Terence Tao

Terence Chi-Shen Tao FAA FRS (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics. He is a professor of mathematics at the University of California, Los Angeles (UCLA). His work focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.[2] As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles.

Terence Chi-Shen Tao
Tao at March 2006 Erdős Memorial Conference in Memphis, Tennessee
Born (1975-07-17) 17 July 1975
Adelaide, South Australia, Australia
NationalityAustralia[1]
United States[1]
Alma mater
Known forGreen–Tao theorem
Erdős discrepancy problem
Compressed sensing
Tao's inequality
Kakeya conjecture
Bounding the de Bruijn-Newman constant
Horn conjecture
Cramer conjecture
Collatz conjecture
Navier-Stokes existence and smoothness
Neutrino oscillations
Uncountable Moore-Schmidt theorem
Spouse(s)Laura Tao
Children2
AwardsFields Medal (2006)
Scientific career
FieldsMathematics
InstitutionsUCLA
ThesisThree Regularity Results in Harmonic Analysis[1] (1996)
Doctoral advisorElias M. Stein
Doctoral studentsMonica Vișan
Websitewww.math.ucla.edu/~tao/ terrytao.wordpress.com
Terence Tao
Traditional Chinese陶哲軒
Simplified Chinese陶哲轩

Tao has made breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory.[3] He was a recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He is also a 2006 MacArthur Fellow. Tao has been the author or co-author of 275 research papers.[4]

Personal life

Family

Tao's parents are first-generation immigrants from Hong Kong to Australia.[5] Tao's father, Dr. Billy Tao (Chinese: 陶象國; pinyin: 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.[6] Tao's mother, Grace (Chinese: 梁蕙蘭, English: Leung Wai-lan), is from Hong Kong; she received a first-class honours degree in astrophysics and mathematics at the University of Hong Kong.[7] She was a secondary school teacher of mathematics and physics in Hong Kong.[8] Billy and Grace met as students at the University of Hong Kong.[9] They then emigrated from Hong Kong to Australia in 1972.[5][7]

Tao has two brothers, Nigel and Trevor, living in Australia. Both formerly represented Australia at the International Mathematical Olympiad.[10]

Tao's wife, Laura, is an electrical engineer at NASA's Jet Propulsion Laboratory.[11][7] They live with their son William and daughter Madeleine in Los Angeles, California.[7]

Childhood

A child prodigy,[12] Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He is one of 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 eight years old; Tao scored a 760.[13][14] Julian Stanley, Director of the Study of Mathematically Precocious Youth stated that he had the greatest mathematical reasoning ability he had found in years of intensive searching.[15] 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 at the age of 12 in 1988.[16] He was said to possibly be the brightest of his age in the whole world.[17]

At 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 the direction of Garth Gaudry.[18] 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 Ph.D. at the age of 21.[18] In 1996, he 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.[18]

Research and awards

Within the field of mathematics, Tao is known for his collaboration with British mathematician 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,[19] reaching 68 co-authors by October 2015.

In a book review, the British mathematician Timothy Gowers remarked on Tao's accomplishments:[20]

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.

Tao has won numerous mathematician honours and awards over the years.[21]

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.[22] 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.[23]

As of 2019, Tao has published nearly 350 research papers and 17 books.[24] He has an Erdős number of 2.[25]

In 2018, Tao proved bounding for the de Bruijn–Newman constant. In 2019, Tao proved for the Collatz Conjecture using probability that almost all Collatz orbits attain almost bounded values.[26][27]

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:[28][29]

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. 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.[30][31]

An article by New Scientist[32] 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].[30]

Tao was a finalist to become Australian of the Year in 2007.[33] He is a corresponding member of the Australian Academy of Science, and in 2007 was elected as a Fellow of the Royal Society.[34][35] In the same year Tao also published Tao's inequality,[36] 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.[37]

In December 2008, he was named the Lars Onsager lecturer[38] 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"[39] at NTNU, Norway.

Tao was also elected a Fellow of the American Academy of Arts and Sciences in 2009.[40]

In 2010, he received the King Faisal International Prize jointly with Enrico Bombieri.[41] Also in 2010, he was awarded the Nemmers Prize in Mathematics[42] and the Pólya Prize (SIAM) jointly with Emmanuel Candès for their work on Compressed Sensing.[43]

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.[44][45] Also, in 2012, he was selected as a Simons Investigator.[46] He proved that every odd integer greater than 1 is the sum of at most five primes.[47]

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 from which Tao graduated. 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.[48]

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.

Publications
  • Solving Mathematical Problems: A Personal Perspective,[53] Oxford University Press, 2006
  • Analysis, Vols I and II, Hindustan Book Agency, 2006
  • Additive Combinatorics, with Van H. Vu, Cambridge University Press, 2006[54]
  • 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, 2011[55]
  • An Epsilon of Room, II: pages from year three of a mathematical blog, American Mathematical Society, 2011[56]
  • 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, 2015[57] (online version)

See also

References
  1. "Vitae and Bibliography for Terence Tao". 12 October 2009. Retrieved 21 January 2010.
  2. "Mathematician Proves Huge Result on 'Dangerous' Problem".
  3. "Mathematics Breakthrough Prize > Laureates > Terence Tao". Archived from the original on 1 November 2014. Retrieved 24 June 2014.
  4. https://arxiv.org/search/?query=%22Terence+Tao%22&searchtype=author&source=header
  5. Wen Wei Po, Page A4, 24 August 2006.
  6. Dr Billy Tao, Healthshare.
  7. Terence Tao: the Mozart of maths, 7 March 2015, Stephanie Wood, The Sydney Morning Herald.
  8. Oriental Daily, Page A29, 24 August 2006.
  9. Terence Chi-Shen Tao, MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland.
  10. Nigel makes Waves: Google's bid to overthrow email, Asher Moses, Sydney Morning Herald, 2009-10-02
  11. "History, Travel, Arts, Science, People, Places - Smithsonian". Archived from the original on 10 September 2012. Retrieved 5 September 2015.
  12. Clements, M. A. (Ken) (1984), "Terence Tao", Educational Studies in Mathematics, 15 (3): 213–238, doi:10.1007/BF00312075, JSTOR 3482178.
  13. Radical acceleration in Australia: Terence Tao
  14. Cook, Gareth (24 July 2015). "The Singular Mind of Terry Tao". The New York Times.
  15. "Radical Acceleration in Australia: Terence Tao". www.davidsongifted.org.
  16. https://www.imo-official.org/TerenceTao.pdf
  17. https://www.youtube.com/watch?v=p6ZUeQv2yFQ
  18. It's prime time as numbers man Tao tops his Field Stephen Cauchi, 23 August 2006. Retrieved 31 August 2006.
  19. The Singular Mind of Terry Tao, 26 July 2015, www.nytimes.com
  20. Mathematical Reviews MR2523047, Review by Timothy Gowers of Terence Tao's Poincaré's legacies, part I, http://mathscinet
  21. "Vitae". UCLA. Retrieved 5 September 2015.
  22. List of Fellows of the American Mathematical Society, retrieved 2013-08-25.
  23. "Media information". UCLA. Retrieved 5 September 2015.
  24. http://ams.math.uni-bielefeld.de/mathscinet/search/publications.html?pg1=IID&s1=361755%5B%5D
  25. "Who am I?". UCLA. Retrieved 5 September 2015.
  26. Tao, Terence (2019). "Almost all orbits of the Collatz map attain almost bounded values". arXiv:1909.03562 [math.PR].
  27. Tao, Terence (10 September 2019). "Almost all Collatz orbits attain almost bounded values". What's new. Retrieved 11 September 2019.
  28. Kenneth Chang (13 March 2007). "Journeys to the Distant Fields of Prime". New York Times.
  29. "Corrections: For the Record". New York Times. 13 March 2007.
  30. "2006 Fields Medals awarded" (PDF). Notices of the American Mathematical Society. 53 (9): 1037–1044. October 2006.
  31. "Reclusive Russian turns down math world's highest honour". Canadian Broadcasting Corporation (CBC). 22 August 2006. Retrieved 26 August 2006.
  32. NewScientist.com, Prestigious Fields Medals for mathematics awarded, 22 August 2006.
  33. National Australia Day Committee, 2007 Australian of the Year Finalists. Retrieved 2013-03-12.
  34. Annual report Archived 7 June 2011 at the Wayback Machine, Australian Academy of Science, 2008.
  35. Fellows and Foreign Members of the Royal Society, retrieved 2010-06-09.
  36. http://www.mathematik.uni-bielefeld.de/ahlswede/homepage/public/217.pdf
  37. National Science Foundation, Alan T. Waterman Award. Retrieved 2008-04-18.
  38. "Archived copy". Archived from the original on 3 February 2009. Retrieved 13 January 2009.CS1 maint: archived copy as title (link)
  39. NTNU's Onsager Lecture, by Terence Tao on YouTube
  40. "Alphabetical Index of Active AAAS Members" (PDF). amacad.org. Retrieved 21 November 2013.
    His 2009 induction ceremony is here.
  41. King Faisal Foundation – retrieved 2010-01-11.
  42. "Major Math and Science Awards Announced: Northwestern University News". Retrieved 5 September 2015.
  43. "SIAM: George Pólya Prize". Retrieved 5 September 2015.
  44. "The Crafoord Prize in Mathematics 2012 and The Crafoord Prize in Astronomy 2012". Royal Swedish Academy of Sciences. 19 January 2012. Retrieved 13 November 2014.
  45. "4 Scholars Win Crafoord Prizes in Astronomy and Math – The Ticker - Blogs - The Chronicle of Higher Education". Retrieved 5 September 2015.
  46. "Simons Investigators Awardees". Simons Foundation. Retrieved 9 September 2017.
  47. Tao, Terence (2012). "Every odd number greater than 1 is the sum of at most five primes". arXiv:1201.6656 [math.NT].
  48. "Terence Tao's Answer to the Erdős Discrepancy Problem". Quanta Magazine.
  49. http://mathisaac.org/Award.html
  50. "CEE Presents Dr. Terence Tao with the Joseph I. Lieberman Award for his Significant Contribution to Mathematics". Retrieved 5 September 2015.
  51. "Riemann Prize laureate 2019: Terence Tao". Retrieved 23 November 2019.
  52. "Yves Meyer, Ingrid Daubechies, Terence Tao and Emmanuel Candès, Princess of Asturias Award for Technical and Scientific Research 2020". Princess of Asturias Foundation. Retrieved 23 June 2020.
  53. Solving Mathematical Problems: A Personal Perspective, Oxford University Press 2006
  54. 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.
  55. An Epsilon of Room, I: Real Analysis, American Mathematical Society, 2011, online version
  56. An Epsilon of Room, II, online version
  57. Lubotzky, Alexander (25 January 2018). "Review of Expansion in finite simple groups of Lie type by Terrence Tao". Bull. Amer. Math. Soc. (N.S.): 1. doi:10.1090/bull/1610; review published electronically
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