Notices of the AMS. 48 (2001), 175–186.) * 2006 – Fields Medal for: ::"his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory" * 2006 – MacArthur Award * 2006 – SASTRA Ramanujan Prize * 2006 – Sloan Fellowship * 2007 –
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
* 2008 – Alan T. Waterman Award for: ::"his surprising and original contributions to many fields of mathematics, including number theory, differential equations, algebra, and harmonic analysis" * 2008 – Onsager Medal for: ::"his combination of mathematical depth, width and volume in a manner unprecedented in contemporary mathematics". His Lars Onsager lecture was entitled "Structure and randomness in the prime numbers" at NTNU, Norway. * 2009 – Inducted into the American Academy of Arts and Sciences * 2010 – King Faisal International Prize * 2010 – Nemmers Prize in Mathematics * 2010 – Polya Prize (with Emmanuel Candès) * 2012 – Crafoord Prize * 2012 – Simons Investigator * 2014 – Breakthrough Prize in Mathematics ::"For numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory." * 2014 – Royal Medal * 2015 – PROSE award in the category of "Mathematics" for: ::"Hilbert's Fifth Problem and Related Topics" * 2019 – Riemann Prize * 2019 – The Carnegie Corporation of New York honored Tao with 2019 Great Immigrant Award. * 2020 – Princess of Asturias Award for Technical and Scientific Research, with Emmanuel Candès, for their work on compressed sensing * 2020 – Bolyai Prize * 2021 – IEEE Jack S. Kilby Signal Processing Medal * 2022 – Global Australian of the Year (Advance Global Australians; Advance.org)World’s greatest mathematician named 2022 Global Australian of the Year
Advance.org, media release 2022-09-08, accessed 2022-09-14
Why this maths genius refuses to work for a hedge fund
Tess Bennett, Australian Financial Review, 2022-09-07, accessed 2022-09-14
* 2022 – Grande Médaille * 2023 – Alexanderson Award (with Kaisa Matomäki, Maksym Radziwiłł, Joni Teräväinen, and Tamar Ziegler) for: ::''Higher uniformity of bounded multiplicative functions in short intervals on average.''
Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...
, Second Series (2023), 197(2): 739–857.


Major publications


Textbooks

* * * * * * * * * * * * * * * * * *


Research articles


Notes


See also

* Cramer conjecture * Erdős discrepancy problem *
Goldbach's weak conjecture In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that : Every odd number greater than 5 can be expressed as the sum of three prime number, prime ...
* Inscribed square problem


References


External links


Terence Tao's home page

Tao's research blog

Tao's MathOverflow page
* * * Terence Tao's entry in th

* {{DEFAULTSORT:Tao, Terence Chi-Shen 1975 births 21st-century American male writers 21st-century American mathematicians 21st-century Australian mathematicians 21st-century science writers Additive combinatorialists American male bloggers American bloggers American people of Chinese descent American people of Hong Kong descent American science writers American textbook writers Australian emigrants to the United States Australian male bloggers Australian people of Chinese descent Australian people of Hong Kong descent Australian science writers Australian textbook writers Clay Research Award recipients Educators from California Fellows of the American Academy of Arts and Sciences Fellows of the American Mathematical Society Fellows of the Australian Academy of Science Fellows of the Royal Society Fields Medalists Flinders University alumni Foreign associates of the National Academy of Sciences Harmonic analysis International Mathematical Olympiad participants Living people MacArthur Fellows Mathematical analysts Mathematicians from California Number theorists Partial differential equation theorists Princeton University alumni Recipients of the SASTRA Ramanujan Prize Science bloggers Scientists from Adelaide Scientists from Los Angeles Simons Investigator Sloan Research Fellows University of California, Los Angeles faculty Writers from Los Angeles Members of the American Philosophical Society