Terence Tao Professor Terence Tao has won the prestigious Fields Medal for his work with prime numbers and harmonic analysis.

Child Prodigy TERENCE Tao showed his mathematical talent from an early age. The South Australian started high school at eight; by age 12 was studying mathematics at third-year university level; and at 14 was studying postgraduate-level maths. He graduated from Flinders University at 16 and 17 with bachelor's and master's degrees in science, gained his PhD from Princeton University at 21, and was appointed professor of mathematics at the University of California in Los Angeles at 24.

Fields Medallist At 31, and still at UCLA, he capped off a stellar career by winning the world's most prestigious prize in mathematics, the Fields Medal, for his trail-blazing work in fields such as prime numbers and harmonic analysis. He received the honour from King Juan Carlos of Spain at the International Congress of Mathematicians in Madrid in Professor Garth Gaudry, from the University of NSW, was at the awards ceremony, having taught a 12-year- old Terence Tao at Flinders University. "Even at that age, he exhibited stunning insight and creativity. Discovering new mathematics was such an enjoyable adventure for Terry. To be Terry's teacher was, for me, the privilege of a lifetime," said Professor Gaudry.

Where will his work eventually lead? Professor Gaudry said Professor Tao's ideas "may well have unforeseen applications. For example, his theory of prime numbers and factorisation are the basis of some of the most important codes for the protection of information, including banking information. So it is intriguing to wonder where his work will eventually lead."

His Citation The citation for Professor Tao described him as an "extraordinary mathematician": "Terence Tao is a supreme problem solver whose spectacular work has had an impact across several mathematical areas. He combines sheer technical power, an other-worldly ingenuity for hitting upon new ideas, and a startlingly natural point of view that leaves other mathematicians wondering, why didn't anyone see that before?“ The citation said "a dramatic new result about the fundamental building blocks of mathematics, the prime numbers" was one of the highlights of his work.

Prime Numbers A prime number is a number, such as three, five, or seven, that can only be divided by itself and one. Professor Tao was recognised for his work in researching prime number sequences, a series of prime numbers that are evenly spaced. For example, 5, 17, 29, 41, and 53 is a sequence of five prime numbers. (The sequence ends at 53 because 65 is not a prime number).

Series of prime numbers that are evenly spaced Series of Prime NumbersSpacing # in series 2, 312 3, 5, 723 3, 7, , 37, , 257, 263, , 11, , 13, , 17, 29, 41, , 139, 151, , 269, 281, , 7829, 7841,

Prime Arithmetic Progression An arithmetic progression of primes is a set of primes of the form p 1 + kd for fixed p 1 and d and consecutive k, i.e. {p 1, p 1 + d, p 1 + 2d, … }. For example, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 is a 10-term arithmetic progression of primes with difference 210.of the form

Primes in Arithmetic Progression It had long been conjectured that there exist arbitrarily long sequences of primes in arithmetic progression. As early as 1770, Lagrange and Waring investigated how large the common difference of an arithmetic progression of n primes must be. In 1923, Hardy and Littlewood made a very general conjecture known as the k-tuple conjecture about the distribution of prime constellations, which includes the hypothesis that there exist infinitely long prime arithmetic progressions as a special case. Important additional theoretical progress was subsequently made by van der Corput (1939), who proved than there are infinitely many triples of primes in arithmetic progression, and Heath-Brown (1981), who proved that there are infinitely many four-term progressions consisting of three primes and a number that is either a prime or semiprime.primesarithmetic progressionk-tuple conjectureprime constellationssemiprime However, despite all this labour, proof of the general result for arbitrarily long sequences of primes has remained an open conjecture. Thanks to new work by Ben Green and Terence Tao, the conjecture seems to finally have been settled in the positive. In a recently published preprint, Green and Tao (2004) use an important result known as Szemerédi's theorem in combination with recent work by Goldston and Yildirim, a clever "transference principle," and 48 pages of dense and technical mathematics, to apparently establish the fundamental theorem that the prime numbers do contain arithmetic progressions of length k for all k.Szemerédi's theorem

Fields Medal The Fields Medal 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 years. The Fields Medal is widely viewed as the top honour a mathematician can receive. mathematicians International Congress International Mathematical Union The Fields Medal features Archimedes and a quote attributed to him which reads in Latin: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world).Archimedes

Conditions of the Award The Fields Medal is often described as the "Nobel Prize of Mathematics" for the prestige it carries. The comparison is not entirely accurate because the Fields Medal is only awarded every four years. The Medal also has an age limit: a recipient's 40th birthday must not occur before January 1 of the year in which the Fields Medal is awarded. This rule is based on Fields' desire thatNobel PrizeMathematicsJanuary 1 … while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others. The monetary award is much lower than the roughly US$1.5 million given with each Nobel Prize. Finally, Fields Medals have generally been awarded for a body of work, rather than for a particular result.

Nature or Nurture? Tao first revealed himself as a child prodigy at two by learning to read from Sesame Street on TV. With a one-in-a-million IQ score of 220, Tao inherited a lucky combination of genes from his father Billy, a pediatrician, and his mother, a former mathematics teacher, who have two other highly talented sons.

An article by New ScientistNew Scientist 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.”

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