Terence Tao

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Terence Tao
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{{Use dmy dates|date=May 2011}}{{Use Australian English|date=May 2011}}

|birth_place = Adelaide, South Australia|spouse = Laura Tao|children = 2|residence = Los Angeles, CaliforniaDATE=12 OCT 2009, 2010-01-21, United States|alma_mater = {{plainlist}} |thesis_title = Three Regularity Results in Harmonic Analysis|thesis_year = 1996|doctoral_advisor = Elias M. Stein|doctoral_students = Monica ViÈ™an|known_for = Green–Tao theoremErdÅ‘s discrepancy problemCompressed sensingTao's inequalityKakeya conjectureBounding the de Bruijn-Newman constantHorn conjecture Cramer conjecture Collatz conjectureNavier-Stokes existence and smoothnessweblink}} {{URLweblink}}|field = MathematicsUniversity of California, Los Angeles>UCLAFields Medal (2006)}}{hide}clist
|framestyle = border:none; padding:0;
|liststyle = list-style-type:disc; text-align:left;
|title = {{nobold|more accolades{edih}
|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)| Convocation Award (2008) | King Faisal International Prize (2010)|Nemmers Prize in Mathematics (2010)
|Pólya Prize (2010)|Crafoord Prize (2012)|Simons Investigator (2012)|Breakthrough Prize in Mathematics (2014)
|Royal Medal (2014)|PROSE Award (2015)}}

Terence Chi-Shen Tao {{post-nominals|country=AUS|FAA|FRS}} (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. {{as of|2015}}, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles.Tao was a recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He is also a 2006 MacArthur Fellow. This prolific mathematician has been the author or co-author of 275 research papers, his most impressive results being those on three-dimensional Navier-Stokes existence and smoothness.weblink is the second ethnic Chinese mathematician to win the Fields medal after Shing-Tung Yau, and the first Australian mathematician to win the medal.

Personal life


Tao's father, Dr. Billy Tao ({{zh|t=陶象國|p=Táo Xiàngguó}}), was a pediatrician who was born in Shanghai, China and earned his medical degree (MBBS) from the University of Hong Kong in 1969.Dr Billy Tao, Healthshare. Tao's mother, Grace (Chinese: 梁蕙蘭, English: Leung Wai-lan), is from Hong Kong; she received a first-class honours degree in physics and mathematics at the University of Hong Kong.Terence Tao: the Mozart of maths, 7 March 2015, Stephanie Wood, The Sydney Morning Herald. She was a secondary school teacher of mathematics and physics in Hong Kong.Oriental Daily, Page A29, 24 August 2006. Billy and Grace met as students at the University of Hong Kong.Terence Chi-Shen Tao, MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland. They then emigrated from Hong Kong to Australia in 1972.Wen Wei Po, Page A4, 24 August 2006.Terence Tao: the Mozart of maths, 7 March 2015, Stephanie Wood, The Sydney Morning Herald.Tao has two brothers, Nigel and Trevor, living in Australia. Both formerly represented Australia at the International Mathematical Olympiad.Nigel makes Waves: Google's bid to overthrow email, Asher Moses, Sydney Morning Herald, 2009-10-02Tao's wife, Laura, is an electrical engineer at NASA's Jet Propulsion Laboratory.WEB,weblinkweblink" title="">weblink dead, 10 September 2012, History, Travel, Arts, Science, People, Places - Smithsonian, 5 September 2015, Terence Tao: the Mozart of maths, 7 March 2015, Stephanie Wood, The Sydney Morning Herald. They live with their son William and daughter Madeleine in Los Angeles, California.Terence Tao: the Mozart of maths, 7 March 2015, Stephanie Wood, The Sydney Morning Herald.


Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He and Lenhard Ng are the only two children in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just nine years old; Tao scored a 760.WEB,weblink Radical Acceleration in Australia: Terence Tao,, Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten; in 1986, 1987, and 1988, he won a bronze, silver, and gold medal. He remains the youngest winner of each of the three medals in the Olympiad's history, winning the gold medal shortly after his thirteenth birthday. File:Paul Erdos with Terence Tao.jpg|right|thumb|10-year-old Tao with Paul ErdősPaul ErdősAt age 14, Tao attended the Research Science Institute. When he was 15, he published his first assistant paper. In 1991, he received his bachelor's and master's degrees at the age of 16 from Flinders University under Garth Gaudry. In 1992, he won a Postgraduate Fulbright Scholarship to undertake research in Mathematics (Topology) at Princeton University in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his PhD at the age of 20.It's prime time as numbers man Tao tops his Field Stephen Cauchi, 23 August 2006. Retrieved 31 August 2006. He then (in 1996) joined the faculty of the University of California, Los Angeles. In 1999, when he was 24, he was promoted to full professor at UCLA and remains the youngest person ever appointed to that rank by the institution.

Research and awards

Within the field of mathematics, Tao is known for his collaboration with Ben J. Green of Oxford University; together they proved the Green–Tao theorem. Known for his collaborative mindset, by 2006, Tao had worked with over 30 others in his discoveries,The Singular Mind of Terry Tao, 26 July 2015, reaching 68 co-authors by October 2015.In a book review, the mathematician Timothy Gowers remarked on Tao's accomplishments:Mathematical Reviews MR2523047, Review by Timothy Gowers of Terence Tao's Poincaré's legacies, part I,weblink has won numerous honours and awards over the years.WEB,weblink Vitae, UCLA, 5 September 2015, He is a Fellow of the Royal Society, the Australian Academy of Science (Corresponding Member), the National Academy of Sciences (Foreign member), the American Academy of Arts and Sciences, and the American Mathematical Society.List of Fellows of the American Mathematical Society, retrieved 2013-08-25. In 2006 he received the Fields Medal "for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory", and was also awarded the MacArthur Fellowship. He has been featured in The New York Times, CNN, USA Today, Popular Science, and many other media outlets.WEB,weblink Media information, UCLA, 5 September 2015, By 2016, Tao had published about 300 research papers and 17 booksweblink{{Dead link|date=June 2018 |bot=InternetArchiveBot |fix-attempted=no }} He has an Erdős number of 2.WEB,weblink Who am I?, UCLA, 5 September 2015, In 2018, Tao proved bounding the de Bruijn–Newman constant. In 2019, Tao proved for the Collatz Conjecture using probability that almost all Collatz orbits attain almost bounded values.ARXIV, Tao, Terence, Terence Tao, 1909.03562, Almost all orbits of the Collatz map attain almost bounded values, math.PR, 2019, WEB, Tao, Terence, Almost all Collatz orbits attain almost bounded values,weblink What's new, 11 September 2019, en, 10 September 2019,

Green–Tao theorem and compressed sensing

In 2004, Ben Green and Tao released a preprint proving what is now known as the Green–Tao theorem. This theorem states that there are arbitrarily long arithmetic progressions of prime numbers. The New York Times described it this way:NEWS,weblink Journeys to the Distant Fields of Prime, Kenneth Chang, 13 March 2007, New York Times, NEWS,weblink Corrections: For the Record, 13 March 2007, New York Times,
For this and other work Tao was awarded the Australian Mathematical Society Medal of 2004.He was awarded a Fields Medal in August 2006 at the 25th International Congress of Mathematicians in Madrid. He was the first Australian, the first UCLA faculty member, and one of the youngest mathematicians to receive the award.JOURNAL, 2006 Fields Medals awarded, Notices of the American Mathematical Society, 53, 9, October 2006,weblink PDF, 1037–1044, NEWS,weblink Reclusive Russian turns down math world's highest honour, Canadian Broadcasting Corporation (CBC), 22 August 2006, 2006-08-26, An article by New, Prestigious Fields Medals for mathematics awarded, 22 August 2006. writes of his ability:Tao was a finalist to become Australian of the Year in 2007.National Australia Day Committee, 2007 Australian of the Year Finalists. Retrieved 2013-03-12. He is a corresponding member of the Australian Academy of Science, and in 2007 was elected as a Fellow of the Royal Society.Annual report {{webarchive|url= |date=7 June 2011 }}, Australian Academy of Science, 2008.Fellows and Foreign Members of the Royal Society, retrieved 2010-06-09. In the same year Tao also published Tao's inequalityweblink an extension to the Szemerédi regularity lemma in the field of information theory.In April 2008, Tao received the Alan T. Waterman Award, 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.National Science Foundation, Alan T. Waterman Award. Retrieved 2008-04-18.In December 2008, he was named the Lars Onsager lecturerWEB,weblink Archived copy, 2009-01-13, dead,weblink" title="">weblink 3 February 2009, dmy-all, 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"{{Youtube|L61HNEWuUbE|NTNU's Onsager Lecture, by Terence Tao}} at NTNU, Norway.Tao was also elected a Fellow of the American Academy of Arts and Sciences in 2009.WEB, Alphabetical Index of Active AAAS Members,weblink American Academy of Arts and Sciences,, 21 November 2013, His 2009 induction ceremony is here.In 2010, he received the King Faisal International Prize jointly with Enrico Bombieri.King Faisal Foundation – retrieved 2010-01-11. Also in 2010, he was awarded the Nemmers Prize in MathematicsWEB,weblink Major Math and Science Awards Announced: Northwestern University News, 5 September 2015, and the Pólya Prize (SIAM) jointly with Emmanuel Candès for their work on Compressed Sensing.WEB,weblink SIAM: George Pólya Prize, 5 September 2015,

Random matrices, Hardy–Littlewood prime tuples conjecture, approximate groups

In 2007, Tao and Van H. Vu solved the circular law conjecture.In 2010, joint work with Ben Green culminated in the proof of the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity.Tao also made contributions to the study of the Erdős–Straus conjecture in 2011, by showing that the number of solutions to the Erdős–Straus equation increases polylogarithmically as n tends to infinity.In 2012, he and Jean Bourgain received the Crafoord Prize in Mathematics from the Royal Swedish Academy of Sciences.WEB, The Crafoord Prize in Mathematics 2012 and The Crafoord Prize in Astronomy 2012, 19 January 2012,weblink Royal Swedish Academy of Sciences, 2014-11-13, WEB,weblink 4 Scholars Win Crafoord Prizes in Astronomy and Math – The Ticker - Blogs - The Chronicle of Higher Education, 5 September 2015, Also, in 2012, he was selected as a Simons Investigator.WEB, Simons Investigators Awardees,weblink Simons Foundation, 2017-09-09, He proved that every odd integer greater than 1 is the sum of at most five primes.ARXIV, 1201.6656, Tao, Terence, Every odd number greater than 1 is the sum of at most five primes, math.NT, 2012,

Other work

In 2012, in joint work with longtime co-author Ben Green, proofs were announced for the Dirac-Motzkin conjecture and the "orchard-planting problem" (which asks for the maximum number of lines through exactly 3 points in a set of n points in the plane, not all on a line). That same year, Tao published the first monograph on the topic of higher order Fourier analysis.In 2014, Tao received a CTY Distinguished Alumni Honor from Johns Hopkins Center for Gifted and Talented Youth in front of 963 attendees in 8th and 9th grade that are in the same program that Tao graduated from. That year, Tao presented work on a possible attack on the Navier–Stokes existence and smoothness Millennium Problem, by establishing finite time blowup for an averaged three-dimensional Navier-Stokes equation.That year he also, jointly with several co-authors, proved several results on short and long prime gaps.In September 2015, Tao announced a proof of the Erdős discrepancy problem, using for the first time entropy-estimates within analytic number theory.WEB,weblink Terence Tao's Answer to the Erdős Discrepancy Problem, Quanta Magazine,

Notable awards

He received the Salem Prize in 2000, the Bôcher Memorial Prize in 2002, and the Clay Research Award in 2003, for his contributions to analysis including work on the Kakeya conjecture and wave maps. In 2005, he received the American Mathematical Society's Levi L. Conant Prize with Allen Knutson for a proof of the Horn conjecture, and in 2006 he was awarded the SASTRA Ramanujan Prize.


  • Solving Mathematical Problems: A Personal Perspective,Solving Mathematical Problems: A Personal Perspective, Oxford University Press 2006 Oxford University Press, 2006
  • Analysis, Vols I and II, Hindustan Book Agency, 2006
  • Additive Combinatorics, with Van H. Vu, Cambridge University Press, 2006JOURNAL, Green, Ben, Ben Green (mathematician), Review: Additive combinatorics by Terence C. Tao and Van H. Vu, Bull. Amer. Math. Soc. (N.S.), 2009, 46, 3, 489–497,weblink 10.1090/s0273-0979-09-01231-2,
  • Nonlinear dispersive equations: local and global analysis, CBMS regional series in mathematics, 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, 2011An Epsilon of Room, I: Real Analysis, American Mathematical Society, 2011, online version
  • An Epsilon of Room, II: pages from year three of a mathematical blog, American Mathematical Society, 2011An Epsilon of Room, II, online version
  • An Introduction to Measure Theory. American Mathematical Society, 2011, (online version)
  • Topics in Random Matrix Theory, American Mathematical Society, 2012 (online version)
  • Higher-order Fourier Analysis, American Mathematical Society, 2012 (online version)
  • Compactness and Contradiction, American Mathematical Society, 2013 (online version)
  • Hilbert's Fifth Problem and Related Topics, American Mathematical Society, 2014 (online version)
  • Expansion in Finite Simple Groups of Lie Type, American Mathematical Society, 2015JOURNAL, Lubotzky, Alexander, Alexander Lubotzky, Review of Expansion in finite simple groups of Lie type by Terrence Tao, Bull. Amer. Math. Soc. (N.S.), 1, 25 January 2018, ; review published electronically, 10.1090/bull/1610, (online version)

See also



External links

{{commons category|Terence Tao}} {{FRS 2007}}{{Fields medalists}}{{Breakthrough Prize laureates}}{{Authority control}}

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