Terence Tao

Terence Tao (2006)

Terence "Terry" Chi-Shen Tao ( Chinese  陶哲軒  /  陶哲轩 , Pinyin Táo Zhéxuān ; born July 17, 1975 in Adelaide ) is an Australian mathematician and Fields Medal Prize winner.

Life

Paul Erdős and Terence Tao (1985)

Tao was known as a math prodigy . At the age of eight he achieved a SAT test result in the mathematical part that corresponds to an above-average student (760 points). At the age of twelve he was the youngest participant and youngest gold medalist in the International Mathematical Olympiad .

Tao attended Flinders University in Australia and graduated with a Masters in 1991 at the age of 16. He then studied from 1992 to 1996 at Princeton University (PhD 1996 with Elias Stein Three Regularity Results in Harmonic Analysis ) and has been a professor at UCLA since 2000 .

His wife, Laura, is an electrical engineer at the Jet Propulsion Laboratory . They live in Los Angeles with their son William and daughter Madeleine .

Services

Tao is a very versatile mathematician who made significant progress in a wide variety of areas ( analytical number theory , harmonic analysis , combinatorics , partial differential equations, etc.). His proof that there are arbitrarily long arithmetic sequences of prime numbers , which he established together with Ben Green in 2004 ( theorem of Green-Tao ), received special attention in the mathematical community . The longest (2020) known arithmetic sequence of prime numbers is 27.

With Emmanuel Candès he founded the research field of compressed sensing (reconstruction of signals from a few randomly arranged samples) in 2004 (independently of David Donoho ).

With Nets Katz he showed that the Minkowski dimension of Besikowitsch sets (in which lines of unit length lie in any orientation) in n-dimensional Euclidean spaces (according to the Kakeya conjecture ) is at least . They thus improved a previously proven lower limit by Thomas Wolff . With Katz and Izabella Laba , he found the best lower limit so far in the three-dimensional case. ${\displaystyle n}$ ${\displaystyle (2-{\sqrt {2}})(n-4)+3}$

In 2014 he published a proof that an averaged version of the Navier-Stokes equation in three dimensions has smooth solutions with blowup in finite time. He also outlined a program of a similar approach to the full Navier-Stokes equations in three dimensions (one of the Millennium Problems ).

With Van H. Vu he published a proof of the semicircle law for the distribution of eigenvalues of random matrices in 2006 and 2010 .

In 2012 he made progress with Goldbach's conjecture by proving that every odd number is a sum of at most five prime numbers. ${\displaystyle n>1}$

In 2015 he proved Paul Erdős ' presumption of discrepancy . That arose from his participation in the Polymath project .

In 2019 he made significant progress on the Collatz problem .

He is known for a math blog , whose posts have also been featured in several books.

Honors

• 1999 Sloan Research Fellowship
• 2000 Salem Prize
• 2002 Bôcher Memorial Prize
• 2003 Clay Research Award
• 2005 Levi L. Conant Prize with Allen Knutson
• 2005 Australian Mathematical Society Medal
• 2005 Ostrowski Prize with Ben Green was awarded to him in 2005 together with Ben Green.
• 2006 Fields Medal , considered the highest honor in the field of mathematics
• 2006 SASTRA Ramanujan Prize
• In 2006 he gave a plenary lecture at the International Congress of Mathematicians in Madrid (The Dichotomy between structure and randomness, arithmetic progressions and the primes).
• 2006 MacArthur Fellow
• 2008 Alan T. Waterman Award
• 2008 Onsager Medal
• 2010 King Faisal International Prize with Enrico Bombieri
• 2010 Nemmers Prize for Mathematics
• 2010 George Pólya Prize
• 2012 Crafoord Prize with Jean Bourgain
• In 2011/12 and 2012/13 he was on the Abel Prize Committee.
• 2014 Breakthrough Prize in Mathematics awarded for various groundbreaking contributions to harmonic analysis, combinatorics, partial differential equations and analytical number theory (laudation).
• 2014 Royal Medal of the Royal Society
• In 2018 he was on the Fields Medal Award Committee .
• 2020 Princess of Asturias Prize in the Science category.

He is a Fellow of the Royal Society , the National Academy of Sciences , the American Mathematical Society , the American Philosophical Society, and the Australian Academy of Science .

Fonts

Books

• Solving Mathematical Problems: A personal perspective. Deakin University Press, Geelong, Vic. 1992, ISBN 0-7300-1365-0 .

• later considerably expanded edition: Solving Mathematical Problems . Oxford University Press 2006, ISBN 0-19-920560-4 .

• Analysis I . Hindustan Books 2006, ISBN 81-85931-62-3 .
• Analysis II . Hindustan Books 2006, ISBN 81-85931-62-3 .
• with Van Vü: Additive Combinatorics , Cambridge University Press 2006.
• Nonlinear dispersive equations: local and global analysis , CBMS regional series in mathematics, 2006.
• Structure and randomness: Pages from Year One of a Mathematical Blog , AMS 2008.
• Poincaré's Legacies: Pages from Year Two of a Mathematical Blog , American Mathematical Society (AMS), 2009.
• An Epsilon of Room: Pages from Year Three of a Mathematical blog, I . AMS 2010, ISBN 978-0-8218-5278-1 ( online edition )
• An Epsilon of Room: Pages from Year Three of a Mathematical Blog, II . AMS 2011, ISBN 978-0-8218-5280-4 ( online edition )
• An Introduction to Measure Theory . AMS 2011, ISBN 978-0-8218-6919-2 ( online edition )
• Topics in Random Matrix Theory . AMS 2012, ISBN 978-0-8218-7430-1 ( online edition )
• Higher Order Fourier Analysis . AMS 2012, ISBN 978-0-8218-8986-2 ( online edition )
• Compactness and Contradiction . AMS 2013, ISBN 978-0-8218-9492-7 ( online edition )
• Complexity and universality , e-enterprise, ISBN 978-3-945059-14-2 , Lemgo, 2014.
• Hilbert's Fifth Problem and Related Topics , American Mathematical Society, 2014
• Expansion in Finite Simple Groups of Lie Type , American Mathematical Society, 2015

Essays and journal publications

• Knutson, Tao: "Honeycombs and the sums of hermitean matrices" , Notices AMS 2001, Issue 2, PDF file, won the Conant Prize
• Tao: "From rotating needles to stability of waves: emerging connections between combinatorics, analysis and PDE" , Notices AMS 2001, issue 3, PDF file
• Green, Tao: Primes contain arbitrary long arithmetic progressions , Annals of Mathematics, Volume 167, 2008, pp. 481-547, Arxiv, 2004 , proof of the existence of arbitrarily long arithmetic sequences of prime numbers

literature

• Stephanie Wood: Terence Tao: the Mozart of maths . The Sydney Morning Herald, March 7, 2015.
• Gareth Cook: The Singular Mind of Terry Tao . The New York Times (magazine), July 24, 2015.
• Mind of a Mathematician , Princeton Mathematical Weekly

Web links

Commons : Terence Tao  - collection of images, videos and audio files

• Terence Tao's website
• personal blog
• John J. O'Connor, Edmund F. Robertson :  Terence Tao. In: MacTutor History of Mathematics archive .
• Bôcher Prize laudation (English; PDF file; 97 kB)
• King Faisal Foundation
• Interview 2003 , Clay Institute Annual Report, PDF file
• The longest known arithmetic sequence of prime numbers
• Interview with Fields medalists Okounkov, Werner, Tao , 2007, Notices AMS, PDF file
• Videos by Terence Tao in the AV portal of the Technical Information Library
• The World's Best Mathematician (*) - Numberphile on YouTube

Individual evidence

1. ↑ Primed for Success. (No longer available online.) Archived from the original on September 9, 2012 ; accessed on July 10, 2020 (English). 
2. ↑ ^{a b} Stephanie Wood: Terence Tao: the Mozart of maths. In: The Sydney Morning Herald . March 5, 2015, accessed July 10, 2020 . 
3. ↑ PrimeGrid: PrimeGrid's AP27 Search. Retrieved February 29, 2020 . 
4. ↑ EJ Candès, J. Romberg, T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math., Vol. 59, 2006, pp. 1207-1223
5. ↑ Tao, Candès "Near-optimal signal recovery from random projections: universal encoding strategies?", IEEE Transactions on Information Theory, Volume 52, Issue 12, 2006, pp. 5406-5425
6. ^ Katz, Tao New bounds for Kakeya problems , J. Anal. Math. 87 (2002), 231-263
7. ↑ Finite time blowup for an averaged three-dimensional Navier-Stokes equation , Arxiv, 2014. Published in J. American Math. Soc., Volume 29, 2016, pp. 601-674
8. ↑ Finite time blowup for an averaged three-dimensional Navier-Stokes equation , blog by Tao 2014
9. ^ Tao, Vu, Random matrices: the circular law, Commun. Contemp. Math., Volume 10, 2008, pp. 261-307, Tao, Vu, Manjunath Krishnapur: Random matrices: Universality of ESD and the Circular Law, Annals of Probability, Volume 38, 2010, pp. 2023-2065, Arxiv
10. ^ Tao, Every odd number greater than 1 is the sum of at most five primes , Preprint, Arxiv 2012, Mathematics of Computation
11. ↑ Kevin Hartnett, Mathematician Proves Huge Result on 'Dangerous' Problem , Quanta Magazine, December 11, 2019
12. ↑ Tao, Almost all orbits of the Collatz map attain almost bounded values, Arxiv 2019
13. ↑ King Faisal Foundation , - accessed January 12, 2010
14. ^ Nemmers Prize 2010
15. ↑ Breakthrough Prize 2014 ( Memento of the original from June 24, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
16. ↑ Princess of Asturias Prize 2020