与数共舞

（转自2006年国际数学家大会官方网站）

Plenary Lecture: Terence Tao
Playing with Numbers

"Is it useful?": a familiar question when speaking about scientific results. However, not every scientist has an application in mind when carrying out research. Sometimes mathematics are simply a challenge to the mind, and for some mathematicians this kind of problem is a paradise in which to work. This is true of Terence Tao, who will give a plenary lecture at the 2006 International Congress of Mathematicians. He is the first to admit that "Prime numbers are a beautiful subject, although they may not have any concrete applications for non-mathematicians".

Professor Tao and the British mathematician Ben Green have proved a result that is easy to understand for a secondary school student, since its elements consist of arithmetic progressions and prime numbers. The challenge first arose some years ago. In 1939, the Dutch mathematician Johannes van der Corput proved the existence of infinite arithmetic progressions of three prime numbers; for example, 3, 5 and 7, or 31, 37, 43. Tao and Green have not only proved the existence of infinite arithmetic progressions of four prime numbers; they have even generalized the result for infinite arithmetic progressions of prime numbers of all lengths.

Some readers may feel like looking for these prime progressions as if they belonged to a sudoku-style numerical puzzle. But Tao's result is more than a game; it constitutes a breakthrough in number theory. Furthermore, as Tao himself adds, "the techniques we are developing may well be useful in future application of greater practical importance; it's hard to predict these things ".

Terence Tao was born in Adelaide (Australia) in 1975. He was the youngest participant in the International Mathematical Olympiad. He participated in the 1986, 1987 and 1988 editions, where he won the bronze, silver and gold medals, respectively. He was just 13 years old when he won the last. In 1991 he graduated in mathematics at the University of Flinders, and in 1996, before his twentieth birthday, he gained his PhD at Princeton University. Since 1996 he has been associated with the UCLA, where he became full professor in 2000. He has received prestigious prizes, such as the Salem prize in 2000, and the Clay Foundation award in 2003 for his work on Kakeya`s Conjecture and wave maps.

Speaker: Terence Tao

Title: Long Arithmetic Progressions in the Primes

Date: Wednesday, 23 of August, 09:00-10:00

ICM2006 scientific programme：http://www.icm2006.org/scientificprogram/plenarylectures/