Terence Tao

Terence Tao

FAA FRS

Tao at UCLA in 2014.

Born (1975-07-17) 17 July 1975 (age 50) Adelaide , South Australia, Australia Citizenship

• Australia • United States [3]

Education

• Flinders University (BSc , MSc )

• Princeton University (PhD )

Known for Partial differential equations , analytic number theory , random matrices , compressed sensing , combinatorics , dynamical systems Spouse Laura Tao Children 2 Awards Fields Medal  (2006)

List

• Salem Prize (2000) • Bôcher Memorial Prize (2002) • Clay Research Award (2003) • Australian Mathematical Society Medal (2005) • Ostrowski Prize (2005)

• Levi L. Conant Prize (2005) • MacArthur Award (2006) • SASTRA Ramanujan Prize (2006) • Sloan Fellowship (2006) • Fellow of the Royal Society (2007)

• Alan T. Waterman Award (2008) • Onsager Medal (2008) • King Faisal International Prize (2010) [1] • Nemmers Prize in Mathematics (2010)

• Pólya Prize (2010) [2] • Crafoord Prize (2012) • Simons Investigator (2012) • Breakthrough Prize in Mathematics (2014)

• Royal Medal (2014) • PROSE Award (2015) • Riemann Prize (2019) • Princess of Asturias Award (2020) • Bolyai Prize (2020) • IEEE Jack S. Kilby Signal Processing Medal (2021) • Global Australian of the Year Award (2022) • Grande Médaille (2023) • Best Paper Award (2023) • Alexanderson Award (2023) • James Madison medal (2025)

• Scientific career Fields Harmonic analysis Institutions University of California, Los Angeles Thesis Three Regularity Results in Harmonic Analysis [3]  (1996) Doctoral advisor Elias M. Stein Doctoral students Monica Vișan , Tim Austin Website •

• University site • Personal blog • Microblog site • YouTube channel

• Terence Tao • • Traditional Chinese 陶哲軒 Simplified Chinese 陶哲轩 • Transcriptions Standard Mandarin Hanyu Pinyin Táo Zhéxuān IPA [tʰǎʊ ʈʂɤ̌.ɕyán] Wu Romanization Dau2 Tseq4 Xi1 (Shanghainese) Yue: Cantonese Yale Romanization Tòuh Jit-hīn Jyutping Tou4 Zit3 Hin1 IPA [tʰɔw˩ tsit̚˧.hin˥] •

Terence Chi-Shen Tao FAA FRS (Chinese: 陶哲軒, born 17 July 1975) is an Australian and American mathematician of considerable repute. He is a distinguished Fields medalist and currently holds a professorship in mathematics at the University of California, Los Angeles (UCLA), where he occupies the esteemed James and Carol Collins Chair within the College of Letters and Science . His extensive research interests span a wide spectrum of mathematical disciplines, including harmonic analysis , partial differential equations , algebraic combinatorics , arithmetic combinatorics , geometric combinatorics , probability theory , compressed sensing , analytic number theory , and the burgeoning applications of artificial intelligence in mathematics .

Tao, born to parents who immigrated from Hong Kong, was raised in Adelaide , South Australia. His prodigious talent was recognized early, culminating in his receipt of the prestigious Fields Medal in 2006. Further accolades include the Royal Medal and the Breakthrough Prize in Mathematics in 2014, and he was named a 2006 MacArthur Fellow . By the time of this writing, Tao has authored or co-authored more than three hundred scholarly papers, [6] cementing his reputation as one of the most influential living mathematicians worldwide. [7] [8] [9] [10] [11]

Early life and career

Family

Terence Tao’s lineage traces back to ethnic Chinese immigrants from Hong Kong who settled in Australia . [12] His father, Billy Tao, [a] is a distinguished paediatrician who was born in Shanghai . He earned his medical degree (MBBS ) from the University of Hong Kong in 1969. [13] Tao’s mother, Grace Leong, [b] also a native of Hong Kong, graduated from the University of Hong Kong with a first-class honours bachelor’s degree, majoring in both mathematics and physics . [11] Prior to their emigration, she was an accomplished secondary school teacher of mathematics and physics in Hong Kong. [14] Billy and Grace first met as students at the University of Hong Kong, and they subsequently relocated from Hong Kong to Australia in 1972. [11] [12]

Terence Tao is one of three brothers; his siblings, Trevor and Nigel, also reside in Australia. Both Trevor and Nigel have represented Australia with distinction at the International Mathematical Olympiad . [16] [17] Trevor Tao, additionally, has achieved international recognition in chess, holding the esteemed title of Chess International Master. [18]

Childhood

Recognized as a true child prodigy , [19] Terence Tao displayed an astonishing ability to accelerate his education, notably skipping five grades in his schooling. [20] [21] His innate mathematical prowess became evident from a remarkably young age, leading him to enroll in university-level mathematics courses by the age of nine. He is among a select group of individuals in the history of the Johns Hopkins Study of Exceptional Talent program to achieve a score of 700 or higher on the SAT mathematics section while merely eight years old, a feat he accomplished with a score of 760. [22] Julian Stanley , the Director of the Study of Mathematically Precocious Youth , once remarked that Tao possessed the most exceptional mathematical reasoning ability he had encountered in his extensive years of searching for such talent. [7] [23]

Tao holds the distinction of being the youngest participant in the history of the International Mathematical Olympiad . He first competed at the tender age of ten. Over his three participations in 1986, 1987, and 1988, he secured a bronze, silver, and gold medal, respectively. To this day, Tao remains the youngest recipient of each of these three medals in the Olympiad’s history, a testament to his extraordinary early achievements. [24]

Career

At the age of fourteen, Tao was admitted to the prestigious Research Science Institute , an intensive summer program designed for gifted secondary school students. By 1991, he had attained both his bachelor’s and master’s degrees from Flinders University , under the guidance of Professor Garth Gaudry, at the remarkably young age of sixteen. [25] In 1992, he was awarded a coveted postgraduate Fulbright Scholarship , enabling him to pursue research in mathematics at the renowned Princeton University in the United States. From 1992 to 1996, Tao was a doctoral candidate at Princeton, working under the supervision of the distinguished Elias Stein , and he successfully defended his PhD dissertation at the age of twenty-one. [25] In 1996, he accepted a faculty position at the University of California, Los Angeles . By 1999, at the age of twenty-four, he achieved the rank of full professor at UCLA, a distinction that still marks him as the youngest individual ever appointed to such a position by the institution. [25]

A defining characteristic of Tao’s scientific approach is his profound commitment to collaboration. By 2006, he had already engaged in collaborative research with over thirty individuals, leading to numerous discoveries. [7] This collaborative spirit continued to flourish, with his list of co-authors expanding to 68 by October 2015.

One of Tao’s most celebrated collaborations has been with the British mathematician Ben J. Green . Together, they achieved a landmark result with their proof of the Green–Tao theorem , a theorem that has garnered significant attention and admiration within both amateur and professional mathematical circles. This profound theorem asserts the existence of arbitrarily long arithmetic progressions composed entirely of prime numbers . The significance of this discovery was eloquently captured by The New York Times , which described it as follows: [26] [27]

In 2004, Dr. Tao, working in tandem with Ben Green, a mathematician now affiliated with the University of Oxford in England, resolved a long-standing problem concerning the Twin Prime Conjecture . Their approach involved an in-depth analysis of prime number progressions – sequences of numbers that are equally spaced. For instance, the numbers 3, 7, and 11 form a progression of prime numbers with a common difference of 4; however, the subsequent number in this sequence, 15, is not prime. Dr. Tao and Dr. Green demonstrated that, within the infinite expanse of integers, it is invariably possible to locate a progression of prime numbers that share a uniform spacing and can extend to any desired length.

Beyond the Green–Tao theorem, numerous other contributions from Tao have garnered widespread recognition in the scientific media. These include:

• His groundbreaking establishment of finite time blowup for a modified version of the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems . [28]

• His 2015 resolution of the notoriously difficult Erdős discrepancy problem . This achievement utilized sophisticated entropy estimates within the field of analytic number theory . [29]

• His significant progress in 2019 on the enigmatic Collatz conjecture . In this work, he proved a probabilistic assertion that nearly all Collatz orbits achieve values that are bounded within a certain range. [30]

Tao has also been instrumental in resolving or advancing progress on a number of other significant conjectures. In 2012, Green and Tao announced proofs for the conjectured solution to the “orchard-planting problem ,” a problem that seeks to determine the maximum number of lines that can intersect exactly three points within a given set of $n$ points in a plane, provided not all points are collinear. In 2018, in collaboration with Brad Rodgers, Tao demonstrated that the de Bruijn–Newman constant —the nonpositivity of which is mathematically equivalent to the truth of the Riemann hypothesis —is, in fact, nonnegative. [31] Further advancing the frontiers of mathematical understanding, in 2020, Tao provided a proof for Sendov’s conjecture , which pertains to the geometric locations of the roots and critical points of a complex polynomial, specifically in the case of polynomials with a sufficiently high degree . [32] Between 2024 and 2025, Tao has also tackled and solved several problems posed by the prolific mathematician Paul Erdős, specifically problems numbered #121, #442, #135, #685, #69, and #1102.

Recognition

Tao at the International Congress of Mathematicians (ICM) in 2006.

Terence Tao has been the recipient of a multitude of prestigious awards and honors throughout his distinguished career. [33] He holds the esteemed title of Fellow of the Royal Society and is a member of the Australian Academy of Science (as a Corresponding Member), the National Academy of Sciences (as a Foreign member), the American Academy of Arts and Sciences , the American Philosophical Society , [34] and the American Mathematical Society . [35] In 2006, he was awarded the Fields Medal , the highest honor in mathematics, making him the first Australian, the first faculty member from UCLA , and one of the youngest mathematicians ever to receive this prestigious prize. [36] [37] That same year, he was also honored with a MacArthur Fellowship . His work and achievements have been extensively covered by major media outlets, including The New York Times , CNN , USA Today , and Popular Science , among others. [38] In 2014, Tao was recognized with a CTY Distinguished Alumni Honor from the Johns Hopkins Center for Gifted and Talented Youth , an award presented in front of an audience of 979 eighth and ninth graders participating in the same program from which Tao himself graduated. In 2021, President Joe Biden announced Tao’s appointment as one of the 30 distinguished members of his President’s Council of Advisors on Science and Technology , a council comprising America’s leading experts in science and technology. [39] In 2021, Tao was also the recipient of the inaugural Riemann Prize 2019, celebrated during Riemann Prize Week at the University of Insubria . [40] In 2007, Tao was a finalist for the highly coveted Australian of the Year award. [41]

As of 2022, Tao’s publication record includes over three hundred articles and sixteen books. [42] He possesses an Erdős number of 2, signifying his close connection to the influential mathematician Paul Erdős. [43] He is also consistently recognized as a highly cited researcher , indicating the significant impact of his work. [44] [45]

A profile in New Scientist magazine [46] eloquently describes his remarkable capabilities:

“Such is Tao’s reputation that mathematicians now compete to interest him in their problems, and he is becoming a kind of Mr. Fix-it for frustrated researchers. ‘If you’re stuck on a problem, then one way out is to interest Terence Tao,’ says Charles Fefferman , a professor of mathematics at Princeton University.” [36]

The renowned British mathematician and Fields medalist Timothy Gowers has commented on the extraordinary breadth of Tao’s mathematical knowledge: [47]

“Tao’s mathematical knowledge has an extraordinary combination of breadth and depth: he can write confidently and authoritatively on topics as diverse as partial differential equations, analytic number theory, the geometry of 3-manifolds, nonstandard analysis, group theory, model theory, quantum mechanics, probability, ergodic theory, combinatorics, harmonic analysis, image processing, functional analysis, and many others. Some of these are areas to which he has made fundamental contributions. Others are areas that he appears to understand at the deep intuitive level of an expert despite officially not working in those areas. How he does all this, as well as writing papers and books at a prodigious rate, is a complete mystery. It has been said that David Hilbert was the last person to know all of mathematics, but it is not easy to find gaps in Tao’s knowledge, and if you do then you may well find that the gaps have been filled a year later.”

Research contributions

Dispersive partial differential equations

From 2001 to 2010, Tao was a key participant in a significant collaboration with James Colliander , Markus Keel, Gigliola Staffilani , and Hideo Takaoka. Their collective efforts yielded numerous novel results, particularly concerning the well-posedness of weak solutions for various fundamental equations, including Schrödinger equations , KdV equations , and related KdV-type equations. [C+03] Tao, at the age of 10, pictured with the eminent mathematician Paul Erdős in 1985. Working alongside Michael Christ , Colliander, and Tao developed innovative methods, building upon the foundations laid by Carlos Kenig , Gustavo Ponce , and Luis Vega , to establish the conditions under which certain Schrödinger and KdV equations exhibit ill-posedness when dealing with Sobolev data of sufficiently low exponents. [CCT03] [48] Crucially, these results demonstrated a level of sharpness that perfectly complemented existing well-posedness results for higher exponents, contributions made by researchers such as Bourgain, Colliander−Keel−Staffilani−Takaoka−Tao, and others. Further significant findings concerning Schrödinger equations were achieved by Tao in his collaborative work with Ioan Bejenaru. [BT06]

A particularly noteworthy achievement from the Colliander−Keel−Staffilani−Takaoka−Tao collaboration was the establishment of the long-time existence and scattering theory for a power-law Schrödinger equation in three dimensions. [C+08] The ingenious methods employed in this work, which cleverly exploited the scale-invariance inherent in the simple power law, were later extended by Tao, in collaboration with Monica Vișan and Xiaoyi Zhang, to address nonlinearities where this scale-invariance is disrupted. [TVZ07] Subsequently, Rowan Killip , Tao, and Vișan made significant advancements on the two-dimensional version of this problem, specifically within the context of radial symmetry. [KTV09]

In a significant 2001 publication, Tao delved into the intricacies of the wave maps equation when applied to a two-dimensional domain and a spherical range. [T01a] This work built directly upon the pioneering innovations of Daniel Tataru , who had previously investigated wave maps within the framework of Minkowski space . [49] Tao’s contribution was the proof of global well-posedness for solutions characterized by sufficiently small initial data. The inherent complexity lay in Tao’s consideration of smallness relative to the critical Sobolev norm, a requirement that necessitated the development and application of highly sophisticated techniques. Tao later adapted some of these groundbreaking methods, originally developed for wave maps, to the domain of the Benjamin–Ono equation ; Alexandru Ionescu and Kenig subsequently achieved improved results by leveraging Tao’s established methodologies. [T04a] [50]

A pivotal moment in the study of the Navier–Stokes equations occurred in 2016 when Tao constructed a modified system that exhibited solutions displaying irregular behavior within a finite timeframe. [T16] This construction carried profound implications for the Navier–Stokes existence and smoothness problem , a major unsolved problem in mathematics. The structural similarities between Tao’s modified system and the original Navier–Stokes equations implied that any valid resolution to the existence and smoothness problem would need to meticulously account for the specific nonlinear structure of the equations. Consequently, certain previously proposed theoretical resolutions were rendered untenable. [51] Tao further speculated that the Navier–Stokes equations might possess the capacity to simulate a Turing complete system. If true, this would suggest the possibility of negatively resolving the existence and smoothness problem through modifications inspired by his earlier work. [7] [28] However, it is important to note that such results remain conjectural as of 2025.

Harmonic analysis

The Fuglede conjecture , introduced by Bent Fuglede in the 1970s, proposed a characterization of Euclidean domains for which a Fourier ensemble could form a basis of L² based on tiling properties. [52] Tao provided a decisive resolution to this conjecture, proving it false for dimensions exceeding five. His proof relied on the construction of a fundamental counterexample within the context of finite groups . [T04b]

In collaboration with Camil Muscalu and Christoph Thiele , Tao investigated a specific class of multilinear singular integral operators where the multiplier function was permitted to degenerate on a hyperplane. They successfully identified the precise conditions necessary to guarantee operator continuity with respect to Lᵖ spaces. [MTT02] This work unified and significantly extended prior seminal results established by researchers such as Ronald Coifman , Carlos Kenig , Michael Lacey , Yves Meyer , Elias Stein , and Thiele. [53] [54] [55] [56] [57] [58] Tao explored similar mathematical problems in 2001, applying the framework of Bourgain spaces rather than the conventional Lᵖ spaces. [T01b] The estimates derived from this research have proven invaluable in establishing well-posedness results for nonlinear dispersive partial differential equations, building upon the foundational work of Jean Bourgain , Kenig, Gustavo Ponce , and Luis Vega , among others. [59] [60]

A substantial portion of Tao’s research contributions address “restriction” phenomena within Fourier analysis, a topic that has been a subject of intense study since the groundbreaking papers of Charles Fefferman , Robert Strichartz , and Peter Tomas in the 1970s. [61] [62] [63] The core of this research involves examining an operation that restricts input functions defined on Euclidean space to a submanifold and subsequently outputs the product of the Fourier transforms of the corresponding measures. A central question is the identification of the specific exponents for which this operation maintains continuity with respect to Lᵖ spaces. Multilinear extensions of these problems emerged in the 1990s, notably through the significant work of Jean Bourgain , Sergiu Klainerman , and Matei Machedon . [64] [65] [66] In collaboration with Ana Vargas and Luis Vega , Tao made foundational contributions to the investigation of the bilinear restriction problem, establishing novel exponents and uncovering connections to the linear restriction problem. Their research also yielded analogous results for the bilinear Kakeya problem, which utilizes the X-ray transform in place of the Fourier transform. [TVV98] In 2003, Tao ingeniously adapted techniques developed by Thomas Wolff for bilinear restriction to conical sets, applying them to the context of restriction to quadratic hypersurfaces. [T03] [67] The multilinear framework for these complex problems was further elaborated by Tao in his collaborations with Jonathan Bennett and Anthony Carbery. Their comprehensive work proved instrumental for Bourgain and Larry Guth in deriving crucial estimates for general oscillatory integral operators . [BCT06] [68]

Compressed sensing and statistics

Working alongside Emmanuel Candes and Justin Romberg, Tao has made substantial contributions to the rapidly evolving field of compressed sensing . From a mathematical perspective, a significant portion of their research focuses on identifying scenarios where a convex optimization problem can accurately recover the solution to a seemingly intractable optimization problem, particularly those involving finding the sparsest solution (i.e., the solution with the fewest non-zero entries) to an underdetermined linear system. Around the same period, David Donoho explored analogous problems through the lens of high-dimensional geometry. [69]

Initially motivated by striking numerical outcomes, Candes, Romberg, and Tao focused their early investigations on the specific case where the measurement matrix is derived from the discrete Fourier transform. [CRT06a] Candes and Tao then generalized this problem, introducing the concept of a “restricted isometry property.” This property quantifies how closely a matrix approximates an isometry when its action is restricted to specific subspaces. [CT05] They demonstrated that satisfying this property is a sufficient condition for the exact or optimally approximate recovery of sufficiently sparse solutions. Their proofs, which initially relied on the theory of convex duality, were subsequently simplified through collaboration with Romberg, utilizing only fundamental principles of linear algebra and harmonic analysis. [CRT06b] These insights and findings were later refined and expanded upon by Candes. [70] Candes and Tao also examined relaxations of the sparsity condition, exploring scenarios involving power-law decay of coefficients. [CT06] Complementing these theoretical advancements, they drew upon a substantial body of existing research in random matrix theory to establish that a significant proportion of matrices naturally satisfy the restricted isometry property, particularly within the context of the Gaussian ensemble. [CT06]

In 2007, Candes and Tao introduced a novel statistical estimation technique for linear regression, which they aptly named the “Dantzig selector.” They presented a series of theoretical results detailing its efficacy as both an estimator and a model selection tool, largely mirroring the conceptual framework of their earlier work on compressed sensing. [CT07] The Dantzig selector has since been the subject of extensive study by numerous researchers, who have compared its performance and properties to similar methods, such as the statistical lasso introduced in the 1990s. [71] Notably, the textbook “The Elements of Statistical Learning” by Trevor Hastie , Robert Tibshirani , and Jerome H. Friedman describes the Dantzig selector as “somewhat unsatisfactory” in certain contexts. [72] Despite these critiques, it continues to hold considerable significance and interest within the statistical research community.

In 2009, Candes and Benjamin Recht addressed a related problem concerning the recovery of a matrix from knowledge of only a subset of its entries, under the assumption that the matrix is of low rank. [73] They formulated this problem as a convex optimization task, focusing on the minimization of the nuclear norm. In 2010, Candes and Tao further developed the theoretical underpinnings and computational techniques for this matrix completion problem. [CT10] Subsequent research by Recht provided refined and improved results in this area. [74] Similar problems and findings have also been explored by a number of other prominent researchers in the field. [75] [76] [77] [78] [79]

Random matrices

The study of random matrices and their eigenvalues was initiated in the 1950s by Eugene Wigner . [80] [81] Wigner’s work primarily focused on hermitian and symmetric matrices , leading to the formulation of the “semicircle law” for their eigenvalues. In 2010, Tao and Van Vu made a pivotal contribution to the understanding of non-symmetric random matrices. They established that for a large matrix size $n$, if the entries of an $n \times n$ matrix $A$ are drawn randomly from any fixed probability distribution with an expectation of 0 and a standard deviation of 1, then the eigenvalues of $A$ tend to be distributed uniformly across a disk of radius $\sqrt{n}$ centered at the origin. This phenomenon can be precisely described using the mathematical framework of measure theory . [TV10] This work provided a rigorous proof of the long-conjectured circular law , which had previously been established in weaker forms by numerous researchers. Tao and Vu’s formulation demonstrated that the circular law is a direct consequence of a “universality principle.” This principle posits that the distribution of eigenvalues is determined solely by the average and standard deviation of the component-wise probability distribution, thereby simplifying the general circular law to a calculation involving specifically chosen distributions.

In 2011, Tao and Vu developed a “four moment theorem” applicable to random hermitian matrices . This theorem applies when the matrix entries are independently distributed, each with an average of 0 and a standard deviation of 1, and exhibit an exponentially low probability of attaining large values, akin to a Gaussian distribution . Their theorem establishes that if two such random matrices share the same average value for any quadratic polynomial involving the diagonal entries, and the same average value for any quartic polynomial involving the off-diagonal entries, then the expected value of a large number of functions of their eigenvalues will coincide. This agreement holds up to a uniformly controllable error term, dependent on the matrix size, which diminishes arbitrarily as the matrix size increases. [TV11] Similar findings were independently reported around the same time by László Erdős, Horng-Tzer Yau , and Jun Yin. [82] [83]

Analytic number theory and arithmetic combinatorics

Tao (pictured second from left) with undergraduate mathematics students at UCLA in 2021.

In 2004, Tao, in collaboration with Jean Bourgain and Nets Katz , conducted a significant investigation into the additive and multiplicative structures of subsets within finite fields of prime order. [BKT04] It is a well-established fact that no nontrivial subrings exist within such fields. Bourgain, Katz, and Tao provided a quantitative refinement of this principle, demonstrating that for any given subset of a finite field, the number of distinct sums and products formed by elements of that subset must be substantially large relative to the size of the field and the subset itself. Subsequent research by Bourgain, Alexey Glibichuk, and Sergei Konyagin yielded further improvements upon their results. [84] [85]

The seminal work by Tao and Ben Green on the existence of arbitrarily long arithmetic progressions within the sequence of prime numbers is widely known as the Green–Tao theorem and is considered one of Tao’s most celebrated achievements. [GT08] The foundation for Green and Tao’s proof lies in Endre Szemerédi ’s pivotal 1975 theorem, which guarantees the existence of arithmetic progressions within specific sets of integers. Green and Tao ingeniously developed a “transference principle” that enabled the extension of Szemerédi’s theorem’s applicability to broader categories of integer sets. The Green–Tao theorem then emerged as a direct consequence of this principle, although proving that the set of prime numbers satisfies the stringent conditions of Green and Tao’s extension proved to be a non-trivial undertaking.

In 2008, Green and Tao presented a multilinear generalization of Dirichlet’s renowned theorem on arithmetic progressions . Their theorem addresses the conditions under which an infinite number of matrices $x$ of size $k \times n$ exist, such that all components of $Ax + v$ are prime numbers, where $A$ is a given $k \times n$ matrix and $v$ is a $k \times 1$ matrix with integer components. [GT10] It is important to note that the initial proof of Green and Tao was contingent upon certain conjectures that remained unproven at the time. These conjectures were subsequently resolved in later collaborative work involving Green, Tao, and [Tamar Ziegler]. [GTZ12]

Personal life

Terence Tao is proficient in Cantonese but does not possess the ability to write Chinese characters. He is married to Laura Tao, who works as an electrical engineer at NASA ’s Jet Propulsion Laboratory . [11] [86] The couple resides in Los Angeles , California, and they are parents to two children. [11]

Political views

On August 18, 2025, Terence Tao published an article expressing his strong opposition to the policies of United States President Donald Trump , specifically those that involved significant cuts to research funding, which directly impacted his own mathematics research. [87] [88] As a consequence of these funding reductions, two of Tao’s research grants, one directly supporting his work at UCLA , and another funding research initiatives at UCLA’s Institute for Pure and Applied Mathematics (IPAM), where Tao holds oversight responsibilities, were suspended by the National Science Foundation as part of a broader federal initiative.

Tao has articulated that these funding cuts have detrimental consequences, not only hindering the recruitment of top academic talent but also impeding the advancement of crucial research endeavors. [90] While his primary research focus is in pure mathematics, he has emphasized the potential for such work to lay foundational groundwork for advancements in applied mathematics , thereby supporting progress in fields like cryptography and cybersecurity . [91] Furthermore, Tao’s past collaborative research in signal processing has demonstrably contributed to significant accelerations in MRI scan speeds. [92]

Notable awards

Terence Tao has been the recipient of numerous prestigious awards throughout his career, recognizing his profound contributions to mathematics. He was awarded the Fields Medal , widely considered the highest honor in the field of mathematics, in 2006.

• 1999 – Packard Fellowship

• 2000 – Salem Prize for his significant work in Lp harmonic analysis and related inquiries in geometric measure theory and partial differential equations .

• 2002 – Bôcher Memorial Prize awarded for his papers: * “Global regularity of wave maps I. Small critical Sobolev norm in high dimensions.” published in International Mathematics Research Notices (2001). * “Global regularity of wave maps II. Small energy in two dimensions.” published in Communications in Mathematical Physics (2001). In addition to these, the prize recognized “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 research on wave maps , his theorems on global existence for KdV-type equations, and for his joint solution with Allen Knutson of Horn’s conjecture.

• 2005 – Australian Mathematical Society Medal

• 2005 – Ostrowski Prize (jointly awarded with Ben Green ) for: “their exceptional achievements in the area of analytic and combinatorial number theory.”

• 2005 – Levi L. Conant Prize (jointly awarded with Allen Knutson ) for: Their expository article titled “Honeycombs and Sums of Hermitian Matrices” published in Notices of the AMS (2001).

• 2006 – Fields Medal for: “his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.”

• 2006 – MacArthur Award

• 2006 – SASTRA Ramanujan Prize [96]

• 2006 – Sloan Fellowship

• 2007 – Inducted as a Fellow of the Royal Society [97]

• 2008 – Alan T. Waterman Award for: [98] “his surprising and original contributions to many fields of mathematics, including number theory, differential equations, algebra, and harmonic analysis.”

• 2008 – Onsager Medal [99] for: “his combination of mathematical depth, width and volume in a manner unprecedented in contemporary mathematics.” His accompanying Lars Onsager lecture, delivered at NTNU in Norway, was titled “Structure and randomness in the prime numbers.” [100]

• 2009 – Inducted into the American Academy of Arts and Sciences [101]

• 2010 – King Faisal International Prize [102]

• 2010 – Nemmers Prize in Mathematics [103]

• 2010 – Polya Prize (jointly awarded with Emmanuel Candès )

• 2012 – Crafoord Prize [104] [105]

• 2012 – Simons Investigator [106]

• 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 “Mathematics” category for his book: “Hilbert’s Fifth Problem and Related Topics” ISBN   978-1-4704-1564-8

• 2019 – Riemann Prize [108]

• 2019 – Recognized by The Carnegie Corporation of New York with the 2019 Great Immigrant Award . [109]

• 2020 – Princess of Asturias Award for Technical and Scientific Research, awarded jointly with Emmanuel Candès , for their pioneering work in compressed sensing .

• 2020 – Bolyai Prize [111]

• 2021 – IEEE Jack S. Kilby Signal Processing Medal [112]

• 2022 – Global Australian of the Year (awarded by Advance Global Australians; Advance.org) [113] [114]

• 2022 – Grande Médaille [115]

• 2023 – Alexanderson Award (jointly awarded with Kaisa Matomäki , Maksym Radziwill , Joni Teräväinen, and Tamar Ziegler ) for their paper: “Higher uniformity of bounded multiplicative functions in short intervals on average.” published in Annals of Mathematics (2023).

• 2025 - James Madison medal

Major publications

Textbooks

• — (2006). Solving mathematical problems. A personal perspective (Second edition of 1992 original ed.). Oxford University Press . ISBN  978-0-19-920560-8. MR  2265113. Zbl  1098.00006.

• — (2006). Nonlinear dispersive equations. Local and global analysis. CBMS Regional Conference Series in Mathematics. Vol. 106. Providence, RI: American Mathematical Society . doi :10.1090/cbms/106. ISBN  0-8218-4143-2. MR  2233925. Zbl  1106.35001.

• —; Vu, Van H. (2006). Additive combinatorics. Cambridge Studies in Advanced Mathematics. Vol. 105. Cambridge University Press . ISBN  978-0-521-85386-6. MR  2289012. Zbl  1127.11002. [117] [118]

• — (2008). Structure and randomness. Pages from year one of a mathematical blog. Providence, RI: American Mathematical Society. doi :10.1090/mbk/059. ISBN  978-0-8218-4695-7. MR  2459552. Zbl  1245.00024.

• — (2009). Poincaré’s legacies, pages from year two of a mathematical blog. Part I. Providence, RI: American Mathematical Society. doi :10.1090/mbk/066. ISBN  978-0-8218-4883-8. MR  2523047. Zbl  1171.00003.

• — (2009). Poincaré’s legacies, pages from year two of a mathematical blog. Part II. Providence, RI: American Mathematical Society. doi :10.1090/mbk/067. ISBN  978-0-8218-4885-2. MR  2541289. Zbl  1175.00010.

• — (2010). An epsilon of room, I: real analysis. Pages from year three of a mathematical blog. Graduate Studies in Mathematics. Vol. 117. Providence, RI: American Mathematical Society. doi :10.1090/gsm/117. ISBN  978-0-8218-5278-1. MR  2760403. Zbl  1216.46002. [119]

• — (2010). An epsilon of room, II. Pages from year three of a mathematical blog. Providence, RI: American Mathematical Society. doi :10.1090/mbk/077. ISBN  978-0-8218-5280-4. MR  2780010. Zbl  1218.00001.

• — (2011). An introduction to measure theory. Graduate Studies in Mathematics. Vol. 126. Providence, RI: American Mathematical Society. doi :10.1090/gsm/126. ISBN  978-0-8218-6919-2. MR  2827917. Zbl  1231.28001. [120]

• — (2012). Topics in random matrix theory. Graduate Studies in Mathematics. Vol. 132. Providence, RI: American Mathematical Society. doi :10.1090/gsm/132. ISBN  978-0-8218-7430-1. MR  2906465. Zbl  1256.15020.

• — (2012). Higher order Fourier analysis. Graduate Studies in Mathematics. Vol. 142. Providence, RI: American Mathematical Society. doi :10.1090/gsm/142. ISBN  978-0-8218-8986-2. MR  2931680. Zbl  1277.11010.

• — (2013). Compactness and contradiction. Providence, RI: American Mathematical Society. doi :10.1090/mbk/081. ISBN  978-0-8218-9492-7. MR  3026767. Zbl  1276.00007.

• — (2014) [2006]. Analysis. I. Texts and Readings in Mathematics. Vol. 37 (3rd ed.). New Delhi: Hindustan Book Agency. ISBN  978-93-80250-64-9. MR  3309891. Zbl  1300.26002.

• — (2014) [2006]. Analysis. II. Texts and Readings in Mathematics. Vol. 38 (3rd ed.). New Delhi: Hindustan Book Agency. ISBN  978-93-80250-65-6. MR  3310023. Zbl  1300.26003.

• — (2014). Hilbert’s fifth problem and related topics. Graduate Studies in Mathematics. Vol. 153. Providence, RI: American Mathematical Society. doi :10.1090/gsm/153. ISBN  978-1-4704-1564-8. MR  3237440. Zbl  1298.22001.

• — (2015). Expansion in finite simple groups of Lie type. Graduate Studies in Mathematics. Vol. 164. Providence, RI: American Mathematical Society. doi :10.1090/gsm/164. ISBN  978-1-4704-2196-0. MR  3309986. S2CID  118288443. Zbl  1336.20015. [121]

• — (2022). Analysis I. Texts and Readings in Mathematics. Vol. 37 (4th ed.). Springer Singapore. ISBN  978-981-19-7261-4.

• — (2022). Analysis II. Texts and Readings in Mathematics. Vol. 38 (4th ed.). Springer Singapore. ISBN  978-981-19-7284-3.

Research articles

• KT98. Keel, Markus; Tao, Terence (1998). “Endpoint Strichartz estimates”. American Journal of Mathematics . 120 (5): 955–980. CiteSeerX  10.1.1.599.1892. doi :10.1353/ajm.1998.0039. JSTOR  25098630. MR  1646048. S2CID  13012479. Zbl  0922.35028.

• TVV98. Tao, Terence; Vargas, Ana; Vega, Luis (1998). “A bilinear approach to the restriction and Kakeya conjectures”. Journal of the American Mathematical Society . 11 (4): 967–1000. doi :10.1090/S0894-0347-98-00278-1. MR  1625056. Zbl  0924.42008.

• KT99. Knutson, Allen ; Tao, Terence (1999). “The honeycomb model of GLn(C) tensor products. I. Proof of the saturation conjecture”. Journal of the American Mathematical Society. 12 (4): 1055–1090. doi :10.1090/S0894-0347-99-00299-4. MR  1671451. Zbl  0944.05097.

• C+01. Colliander, J. ; Keel, M.; Staffilani, G. ; Takaoka, H.; Tao, T. (2001). “Global well-posedness for Schrödinger equations with derivative”. SIAM Journal on Mathematical Analysis . 33 (3): 649–669. arXiv :math/0101263. doi :10.1137/S0036141001384387. MR  1871414. Zbl  1002.35113.

• T01a. Tao, Terence (2001). “Global regularity of wave maps. II. Small energy in two dimensions”. Communications in Mathematical Physics . 224 (2): 443–544. arXiv :math/0011173. Bibcode :2001CMaPh.224..443T. doi :10.1007/PL00005588. MR  1869874. S2CID  119634411. Zbl  1020.35046. (Erratum:  [1])

• T01b. Tao, Terence (2001). “Multilinear weighted convolution of L2-functions, and applications to nonlinear dispersive equations”. American Journal of Mathematics . 123 (5): 839–908. arXiv :math/0005001. doi :10.1353/ajm.2001.0035. JSTOR  25099087. MR  1854113. S2CID  984131. Zbl  0998.42005.

• C+02a. Colliander, J. ; Keel, M.; Staffilani, G. ; Takaoka, H.; Tao, T. (2002). “A refined global well-posedness result for Schrödinger equations with derivative”. SIAM Journal on Mathematical Analysis . 34 (1): 64–86. arXiv :math/0110026. doi :10.1137/S0036141001394541. MR  1950826. S2CID  9007785. Zbl  1034.35120.

• C+02b. Colliander, J. ; Keel, M.; Staffilani, G. ; Takaoka, H.; Tao, T. (2002). “Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation”. Mathematical Research Letters. 9 (5–6): 659–682. arXiv :math/0203218. doi :10.4310/MRL.2002.v9.n5.a9. MR  1906069. Zbl  1152.35491.

• MTT02. Muscalu, Camil; Tao, Terence; Thiele, Christoph (2002). “Multi-linear operators given by singular multipliers”. Journal of the American Mathematical Society . 15 (2): 469–496. doi :10.1090/S0894-0347-01-00379-4. MR  1887641. Zbl  0994.42015.

• CCT03. Christ, Michael ; Colliander, James ; Tao, Terrence (2003). “Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations”. American Journal of Mathematics . 125 (6): 1235–1293. arXiv :math/0203044. doi :10.1353/ajm.2003.0040. MR  2018661. S2CID  11001499. Zbl  1048.35101.

• C+03. Colliander, J. ; Keel, M.; Staffilani, G. ; Takaoka, H.; Tao, T. (2003). “Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋”. Journal of the American Mathematical Society . 16 (3): 705–749. doi :10.1090/S0894-0347-03-00421-1. MR  1969209. Zbl  1025.35025.

• T03. Tao, T. (2003). “A sharp bilinear restrictions estimate for paraboloids”. Geometric and Functional Analysis . 13 (6): 1359–1384. arXiv :math/0210084. doi :10.1007/s00039-003-0449-0. MR  2033842. S2CID  15873489. Zbl  1068.42011.

• BKT04. Bourgain, J. ; Katz, N. ; Tao, T. (2004). “A sum-product estimate in finite fields, and applications”. Geometric and Functional Analysis . 14 (1): 27–57. arXiv :math/0301343. doi :10.1007/s00039-004-0451-1. MR  2053599. S2CID  14097626. Zbl  1145.11306.

• C+04. Colliander, J. ; Keel, M.; Staffilani, G. ; Takaoka, H.; Tao, T. (2004). “Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ3”. Communications on Pure and Applied Mathematics . 57 (8): 987–1014. arXiv :math/0301260. doi :10.1002/cpa.20029. MR  2053757. S2CID  16423475. Zbl  1060.35131.

• KTW04. Knutson, Allen ; Tao, Terence; Woodward, Christopher (2004). “The honeycomb model of GLn(C) tensor products. II. Puzzles determine facets of the Littlewood–Richardson cone”. Journal of the American Mathematical Society . 17 (1): 19–48. doi :10.1090/S0894-0347-03-00441-7. MR  2015329. Zbl  1043.05111.

• T04a. Tao, Terence (2004). “Global well-posedness of the Benjamin–Ono equation in H1(ℝ)”. Journal of Hyperbolic Differential Equations . 1 (1): 27–49. arXiv :math/0307289. doi :10.1142/S0219891604000032. MR  2052470. Zbl  1055.35104.

• T04b. Tao, Terence (2004). “Fuglede’s conjecture is false in 5 and higher dimensions”. Mathematical Research Letters. 11 (2–3): 251–258. arXiv :math/0306134. doi :10.4310/MRL.2004.v11.n2.a8. MR  2067470. Zbl  1092.42014.

• CT05. Candes, Emmanuel J. ; Tao, Terence (2005). “Decoding by linear programming”. IEEE Transactions on Information Theory . 51 (12): 4203–4215. arXiv :math/0502327. Bibcode :2005ITIT…51.4203C. doi :10.1109/TIT.2005.858979. MR  2243152. S2CID  12605120. Zbl  1264.94121.

• BT06. Bejenaru, Ioan; Tao, Terence (2006). “Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation”. Journal of Functional Analysis . 233 (1): 228–259. arXiv :math/0508210. doi :10.1016/j.jfa.2005.08.004. MR  2204680. Zbl  1090.35162.

• BCT06. Bennett, Jonathan ; Carbery, Anthony; Tao, Terence (2006). “On the multilinear restriction and Kakeya conjectures”. Acta Mathematica . 196 (2): 261–302. arXiv :math/0509262. doi :10.1007/s11511-006-0006-4. MR  2275834. Zbl  1203.42019.

• CRT06a. Candès, Emmanuel J. ; Romberg, Justin K.; Tao, Terence (2006). “Stable signal recovery from incomplete and inaccurate measurements”. Communications on Pure and Applied Mathematics . 59 (8): 1207–1223. arXiv :math/0503066. doi :10.1002/cpa.20124. MR  2230846. S2CID  119159284. Zbl  1098.94009.

• CRT06b. Candès, Emmanuel J. ; Romberg, Justin; Tao, Terence (2006). “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information”. IEEE Transactions on Information Theory . 52 (2): 489–509. arXiv :math/0409186. Bibcode :2006ITIT…52..489C. doi :10.1109/TIT.2005.862083. MR  2236170. S2CID  7033413. Zbl  1231.94017.

• CT06. Candes, Emmanuel J. ; Tao, Terence (2006). “Near-optimal signal recovery from random projections: universal encoding strategies?”. IEEE Transactions on Information Theory . 52 (12): 5406–5425. arXiv :math/0410542. Bibcode :2006ITIT…52.5406C. doi :10.1109/TIT.2006.885507. MR  2300700. S2CID  1431305. Zbl  1309.94033.

• CT07. Candes, Emmanuel ; Tao, Terence (2007). “The Dantzig selector: statistical estimation when p is much larger than n”. Annals of Statistics . 35 (6): 2313–2351. arXiv :math/0506081. doi :10.1214/009053606000001523. MR  2382644. Zbl  1139.62019.

• TVZ07. Tao, Terence; Visan, Monica ; Zhang, Xiaoyi (2007). “The nonlinear Schrödinger equation with combined power-type nonlinearities”. Communications in Partial Differential Equations. 32 (7–9): 1281–1343. arXiv :math/0511070. doi :10.1080/03605300701588805. MR  2354495. S2CID  15109526. Zbl  1187.35245.

• C+08. Colliander, J. ; Keel, M.; Staffilani, G. ; Takaoka, H.; Tao, T. (2008). “Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in ℝ3”. Annals of Mathematics . Second Series. 167 (3): 767–865. doi :10.4007/annals.2008.167.767. MR  2415387. Zbl  1178.35345.

• GT08. Green, Ben ; Tao, Terence (2008). “The primes contain arbitrarily long arithmetic progressions”. Annals of Mathematics . Second Series. 167 (2): 481–547. arXiv :math/0404188. doi :10.4007/annals.2008.167.481. MR  2415379. Zbl  1191.11025.

• KTV09. Killip, Rowan; Tao, Terence; Visan, Monica (2009). “The cubic nonlinear Schrödinger equation in two dimensions with radial data”. Journal of the European Mathematical Society . 11 (6): 1203–1258. arXiv :0707.3188. doi :10.4171/JEMS/180. MR  2557134. Zbl  1187.35237.

• CT10. Candès, Emmanuel J. ; Tao, Terence (2010). “The power of convex relaxation: near-optimal matrix completion”. IEEE Transactions on Information Theory . 56 (5): 2053–2080. arXiv :0903.1476. Bibcode :2010ITIT…56.2053C. doi :10.1109/TIT.2010.2044061. MR  2723472. S2CID  1255437. Zbl  1366.15021.

• GT10. Green, Ben ; Tao, Terence (2010). “Linear Szemeredi theorem for primes”. ArXiv :1003.3737 [math.NT].

• TV10. Tao, Terence; Vu, Van (2010). “Random matrices: universality of ESDs and the circular law”. Annals of Probability . 38 (5). With an appendix by Manjunath Krishnapur: 2023–2065. arXiv :0807.4898. doi :10.1214/10-AOP534. MR  2722794. Zbl  1203.15025.

• TV11. Tao, Terence; Vu, Van (2011). “Random matrices: universality of local eigenvalue statistics”. Acta Mathematica . 206 (1): 127–204. arXiv :0908.1982. doi :10.1007/s11511-011-0061-3. MR  2784665. Zbl  1217.15043.

• GTZ12. Green, Ben ; Tao, Terence; Ziegler, Tamar (2012). “An inverse theorem for the Gowers U s+1 [N]-norm”. Annals of Mathematics . Second Series. 176 (2): 1231–1372. arXiv :1006.0205. doi :10.4007/annals.2012.176.2.11. MR  2950773. Zbl  1282.11007.

• T16. Tao, Terence (2016). “Finite time blowup for an averaged three-dimensional Navier–Stokes equation”. Journal of the American Mathematical Society . 29 (3): 601–674. arXiv :1402.0290. doi :10.1090/jams/838. MR  3486169. Zbl  1342.35227.

Notes

• ^ Chinese : 陶象國; pinyin : Táo Xiàngguó; Shanghainese : Dau2 Zian3 Goh4 • ^ Chinese : 梁蕙蘭; Jyutping : Loeng4 Wai6 Laan4

See also

• Cramer conjecture • Erdős discrepancy problem • Goldbach’s weak conjecture • Inscribed square problem

References

• ^ King Faisal Foundation – retrieved 11 January 2010. • ^ “SIAM: George Pólya Prize”. Archived from the original on 23 October 2021. Retrieved 5 September 2015. • ^ a b “Vitae and Bibliography for Terence Tao”. 12 October 2009. Retrieved 21 January 2010. • ^ “Mathematician Proves Huge Result on ‘Dangerous’ Problem”. 11 December 2019. Archived from the original on 23 October 2021. • ^ “Mathematical exploration and discovery at scale”. What’s new. 6 November 2025. Retrieved 17 November 2025. • ^ “Search | arXiv e-print repository”. arxiv.org. • ^ a b c d Cook, Gareth (24 July 2015). “The Singular Mind of Terry Tao (Published 2015)”. The New York Times. ISSN  0362-4331. Retrieved 15 February 2021. • ^ Mackenzie, Dana (2 October 2007). “Primed for Success”. Smithsonian Magazine. Retrieved 5 July 2025. • ^ “PRESIDENT’S COUNCIL OF ADVISORS ON SCIENCE AND TECHNOLOGY: Terence Tao, PhD”. bidenwhitehouse.archives.gov. 2021. Retrieved 5 July 2025. • ^ Wolpert, Stuart (8 August 2006). “Terence Tao, ‘Mozart of Math,’ is first UCLA math prof to win Fields Medal”. newsroom.ucla.edu. Retrieved 5 July 2025. • ^ a b c Wood, Stephanie (4 March 2015). “Terence Tao: the Mozart of maths”. The Sydney Morning Herald. Retrieved 13 February 2023. • ^ Wen Wei Po , Page A4, 24 August 2006. • ^ Dr Billy Tao, Healthshare. • ^ Oriental Daily , Page A29, 24 August 2006. • ^ Terence Chi-Shen Tao, MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland. • ^ “International Mathematical Olympiad”. International Mathematical Olympiad - Nigel Tao. Retrieved 5 October 2024. • ^ “International Mathematical Olympiad”. International Mathematical Olympiad - Trevor Tao. Retrieved 5 October 2024. • ^ “Tao, Trevor”. • ^ Clements, M. A. (Ken) (1984), “Terence Tao”, Educational Studies in Mathematics, 15 (3): 213–238, doi :10.1007/BF00312075, JSTOR  3482178, S2CID  189827772. • ^ “An Interview with Terence Tao”. Asia Pacific Math Newsletter. Retrieved 5 July 2025. • ^ “Terence Tao’s Journey”. masterclass.com. Retrieved 5 July 2025. • ^ “Smithsonian executive Kevin Gover ‘78 and Fields Medalist mathematician Terence Tao *96 to receive top alumni awards”. Princeton University . 3 November 2025. Archived from the original on 14 December 2025. Retrieved 14 December 2025. • ^ “Radical Acceleration in Australia: Terence Tao”. www.davidsongifted.org . Archived from the original on 23 October 2021. • ^ “International Mathematical Olympiad”. www.imo-official.org . • ^ a b It’s prime time as numbers man Tao tops his Field Stephen Cauchi, 23 August 2006. Retrieved 31 August 2006. • ^ Kenneth Chang (13 March 2007). “Journeys to the Distant Fields of Prime”. The New York Times. Archived from the original on 23 October 2021. • ^ “Corrections: For the Record”. The New York Times. 13 March 2007. Archived from the original on 23 October 2021. • ^ a b “Quanta Magazine”. 24 February 2014. • ^ “Terence Tao’s Answer to the Erdős Discrepancy Problem”. Quanta Magazine. October 2015. Archived from the original on 26 February 2019. • ^ Tao, Terence (2019). “Almost all orbits of the Collatz map attain almost bounded values”. arXiv :1909.03562 [math.PR]. • ^ Rodgers, Brad; Tao, Terence (6 April 2020). “The De Bruijn-Newman constant is non-negative”. Forum of Mathematics, Pi. 8 e6. arXiv :1801.05914. doi :10.1017/fmp.2020.6. • ^ Tao, Terence (2022). “Sendov’s conjecture for sufficiently high degree polynomials”. Acta Mathematica. 229 (2): 347–392. arXiv :2012.04125. doi :10.4310/ACTA.2022.v229.n2.a3. • ^ “Vitae”. UCLA. Retrieved 5 September 2015. • ^ “APS Member History”. search.amphilsoc.org. Archived from the original on 16 April 2021. Retrieved 19 March 2021. • ^ List of Fellows of the American Mathematical Society, retrieved 25 August 2013. • ^ a b “2006 Fields Medals awarded” (PDF). Notices of the American Mathematical Society . 53 (9): 1037–1044. October 2006. Archived from the original (PDF) on 2 November 2006. • ^ “Reclusive Russian turns down math world’s highest honour”. Canadian Broadcasting Corporation (CBC). 22 August 2006. Archived from the original on 23 October 2021. Retrieved 26 August 2006. • ^ “Media information”. UCLA. Archived from the original on 23 October 2021. Retrieved 5 September 2015. • ^ “President Biden Announces Members of President’s Council of Advisors on Science and Technology”. White House. 22 September 2021. Archived from the original on 23 October 2021. • ^ “Terence Tao, il matematico con il QI più alto al mondo: ‘Non so cantare e ho fallito un paio di esami’”. Huffington Post Italy. 21 September 2021. Archived from the original on 23 October 2021. • ^ National Australia Day Committee, Terence Tao – Australian of the Year. Retrieved 3 February 2023. • ^ “Terence C. Tao”. MathSciNet . American Mathematical Society . Retrieved 24 November 2022. • ^ “Who am I?”. UCLA. Archived from the original on 23 October 2021. Retrieved 5 September 2015. • ^ “Terence Tao’s Publons profile”. publons.com. Archived from the original on 23 October 2021. Retrieved 6 February 2021. • ^ “Highly Cited Researchers”. publons.com. Archived from the original on 23 October 2021. Retrieved 6 February 2021. • ^ NewScientist.com , Prestigious Fields Medals for mathematics awarded, 22 August 2006. • ^ Mathematical Reviews, Review by Timothy Gowers of Terence Tao’s Poincaré’s legacies, part I, MR  2523047. • ^ Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis. On the ill-posedness of some canonical dispersive equations. Duke Math. J. 106 (2001), no. 3, 617–633. • ^ Tataru, Daniel. On global existence and scattering for the wave maps equation. Amer. J. Math. 123 (2001), no. 1, 37–77. • ^ Ionescu, Alexandru D.; Kenig, Carlos E. Global well-posedness of the Benjamin-Ono equation in low-regularity spaces. J. Amer. Math. Soc. 20 (2007), no. 3, 753–798. • ^ Lemarié-Rieusset, Pierre Gilles (2016). The Navier–Stokes problem in the 21st century. Boca Raton, FL: CRC Press . doi :10.1201/b19556. ISBN  978-1-4665-6621-7. MR  3469428. S2CID  126089972. Zbl  1342.76029. • ^ Fuglede, Bent. Commuting self-adjoint partial differential operators and a group theoretic problem. J. Functional Analysis 16 (1974), 101–121. • ^ Coifman, R. R.; Meyer, Yves. On commutators of singular integrals and bilinear singular integrals. Trans. Amer. Math. Soc. 212 (1975), 315–331. • ^ Coifman, R.; Meyer, Y. Commutateurs d’intégrales singulières et opérateurs multilinéaires. (French) Ann. Inst. Fourier (Grenoble) 28 (1978), no. 3, xi, 177–202. • ^ Coifman, Ronald R.; Meyer, Yves. Au delà des opérateurs pseudo-différentiels. Astérisque, 57. Société Mathématique de France, Paris, 1978. i+185 pp. • ^ Lacey, Michael; Thiele, Christoph. L p estimates on the bilinear Hilbert transform for 2<p<∞. Ann. of Math. (2) 146 (1997), no. 3, 693–724. • ^ Lacey, Michael; Thiele, Christoph. On Calderón’s conjecture. Ann. of Math. (2) 149 (1999), no. 2, 475–496. • ^ Kenig, Carlos E.; Stein, Elias M. Multilinear estimates and fractional integration. Math. Res. Lett. 6 (1999), no. 1, 1–15. • ^ Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis. A bilinear estimate with applications to the KdV equation. J. Amer. Math. Soc. 9 (1996), no. 2, 573–603. • ^ Ginibre, Jean. Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace (d’après Bourgain). Séminaire Bourbaki, Vol. 1994/95. Astérisque No. 237 (1996), Exp. No. 796, 4, 163–187. • ^ Fefferman, Charles. Inequalities for strongly singular convolution operators. Acta Math. 124 (1970), 9–36. • ^ Tomas, Peter A. A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc. 81 (1975), 477–478. • ^ Strichartz, Robert S. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 (1977), no. 3, 705–714. • ^ Bourgain, J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3 (1993), no. 2, 107–156. • ^ Bourgain, J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation. Geom. Funct. Anal. 3 (1993), no. 3, 209–262. • ^ Klainerman, S.; Machedon, M. Space-time estimates for null forms and the local existence theorem. Comm. Pure Appl. Math. 46 (1993), no. 9, 1221–1268. • ^ Wolff, Thomas. A sharp bilinear cone restriction estimate. Ann. of Math. (2) 153 (2001), no. 3, 661–698. • ^ Bourgain, Jean; Guth, Larry. Bounds on oscillatory integral operators based on multilinear estimates. Geom. Funct. Anal. 21 (2011), no. 6, 1239–1295. • ^ Donoho, David L. Compressed sensing. IEEE Trans. Inform. Theory 52 (2006), no. 4, 1289–1306. • ^ Candès, Emmanuel J. The restricted isometry property and its implications for compressed sensing. C. R. Math. Acad. Sci. Paris 346 (2008), no. 9-10, 589–592. • ^ Bickel, Peter J.; Ritov, Ya’acov; Tsybakov, Alexandre B. Simultaneous analysis of lasso and Dantzig selector. Ann. Statist. 37 (2009), no. 4, 1705–1732. • ^ Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome. The elements of statistical learning. Data mining, inference, and prediction. Second edition. Springer Series in Statistics. Springer, New York, 2009. xxii+745 pp. ISBN  978-0-387-84857-0. • ^ Candès, Emmanuel J.; Recht, Benjamin. Exact matrix completion via convex optimization. Found. Comput. Math. 9 (2009), no. 6, 717–772. • ^ Recht, Benjamin. A simpler approach to matrix completion. J. Mach. Learn. Res. 12 (2011), 3413–3430. • ^ Keshavan, Raghunandan H.; Montanari, Andrea; Oh, Sewoong. Matrix completion from a few entries. IEEE Trans. Inform. Theory 56 (2010), no. 6, 2980–2998. • ^ Recht, Benjamin; Fazel, Maryam; Parrilo, Pablo A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52 (2010), no. 3, 471–501. • ^ Candès, Emmanuel J.; Plan, Yaniv. Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements. IEEE Trans. Inform. Theory 57 (2011), no. 4, 2342–2359. • ^ Koltchinskii, Vladimir; Lounici, Karim; Tsybakov, Alexandre B. Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. Ann. Statist. 39 (2011), no. 5, 2302–2329. • ^ Gross, David. Recovering low-rank matrices from few coefficients in any basis. IEEE Trans. Inform. Theory 57 (2011), no. 3, 1548–1566. • ^ Wigner, Eugene P. Characteristic vectors of bordered matrices with infinite dimensions. Annals of Mathematics (2) 62 (1955), 548–564. • ^ Wigner, Eugene P. On the distribution of the roots of certain symmetric matrices. Ann. of Math. (2) 67 (1958), 325–327. • ^ Erdős, László; Yau, Horng-Tzer ; Yin, Jun (2012). “Rigidity of eigenvalues of generalized Wigner matrices”. Advances in Mathematics . 229 (3): 1435–1515. arXiv :1007.4652. doi :10.1016/j.aim.2011.12.010. • ^ Erdős, László; Yau, Horng-Tzer ; Yin, Jun (2012). “Bulk universality for generalized Wigner matrices”. Probability Theory and Related Fields. 154 (1–2): 341–407. arXiv :1001.3453. doi :10.1007/s00440-011-0390-3. S2CID  253977494. • ^ Bourgain, J. More on the sum-product phenomenon in prime fields and its applications. Int. J. Number Theory 1 (2005), no. 1, 1–32. • ^ Bourgain, J.; Glibichuk, A.A.; Konyagin, S.V. Estimates for the number of sums and products and for exponential sums in fields of prime order. J. London Math. Soc. (2) 73 (2006), no. 2, 380–398. • ^ “History, Travel, Arts, Science, People, Places – Smithsonian”. Archived from the original on 10 September 2012. Retrieved 5 September 2015. • ^ Tao, Terence (18 August 2025). “I’m an award-winning mathematician. Trump just cut my funding”. newsletter.ofthebrave.org. Archived from the original on 22 August 2025. Retrieved 2 October 2025. • ^ Hasson, Emma R. (18 July 2025). “Math Is Quietly in Crisis over NSF Funding Cuts”. Scientific American. Retrieved 10 September 2025. • ^ Johnson, Carolyn Y. (7 September 2025). “The world’s greatest mathematician avoided politics. Then Trump cut science funding”. The Washington Post. Retrieved 10 September 2025. • ^ “UCLA’s Terence Tao: Losing support for research means losing our best and brightest”. UCLA. 9 September 2025. Retrieved 10 September 2025. • ^ Cohn, Jonathan (6 August 2025). “He’s the ‘Mozart’ of Math and Trump Killed His Funding”. The Bulwark. Retrieved 10 September 2025. • ^ “The ‘Mozart of Math’ rarely speaks about politics. The wide-ranging cuts to science funding made him change that”. NBC News. 26 August 2025. Retrieved 10 September 2025. • ^ Mathematics People. Notices of the AMS. • ^ “2002 Bôcher Prize” (PDF). Notices of the American Mathematical Society . 49 (4): 472–475. April 2002. • ^ “Research Fellow: James Maynard”. Clay Mathematics Institute. • ^ Alladi, Krishnaswami (9 December 2019). “Ramanujan’s legacy: the work of the SASTRA prize winners”. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 378 (2163) 20180438. The Royal Society. doi :10.1098/rsta.2018.0438. ISSN  1364-503X. PMID  31813370. S2CID  198231874. • ^ Fellows and Foreign Members of the Royal Society, retrieved 9 June 2010. • ^ National Science Foundation , Alan T. Waterman Award. Retrieved 18 April 2008. • ^ “The Lars Onsager Lecture and Professorship – IMF”. Archived from the original on 3 February 2009. Retrieved 13 January 2009. • ^ NTNU’s Onsager Lecture, by Terence Tao on YouTube . • ^ “Alphabetical Index of Active AAAS Members” (PDF). amacad.org . Archived from the original (PDF) on 5 October 2013. Retrieved 21 November 2013. His 2009 induction ceremony is here. • ^ “Bombieri and Tao Receive King Faisal Prize” (PDF). Notices of the American Mathematical Society . 57 (5): 642–643. May 2010. • ^ “Major Math and Science Awards Announced: Northwestern University News”. Archived from the original on 16 April 2010. Retrieved 5 September 2015. • ^ “The Crafoord Prize in Mathematics 2012 and The Crafoord Prize in Astronomy 2012”. Royal Swedish Academy of Sciences. 19 January 2012. Archived from the original on 23 October 2021. Retrieved 13 November 2014. • ^ “4 Scholars Win Crafoord Prizes in Astronomy and Math – The Ticker – Blogs – The Chronicle of Higher Education”. 19 January 2012. Archived from the original on 23 October 2021. Retrieved 5 September 2015. • ^ “Simons Investigators Awardees”. Simons Foundation. Archived from the original on 23 October 2021. Retrieved 9 September 2017. • ^ “2015 Award Winners”. PROSE Awards. • ^ “Riemann Prize laureate 2019: Terence Tao”. Archived from the original on 20 December 2019. Retrieved 23 November 2019. • ^ “Terence Tao”. Carnegie Corporation of New York. Retrieved 27 June 2024. • ^ “Yves Meyer, Ingrid Daubechies, Terence Tao and Emmanuel Candès, Princess of Asturias Award for Technical and Scientific Research 2020”. The Princess of Asturias Foundation. Princess of Asturias Foundation. Archived from the original on 26 June 2020. Retrieved 23 June 2020. • ^ “Vitae and Bibliography for Terence Tao”. UCLA. Retrieved 13 November 2020. • ^ “IEEE Awards”. IEEE Awards. 27 June 2022. Retrieved 10 September 2022. • ^ 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. • ^ “Séance de remise de la Grande médaille de l’Académie des sciences 2022 à Terence Tao”. French Academy of Sciences. 21 March 2023. Retrieved 10 July 2024. • ^ “Alexanderson Award 2023”. American Institute of Mathematics. Retrieved 7 October 2024. • ^ Green, Ben (2009). “Review: Additive combinatorics by Terence C. Tao and Van H. Vu” (PDF). Bull. Amer. Math. Soc. (N.S.). 46 (3): 489–497. doi :10.1090/s0273-0979-09-01231-2. Archived from the original (PDF) on 11 March 2012. • ^ Vestal, Donald L. (6 June 2007). “Review of Additive Combinatorics by Terence Tao and Van H. Vu”. Mathematical Association of America. • ^ Stenger, Allen (4 March 2011). “Review of An Epsilon of Room, I: Real Analysis: Pages from year three of a mathematical blog by Terence Tao”. Mathematical Association of America. • ^ Poplicher, Mihaela (14 April 2012). “Review of An Introduction to Measure Theory by Terence Tao”. Mathematical Association of America. • ^ Lubotzky, Alexander (25 January 2018). “Review of Expansion in finite simple groups of Lie type by Terence Tao”. Bull. Amer. Math. Soc. (N.S.). 1. doi :10.1090/bull/1610.

External links

• Wikiquote has quotations related to Terence Tao. • Wikimedia Commons has media related to Terence Tao. • Terence Tao’s home page • Tao’s research blog • Tao’s MathOverflow page • O’Connor, John J.; Robertson, Edmund F. , “Terence Tao”, MacTutor History of Mathematics Archive , University of St Andrews . • Terence Tao at the Mathematics Genealogy Project . • Terence Tao’s entry in the Numericana Hall of Fame. • Terence Tao’s results at International Mathematical Olympiad .

[[Category:Fields Medalists]] [[Category:Mathematics portal]]

[v · t · e] Fellows of the Royal Society elected in 2007 Fellows • Brad Amos • Peter Barnes • Gillian Bates • Samuel Berkovic • Michael Bickle • Jeremy Bloxham • David Boger • Peter Bruce • Michael Cates • Geoffrey Cloke • Richard Cogdell • Stewart Cole • George Coupland • George F. R. Ellis • Barry Everitt • Andre Geim • Siamon Gordon • Rosemary Grant • Grahame Hardie • Bill Harris • Nicholas Higham • Anthony A. Hyman • Anthony Kinloch • Richard Leakey • Malcolm Levitt • Ottoline Leyser • Paul Linden • Peter Littlewood • Ravinder N. Maini • Robert Mair, Baron Mair • Michael Malim • Andrew McMahon • Richard Moxon • John A. Peacock • Edward Arend Perkins • Stephen Pope • Daniela Rhodes • Morgan Sheng • David C. Sherrington • Terence Tao • Veronica van Heyningen • David Lee Wark • Trevor Wooley • Andrew Zisserman Foreign • Wallace Broecker • James Cronin • Stanley Falkow • Tom Fenchel • Jeremiah P. Ostriker • Michael O. Rabin • Gerald M. Rubin • Peter Wolynes Honorary • Onora O’Neill

[v · t · e] Fields Medalists • 1936: Ahlfors , Douglas • 1950: Schwartz , Selberg • 1954: Kodaira , Serre • 1958: Roth , Thom • 1962: Hörmander , Milnor • 1966: Atiyah , Cohen , Grothendieck , Smale • 1970: Baker , Hironaka , Novikov , Thompson • 1974: Bombieri , Mumford • 1978: Deligne , Fefferman , Margulis , Quillen • 1982: Connes , Thurston , Yau • 1986: Donaldson , Faltings , Freedman • 1990: Drinfeld , Jones , Mori , Witten • 1994: Bourgain , Lions , Yoccoz , Zelmanov • 1998: Borcherds , Gowers , Kontsevich , McMullen • 2002: Lafforgue , Voevodsky • 2006: Okounkov , Perelman , Tao, Werner • 2010: Lindenstrauss , Ngô , Smirnov , Villani • 2014: Avila , Bhargava , Hairer , Mirzakhani • 2018: Birkar , Figalli , Scholze , Venkatesh • 2022: Duminil-Copin , Huh , Maynard , Viazovska

[Category:Fields Medalists] [Portal:Mathematics]

[v · t · e] Breakthrough Prize laureates Mathematics • Simon Donaldson , Maxim Kontsevich , Jacob Lurie , Terence Tao and Richard Taylor (2015) • Ian Agol (2016) • Jean Bourgain (2017) • Christopher Hacon , James McKernan (2018) • Vincent Lafforgue (2019) • Alex Eskin (2020) • Martin Hairer (2021) • Takuro Mochizuki (2022) • Daniel A. Spielman (2023) • Simon Brendle (2024) • Dennis Gaitsgory (2025) Fundamental physics • Nima Arkani-Hamed , Alan Guth , Alexei Kitaev , Maxim Kontsevich , Andrei Linde , Juan Maldacena , Nathan Seiberg , Ashoke Sen , Edward Witten (2012) • Special: Stephen Hawking , Peter Jenni , Fabiola Gianotti (ATLAS), Michel Della Negra , Tejinder Virdee , Guido Tonelli , Joseph Incandela (CMS) and Lyn Evans (LHC) (2013) • Alexander Polyakov (2013) • Michael Green and John Henry Schwarz (2014) • Saul Perlmutter and members of the Supernova Cosmology Project ; Brian Schmidt , Adam Riess and members of the High-Z Supernova Team (2015) • Special: Ronald Drever , Kip Thorne , Rainer Weiss and contributors to LIGO project (2016) • Yifang Wang , Kam-Biu Luk and the Daya Bay team , Atsuto Suzuki and the KamLAND team, Kōichirō Nishikawa and the K2K / T2K team, Arthur B. McDonald and the Sudbury Neutrino Observatory team, Takaaki Kajita and Yōichirō Suzuki and the Super-Kamiokande team (2016) • Joseph Polchinski , Andrew Strominger , Cumrun Vafa (2017) • Charles L. Bennett , Gary Hinshaw , Norman Jarosik , Lyman Page Jr. , David Spergel (2018) • Special: Jocelyn Bell Burnell (2018) • Charles Kane and Eugene Mele (2019) • Special: Sergio Ferrara , Daniel Z. Freedman , Peter van Nieuwenhuizen (2019) • The Event Horizon Telescope Collaboration (2020) • Eric Adelberger , Jens H. Gundlach and Blayne Heckel (2021) • Special: Steven Weinberg (2021) • Hidetoshi Katori and Jun Ye (2022) • Charles H. Bennett , Gilles Brassard , David Deutsch , Peter W. Shor (2023) • John Cardy and Alexander Zamolodchikov (2024) Life sciences • Cornelia Bargmann , David Botstein , Lewis C. Cantley , Hans Clevers , Titia de Lange , Napoleone Ferrara , Eric Lander , Charles Sawyers , Robert Weinberg , Shinya Yamanaka and Bert Vogelstein (2013) • James P. Allison , Mahlon DeLong , Michael N. Hall , Robert S. Langer , Richard P. Lifton and Alexander Varshavsky (2014) • Alim Louis Benabid , Charles David Allis , Victor Ambros , Gary Ruvkun , Jennifer Doudna and Emmanuelle Charpentier (2015) • Edward Boyden , Karl Deisseroth , John Hardy , Helen Hobbs and Svante Pääbo (2016) • Stephen J. Elledge , Harry F. Noller , Roeland Nusse , Yoshinori Ohsumi , Huda Zoghbi (2017) • Joanne Chory , Peter Walter , Kazutoshi Mori , Kim Nasmyth , Don W. Cleveland (2018) • C. Frank Bennett and Adrian R. Krainer , Angelika Amon , Xiaowei Zhuang , Zhijian Chen (2019) • Jeffrey M. Friedman , Franz-Ulrich Hartl , Arthur L. Horwich , David Julius , Virginia Man-Yee Lee (2020) • David Baker , Catherine Dulac , Dennis Lo , Richard J. Youle (de) (2021) • Jeffery W. Kelly , Katalin Karikó , Drew Weissman , Shankar Balasubramanian , David Klenerman and Pascal Mayer (2022) • Clifford P. Brangwynne , Anthony A. Hyman , Demis Hassabis , John Jumper , Emmanuel Mignot , Masashi Yanagisawa (2023) • Carl June , Michel Sadelain , Sabine Hadida , Paul Negulescu , Fredrick Van Goor, Thomas Gasser, Ellen Sidransky and Andrew Singleton (2024)

[v · t · e] Laureates of the Prince or Princess of Asturias Award for Technical and Scientific Research Prince of Asturias Award for Technical and Scientific Research • 1981: Alberto Sols • 1982: Manuel Ballester • 1983: Luis Antonio Santaló Sors • 1984: Antonio García-Bellido • 1985: David Vázquez Martínez and Emilio Rosenblueth • 1986: Antonio González González • 1987: Jacinto Convit and Pablo Rudomín • 1988: Manuel Cardona and Marcos Moshinsky • 1989: Guido Münch • 1990: Santiago Grisolía and Salvador Moncada • 1991: Francisco Bolívar Zapata • 1992: Federico García Moliner • 1993: Amable Liñán • 1994: Manuel Patarroyo • 1995: Manuel Losada Villasante and Instituto Nacional de Biodiversidad of Costa Rica • 1996: Valentín Fuster • 1997: Atapuerca research team • 1998: Emilio Méndez Pérez and Pedro Miguel Echenique Landiríbar • 1999: Ricardo Miledi and Enrique Moreno González • 2000: Robert Gallo and Luc Montagnier • 2001: Craig Venter , John Sulston , Francis Collins , Hamilton Smith , and Jean Weissenbach • 2002: Lawrence Roberts , Robert E. Kahn , Vinton Cerf , and Tim Berners-Lee • 2003: Jane Goodall • 2004: Judah Folkman , Tony Hunter , Joan Massagué , Bert Vogelstein , and Robert Weinberg • 2005: Antonio Damasio • 2006: Juan Ignacio Cirac • 2007: Peter Lawrence and Ginés Morata • 2008: Sumio Iijima , Shuji Nakamura , Robert Langer , George M. Whitesides , and Tobin Marks • 2009: Martin Cooper and Raymond Tomlinson • 2010: David Julius , Baruch Minke , and Linda Watkins • 2011: Joseph Altman , Arturo Álvarez-Buylla , and Giacomo Rizzolatti • 2012: Gregory Winter and Richard A. Lerner • 2013: Peter Higgs , François Englert , and European Organization for Nuclear Research CERN • 2014: Avelino Corma Canós , Mark E. Davis , and Galen D. Stucky Princess of Asturias Award for Technical and Scientific Research • 2015: Emmanuelle Charpentier and Jennifer Doudna • 2016: Hugh Herr • 2017: Rainer Weiss , Kip S. Thorne , Barry C. Barish , and the LIGO Scientific Collaboration • 2018: Svante Pääbo • 2019: Joanne Chory and Sandra Myrna Díaz • 2020: Yves Meyer , Ingrid Daubechies , Terence Tao, and Emmanuel Candès • 2021: Katalin Karikó , Drew Weissman , Philip Felgner , Uğur Şahin , Özlem Türeci , Derrick Rossi , and Sarah Gilbert • 2022: [Geoffrey Hinton](/