Terence Tao

Terence Chi-Shen Tao

Tao at March 2006 Erdős Memorial Conference in Memphis, Tennessee
Born (1975-07-17) 17 July 1975
Adelaide, South Australia
Residence Los Angeles, California
Nationality Australia[1]
United States[1]
Fields Mathematics
Institutions University of California, Los Angeles (UCLA)
Alma mater Flinders University
Princeton University
Doctoral advisor Elias M. Stein
Known for Green–Tao theorem
Erdős discrepancy problem
Compressed Sensing
Tao's inequality
Kakeya conjecture
Horn Conjecture
Notable awards
Website
www.math.ucla.edu/~tao/

Terence "Terry" Chi-Shen Tao FAA FRS (simplified Chinese: 陶哲轩; traditional Chinese: 陶哲軒; pinyin: Táo Zhéxuān) (born 17 July 1975, Adelaide), 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 co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics.

Tao maintains a personal mathematics blog,[2] which has been said by Timothy Gowers to be "the undisputed king of all mathematics blogs".

Personal life

Family

Tao's father, Dr. Billy Tao (Chinese: 陶象國; pinyin: Táo Xiàngguó), was a paediatrician who born in Shanghai and earned a MBBS at University of Hong Kong in 1969.[3] Tao's mother, Grace (Chinese:梁蕙蘭, English: Leung Wai-lan), is a Hongkonger who got first-class honours in physics and mathematics at HKU, too.[4] She was a secondary school teacher of mathematics in Hong Kong.[5] They met at the university while they were studying there.[6] His parents are first generation immigrants from Hong Kong to Australia.[7]

Tao has two brothers living in Australia, both of whom represented Australia at the International Mathematical Olympiad.

Tao, his wife Laura, an engineer at NASA's Jet Propulsion Laboratory,[9] and their son and daughter live in Los Angeles, California.

Childhood

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.[10] In 1986, 1987, and 1988, Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten, winning a bronze, silver, and gold medal respectively. 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.

10yr old Tao with Paul Erdős in 1985

At age 14, Tao attended the Research Science Institute. When he was 15 he published his first assistant paper. 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 Fulbright Scholarship to undertake postgraduate study in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his PhD at the age of 21.[11] He joined the faculty of the University of California, Los Angeles in 1996. 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,[12] reaching 68 co-authors by October 2015.

In a book review, the mathematician Timothy Gowers remarked on Tao's accomplishments:

“ 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 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. ”

Tao has won numerous honors and awards over the years.[13]

He is a Fellow of the Royal Society, the Australian Academy of Sciences (Corresponding Member), the National Academy of Sciences (Foreign member), the American Academy of Arts and Sciences, and the American Mathematical Society.[14] In 2006, he received the Fields Medal "for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory", and in 2006, he was awarded the MacArthur Fellowship. He has been featured in The New York Times, CNN, USA Today, Popular Science, and many other media outlets.[15]

As of 2013 Tao has published over 250 research papers and 17 books.[16] He has an Erdős number of 2.[17]

Early years: PDEs, Kakeya conjecture, and Horn conjecture

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.

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:[18][19]

“ In 2004, Dr. Tao, along with Ben Green, a mathematician now at the University of Cambridge in England, solved a problem related to the Twin Prime Conjecture by looking at prime number progressions—series of numbers equally spaced. (For example, 3, 7 and 11 constitute a progression of prime numbers with a spacing of 4; the next number in the sequence, 15, is not prime.) Dr. Tao and Dr. Green proved that it is always possible to find, somewhere in the infinity of integers, a progression of prime numbers of equal spacing and any length. ”

For this and other work Tao was awarded the Australian Mathematical Society Medal of 2004.

Tao in his UCLA office, 2006

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.[20][21]

An article by New Scientist[22] writes of his ability:

“ 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 [professor of mathematics at Princeton University].[20] ”

Tao was a finalist to become Australian of the Year in 2007.[23] He is a corresponding member of the Australian Academy of Science, and in 2007 was elected as a Fellow of the Royal Society.[24][25] In the same year Tao also published Tao's inequality,[26] 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.[27]

In December 2008, he was named the Lars Onsager lecturer[28] 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"[29] at NTNU, Norway.

Tao was also elected a Fellow of the American Academy of Arts and Sciences in 2009.[30]

In 2010, he received the King Faisal International Prize jointly with Enrico Bombieri.[31] Also in 2010, he was awarded the Nemmers Prize in Mathematics[32] and the Polya Prize (SIAM) jointly with Emmanuel Candès for their work on Compressed Sensing.[33]

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.[34][35] Also, in 2012, he was selected as a Simons Investigator.[36] He proved that every odd integer greater than 1 is the sum of at most five primes.[37]

Higher Order Fourier analysis, Dirac-Motzkin conjecture, Navier-Stokes equation, Prime gaps, Erdős Discrepancy Problem

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 of the notorious 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.[38]

Notable awards

Book publications

See also

References

  1. 1 2 "Vitae and Bibliography for Terence Tao". 12 Oct 2009. Retrieved 2010-01-21.
  2. ↑ "What's new". What's new. Retrieved 5 September 2015.
  3. ↑ Dr Billy Tao, Healthshare.
  4. ↑ Terence Tao: the Mozart of maths, March 7, 2015, Stephanie Wood, The Sydney Morning Herald.
  5. ↑ Oriental Daily, Page A29, 24 August 2006.
  6. ↑ Terence Chi-Shen Tao, MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland.
  7. ↑ Wen Wei Po, Page A4, 24 August 2006.
  8. 1 2 Nigel makes Waves: Google's bid to overthrow email, Asher Moses, Sydney Morning Herald, 2009-10-02
  9. ↑ "History, Travel, Arts, Science, People, Places - Smithsonian". Retrieved 5 September 2015.
  10. ↑ Radical acceleration in Australia: Terence Tao
  11. ↑ It's prime time as numbers man Tao tops his Field Stephen Cauchi, 23 August 2006. Retrieved 31 August 2006.
  12. ↑ The Singular Mind of Terry Tao
  13. ↑ "Vitae". Retrieved 5 September 2015.
  14. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-08-25.
  15. ↑ "Media information". Retrieved 5 September 2015.
  16. ↑ http://ams.math.uni-bielefeld.de/mathscinet/search/publications.html?pg1=IID&s1=361755
  17. ↑ "Who am I?". Retrieved 5 September 2015.
  18. ↑ Kenneth Chang (13 March 2007). "Journeys to the Distant Fields of Prime". New York Times.
  19. ↑ "Corrections: For the Record". New York Times. 13 March 2007.
  20. 1 2 "2006 Fields Medals awarded" (PDF). Notices of the American Mathematical Society (American Mathematical Society) 53 (9): 1037–1044. October 2006.
  21. ↑ "Reclusive Russian turns down math world's highest honour". Canadian Broadcasting Corporation (CBC). 22 August 2006. Retrieved 2006-08-26.
  22. ↑ NewScientist.com, Prestigious Fields Medals for mathematics awarded, 22 August 2006.
  23. ↑ National Australia Day Committee, 2007 Australian of the Year Finalists. Retrieved 2013-03-12.
  24. ↑ Annual report, Australian Academy of Science, 2008.
  25. ↑ Fellows and Foreign Members of the Royal Society, retrieved 2010-06-09.
  26. ↑ http://www.mathematik.uni-bielefeld.de/ahlswede/homepage/public/217.pdf
  27. ↑ National Science Foundation, Alan T. Waterman Award. Retrieved 2008-04-18.
  28. ↑ http://www.ntnu.no/imf/onsager
  29. ↑ NTNU's Onsager Lecture, by Terence Tao on YouTube
  30. ↑ "Alphabetical Index of Active AAAS Members" (PDF). amacad.org. Retrieved 21 November 2013.
    His 2009 induction ceremony is here.
  31. ↑ King Faisal Foundation – retrieved 2010-01-11.
  32. ↑ "Major Math and Science Awards Announced: Northwestern University News". Retrieved 5 September 2015.
  33. ↑ "SIAM: George Pólya Prize". Retrieved 5 September 2015.
  34. ↑ "The Crafoord Prize in Mathematics 2012 and The Crafoord Prize in Astronomy 2012". Royal Swedish Academy of Sciences. 19 January 2012. Retrieved 2014-11-13.
  35. ↑ "4 Scholars Win Crafoord Prizes in Astronomy and Math – The Ticker - Blogs - The Chronicle of Higher Education". Retrieved 5 September 2015.
  36. ↑ "Simons Investigators 2012". Simons Foundation. Retrieved 2013-10-28.
  37. ↑ Tao, Terence (2012). "Every odd number greater than 1 is the sum of at most five primes". arXiv:1201.6656 [math.NT].
  38. ↑ https://www.quantamagazine.org/20151001-tao-erdos-discrepancy-problem/
  39. ↑ http://mathisaac.org/Award.html
  40. ↑ "CEE Presents Dr. Terence Tao with the Joseph I. Lieberman Award for his Significant Contribution to Mathematics". Retrieved 5 September 2015.
  41. ↑ Solving Mathematical Problems: A Personal Perspective, Oxford University Press 2006
  42. ↑ Green, Ben (2009). Review: Additive combinatorics by Terence C. Tao and Van H. Vu (PDF). Bull. Amer. Math. Soc. (N.S.) 46. pp. 489–497.

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