Terence Tao

# Terence Tao

Discussion

Encyclopedia
Terence Chi-Shen Tao FRS  (born 17 July 1975, Adelaide, South Australia
South Australia
South Australia is a state of Australia in the southern central part of the country. It covers some of the most arid parts of the continent; with a total land area of , it is the fourth largest of Australia's six states and two territories.South Australia shares borders with all of the mainland...

) is an Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

working primarily on harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...

, partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

, analytic number theory
Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...

and representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...

. Tao is a professor of mathematics at the University of California, Los Angeles
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...

.

His single most famous contribution to mathematics is the proof that there exists arbitrarily long arithmetic progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...

s of prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

s (the Green–Tao theorem).

## Personal life

Tao was a child prodigy
Child prodigy
A child prodigy is someone who, at an early age, masters one or more skills far beyond his or her level of maturity. One criterion for classifying prodigies is: a prodigy is a child, typically younger than 18 years old, who is performing at the level of a highly trained adult in a very demanding...

, one of the subjects in the longitudinal research on exceptionally gifted children by education researcher Miraca Gross
Miraca Gross
Miraca Una Murdoch Gross AM is an Australian author and scholar recognised as an authority on the academic, social and emotional needs of gifted children....

. His father told the press that at the age of two, during a family gathering, Tao attempted to teach a 5-year-old child mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

and English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

. According to Smithsonian Online Magazine, Tao could carry out basic arithmetic by the age of two. When asked by his father how he knew numbers and letters, he said he learned them from Sesame Street
Sesame Street
Sesame Street has undergone significant changes in its history. According to writer Michael Davis, by the mid-1970s the show had become "an American institution". The cast and crew expanded during this time, including the hiring of women in the crew and additional minorities in the cast. The...

. Aside from English, Tao speaks Cantonese, but does not write Chinese
Chinese language
The Chinese language is a language or language family consisting of varieties which are mutually intelligible to varying degrees. Originally the indigenous languages spoken by the Han Chinese in China, it forms one of the branches of Sino-Tibetan family of languages...

.

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. Tao's father was born and grew up in Shanghai
Shanghai
Shanghai is the largest city by population in China and the largest city proper in the world. It is one of the four province-level municipalities in the People's Republic of China, with a total population of over 23 million as of 2010...

, and Tao's mother is Cantonese
Cantonese people
The Cantonese people are Han people whose ancestral homes are in Guangdong, China. The term "Cantonese people" would then be synonymous with the Bun Dei sub-ethnic group, and is sometimes known as Gwong Fu Jan for this narrower definition...

by ethnicity. His parents are first generation immigrants from Hong Kong
Hong Kong
Hong Kong is one of two Special Administrative Regions of the People's Republic of China , the other being Macau. A city-state situated on China's south coast and enclosed by the Pearl River Delta and South China Sea, it is renowned for its expansive skyline and deep natural harbour...

to Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

. His father, Billy Tao is a pediatrician, and his mother is a physics and mathematics graduate from the University of Hong Kong, formerly a secondary school teacher of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

in Hong Kong
Hong Kong
Hong Kong is one of two Special Administrative Regions of the People's Republic of China , the other being Macau. A city-state situated on China's south coast and enclosed by the Pearl River Delta and South China Sea, it is renowned for its expansive skyline and deep natural harbour...

.

Tao has two brothers living in Australia, both of whom represented Australia at the International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...

.
• Nigel Tao is part of the team at Google Australia that created Google Wave
Apache Wave is a software framework for real-time collaborative editing online. Google Inc. originally developed it as Google Wave.It was announced at the Google I/O conference on May 27, 2009....

.
• Trevor Tao has a double degree in maths and music and will soon be featured in a book on autistic savants.

Tao currently lives with his wife Laura, son, and daughter in Los Angeles
Los Ángeles
Los Ángeles is the capital of the province of Biobío, in the commune of the same name, in Region VIII , in the center-south of Chile. It is located between the Laja and Biobío rivers. The population is 123,445 inhabitants...

, California
California
California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...

.

Tao exhibited extraordinary mathematical abilities from an early age, attending university level mathematics courses at the age of nine. He is one of only two children (besides Lenhard Ng
Lenhard Ng
Lenhard Ng is an American mathematician working primarily on symplectic geometry. Ng is an associate professor of mathematics at Duke University.- Personal life :...

) in the history of the Johns Hopkins' Study of Exceptional Talent
Study of Exceptional Talent
The Julian C. Stanley Study of Exceptional Talent is an outgrowth of the Study of Mathematically Precocious Youth at Johns Hopkins University...

program to have achieved a score of 700 or greater on the SAT math section while just 8 years old (he scored a 760). In 1986, 1987, and 1988, Tao was the youngest participant to date in the International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...

, first competing at the age of ten, winning a bronze, silver, and gold medal respectively. He won the gold medal when he just turned thirteen and remains the youngest gold medallist in the Olympiad's history. At age 14, Tao attended the Research Science Institute
Research Science Institute
The Research Science Institute is a highly competitive summer research program for rising high school seniors around the world, sponsored by the Center for Excellence in Education and hosted by MIT. It is often regarded as "the most prestigious and competitive high-school science program in the...

. When he was 15 he published his first assistant paper. He received his bachelor's and master's degrees (at the age of 17) from Flinders University
Flinders University
Flinders University, , is a public university in Adelaide, South Australia. Founded in 1966, it was named in honour of navigator Matthew Flinders, who explored and surveyed the South Australian coastline in the early 19th century.The university has established a reputation as a leading research...

under Garth Gaudry. In 1992 he won a Fulbright Scholarship to undertake postgraduate study in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

. From 1992 to 1996, Tao was a graduate student at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

under the direction of Elias Stein, receiving his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...

at the age of 20. He joined the faculty of the University of California, Los Angeles
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...

in 1996.

## Research and awards

In August 2006, he was awarded a Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...

, widely considered the top honour a mathematician can receive. In September 2006, he was awarded a MacArthur Fellowship. He was elected a Fellow of the Royal Society on 18 May 2007. He became a foreign associate of the United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...

in 2008 and elected a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...

in 2009. On 11 January 2010, the King Faisal Foundation
King Faisal Foundation
The King Faisal Foundation was established in 1976 by the sons of King Faisal of Saudi Arabia. The Director-General is HRH Prince Khalid Al-Faisal...

announced that Tao is the co-winner of the King Faisal International Prize in the field of science for his works in mathematics.

Salem Prize
The Salem Prize, founded by the widow of Raphael Salem, is awarded every year to a young mathematician judged to have done outstanding work in Salem's field of interest, primarily the theory of Fourier series.-Past winners:...

in 2000, the Bôcher Prize in 2002, and the Clay Research Award
Clay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...

in 2003, for his contributions to analysis including work on the Kakeya conjecture and wave maps. In 2005 he received the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...

's Levi L. Conant Prize with Allen Knutson, and in 2006 he was awarded the SASTRA Ramanujan Prize
SASTRA Ramanujan Prize
The SASTRA Ramanujan Prize, founded by Shanmugha Arts, Science, Technology & Research Academy University in Kumbakonam, India, Srinivasa Ramanujan's hometown, is awarded every year to a young mathematician judged to have done outstanding work in Ramanujan's fields of interest...

.

In 2004, Ben Green
Ben Green (mathematician)
Ben Joseph Green FRS is a British mathematician, specializing in combinatorics and number theory. He is the Herchel Smith Professor of Pure Mathematics at the University of Cambridge.- Early years :...

and Tao released a preprint proving what is now known as the Green–Tao theorem. This theorem states that there are arbitrarily long arithmetic progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...

s of prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

s. The New York Times
The New York Times
The New York Times is an American daily newspaper founded and continuously published in New York City since 1851. The New York Times has won 106 Pulitzer Prizes, the most of any news organization...

described it this way: For this and other work, he was awarded the Australian Mathematical Society Medal
Australian Mathematical Society Medal
Australian Mathematical Society Medal recognises distinguished mathematical sciences research by members of the Australian Mathematical Society. Eligibility for the medal include the requirements that the Society member must be under the age of 40 years, and that a significant portion of the...

in 2005.

In 2006, at the 25th International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....

Madrid is the capital and largest city of Spain. The population of the city is roughly 3.3 million and the entire population of the Madrid metropolitan area is calculated to be 6.271 million. It is the third largest city in the European Union, after London and Berlin, and its metropolitan...

, he became one of the youngest, the first Australian, and the first UCLA faculty member ever to be awarded a Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...

. An article by New Scientist
New Scientist
New Scientist is a weekly non-peer-reviewed English-language international science magazine, which since 1996 has also run a website, covering recent developments in science and technology for a general audience. Founded in 1956, it is published by Reed Business Information Ltd, a subsidiary of...

writes of his ability:
Tao was a finalist to become Australian of the Year
Australian of the Year
Since 1960 the Australian of the Year Award has been part of the celebrations surrounding Australia Day , during which time the award has grown steadily in significance to become Australia’s pre-eminent award. The Australian of the Year announcement has become a very prominent part of the annual...

in 2007. He is a corresponding member of the Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The Academy is modelled after the Royal Society and operates under a Royal Charter; as such it is...

, and in 2007 was elected as a Fellow of the Royal Society. In the same year Tao also published Tao's inequality, an extension to the Szemerédi regularity lemma
Szemerédi regularity lemma
In mathematics, the Szemerédi regularity lemma states that every large enough graph can be divided into subsets of about the same size so that the edges between different subsets behave almost randomly. introduced a weaker version of this lemma, restricted to bipartite graphs, in order to prove ...

in the field of information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

.

In April 2008, Tao received the Alan T. Waterman Award
Alan T. Waterman Award
The Alan T. Waterman Award is the United States's highest honorary award for scientists no older than 35. It is awarded on a yearly basis by the National Science Foundation. In addition to the medal, the awardee receives a grant of $500,000 to be used for advanced scientific research at the... , which recognizes an early career scientist for outstanding contributions in their field. In addition to a medal, Waterman awardees also receive a$500,000 grant for advanced research.

In December 2008, he was named The Lars Onsager
Lars Onsager
Lars Onsager was a Norwegian-born American physical chemist and theoretical physicist, winner of the 1968 Nobel Prize in Chemistry.He held the Gibbs Professorship of Theoretical Chemistry at Yale University....

lecturer of 2008, for "his combination of mathematical depth, width and volume in a manner unprecedented in contemporary mathematics". He was presented the Onsager Medal, and held his Lars Onsager lecture entitled "Structure and randomness in the prime numbers" at NTNU
Norwegian University of Science and Technology
The Norwegian University of Science and Technology , commonly known as NTNU, is located in Trondheim. NTNU is the second largest of the eight universities in Norway, and, as its name suggests, has the main national responsibility for higher education in engineering and technology...

, Norway
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...

.

In 2010, he received the King Faisal International Prize jointly with Enrico Bombieri
Enrico Bombieri
Enrico Bombieri is a mathematician who has been working at the Institute for Advanced Study in Princeton, New Jersey. Bombieri's research in number theory, algebraic geometry, and mathematical analysis have earned him many international prizes --- a Fields Medal in 1974 and the Balzan Prize in 1980...

. Also in 2010, he was awarded the Nemmers Prize in Mathematics
Nemmers Prize in Mathematics
The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Erwin Plein Nemmers Prize in Economics, as part of a \$14 million donation from the Nemmers brothers. They envisioned creating an award that...

along with the Polya Prize(SIAM)
Pólya Prize (SIAM)
The Pólya Prize is a prize in mathematics, awarded by the Society for Industrial and Applied Mathematics. First given in 1969, the prize is named after Hungarian mathematician George Pólya...

. Tao and Van H. Vu
Van H. Vu
Van H. Vu is a Vietnamese mathematician, a professor of mathematics at Yale University and the 2008 winner of the Pólya Prize of the Society for Industrial and Applied Mathematics for his work on concentration of measure. He is a collaborator of Terence Tao....

solved the circular law
Circular law
In probability theory, more specifically the study of random matrices, the circular law describes the distribution of eigenvalues of an n \times n random matrix with independent and identically distributed entries in the limit n \to \infty ....

conjecture.

In 2011, he was one of the many to be nominated as Australian of the Year
Australian of the Year
Since 1960 the Australian of the Year Award has been part of the celebrations surrounding Australia Day , during which time the award has grown steadily in significance to become Australia’s pre-eminent award. The Australian of the Year announcement has become a very prominent part of the annual...

. However, he did not win.

As of 2007 Tao has published over 140 research papers and has won 13 different awards.

## Publications

• Solving Mathematical Problems: A Personal Perspective, Oxford University Press, 2006
• Analysis, Vols I and II, Hindustan Book Agency, 2006
• Additive Combinatorics, with Van H. Vu
Van H. Vu
Van H. Vu is a Vietnamese mathematician, a professor of mathematics at Yale University and the 2008 winner of the Pólya Prize of the Society for Industrial and Applied Mathematics for his work on concentration of measure. He is a collaborator of Terence Tao....

, Cambridge University Press, 2006
• Structure and Randomness: pages from year one of a mathematical blog, American Mathematical Society. 2008
• Poincaré's legacies: pages from year two of a mathematical blog, Vols. I and II, American Mathematical Society, 2009
• An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog, American Mathematical Society, 2011
• An Epsilon of Room, II: pages from year three of a mathematical blog, American Mathematical Society, 2011