Mozart of Maths

He had learnt to read by 2. Attended college maths classes at 9. Got his PhD at 20. Meet Terence Tao...


LOS ANGELES - FOUR hundred people packed into an auditorium at the University of California in Los Angeles in January to listen to a public lecture on prime numbers, one of the rare occasions that the topic drew a standing-room-only audience.

Another 35 people watched on a video screen in a classroom next door. Eighty people were turned away.

The speaker, Dr Terence Tao, a professor of mathematics at the university, promised 'a whirlwind tour, the equivalent to going through Paris and just seeing the Eiffel Tower and the Arc de Triomphe'.

His words were polite, unassuming and tinged with an Australian accent.

After Dr Tao finished his one-hour talk, which was broadcast live on the Internet, several students asked for his autograph.

Dr Tao has drawn attention and curiosity throughout his life for his prodigious abilities. By age two, he had learnt to read. At nine, he attended college maths classes. At 20, he finished his PhD. Now 31, he has grown from prodigy to one of the world's top mathematicians, tackling an unusually broad range of problems, including those involving prime numbers and the compression of images.

Last year, he won a Fields Medal, often considered the Nobel Prize of mathematics, and a MacArthur Fellowship, the 'genius' award that comes with US$500,000 (S$760,000) and no strings attached.

'He's wonderful,' said Mr Charles Fefferman of Princeton University, himself a former child prodigy and a Fields Medallist. 'He's as good as they come. There are a few in a generation, and he's one of the few.'

Colleagues have teasingly called Dr Tao a rock star and the Mozart of Maths. Two museums in Australia have requested his photograph for their permanent exhibits. And he was a finalist for the 2007 Australian of the Year award.

'You start getting famous for being famous,' Dr Tao said. 'The Paris Hilton effect.'

Not that any of that has noticeably affected him. His campus office is adorned with a poster of 'Ranma 1/2', a Japanese comic book. As he walks through the halls of the maths building, he might be wearing an Adidas sweatshirt, blue jeans and scruffy sneakers, looking much like one of his graduate students.

He said he did not know how he would spend the MacArthur money, though he mentioned the mortgage on the house that he and his wife, Laura, an engineer at the Nasa Jet Propulsion Laboratory, bought last year.

Dr Tao, who grew up in Adelaide, Australia, and attended graduate school at Princeton, has settled into sunny southern California.

'I love it a lot,' he said. But not necessarily for what the area offers. 'It's sort of the absence of things I like,' he said. No snow to shovel, for instance.

One area of his research - compressed sensing - could have real-world use. Digital cameras use millions of sensors to record an image, and then a computer chip in the camera compresses the data. 'Compressed sensing is a different strategy,' Dr Tao said. 'You also compress the data, but you try to do it in a very dumb way, one that doesn't require much computer power at the sensor end.'

With Dr Emmanuel Candès, a professor of applied and computational mathematics at the California Institute of Technology, Dr Tao showed that even if most of the information was immediately discarded, the use of powerful algorithms could still reconstruct the original image.

The military is interested in using the work for reconnaissance: blanket a battlefield with simple, cheap cameras that might each record a single pixel of data.

Each camera would transmit the data to a central computer that, using the mathematical technique developed by Dr Tao and Dr Candès, would construct a comprehensive view.

Dr Tao's best-known mathematical work involves prime numbers - positive whole numbers that can be divided evenly only by themselves and 1. The first few prime numbers are 2, 3, 5, 7, 11 and 13 (1 is excluded).

As numbers get larger, prime numbers become sparser, but the Greek mathematician Euclid proved some time around 300 BC that there is nonetheless an infinite number of primes.

Many questions about prime numbers continue to elude answers. Euclid also believed that there was an infinite number of 'twin primes' - pairs of prime numbers separated by 2, like 3 and 5 or 11 and 13 - but he was unable to prove his conjecture. Nor has anyone else in the succeeding 2,300 years.

A larger unknown question is whether hidden patterns exist in the sequence of prime numbers or whether they appear randomly.

In 2004, Dr Tao, along with Mr 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 Mr Green proved that it is always possible to find, somewhere in the infinity of integers, a progression of any length of equally spaced prime numbers.

'Terry has a style that very few have,' Mr Fefferman said. 'When he solves the problem, you think to yourself, 'This is so obvious and why didn't I see it? Why didn't the 100 distinguished people who thought about this before not think of it?''

Dr Tao's proficiency with numbers appeared at a very young age. A two-year-old Terry Tao used toy blocks to show older children how to count.

'He probably was quietly learning these things from watching Sesame Street,' said his father, Dr Billy Tao, a paediatrician who migrated to Australia from Hong Kong in 1972. 'We basically used Sesame Street as a baby-sitter.'

The blocks had been bought as toys, not learning tools. 'You expect them to throw them around,' said Dr Billy Tao.

Terry's parents placed him in a private school when he was 31/2. They pulled him out six weeks later because he was not ready to spend that much time in a classroom, and the teacher was not ready to teach someone like him.

At five, he was enrolled in a public school, and his parents, administrators and teachers set up an individualised programme for him. He proceeded through each subject at his own pace, quickly accelerating through several grades in maths and science while remaining closer to his age group in other subjects. In English classes, for instance, he became flustered when he had to write essays.

'I never really got the hang of that,' he said. 'These very vague, undefined questions. I always liked situations where there were very clear rules of what to do.'

Assigned to write a story about what was going on at home, Terry went from room to room and made detailed lists of the contents.

When he was 71/2, he began attending maths classes at the local high school. Dr Billy Tao also arranged for maths professors to mentor Terry.

A couple of years later, he was taking university-level maths and physics classes. He excelled in international maths competitions. His parents decided not to push him into college full-time, so he split his time between high school and Flinders University, the local university in Adelaide.

He finally enrolled as a full-time college student at Flinders when he was 14, two years after he would have graduated had his parents pushed him only according to his academic abilities.

The Taos had different challenges in raising their other two sons, although all three excelled in maths. Trevor, two years younger than Terry, is autistic with top-level chess skills and the musical savant gift to play back on the piano a musical piece - even one played by an entire orchestra - after hearing it just once. He completed a PhD in maths and now works for the Defence Science and Technology Organisation in Australia.

The youngest, Nigel, told his father that he was 'not another Terry', and his parents let him learn at a slower pace. Nigel, with degrees in economics, maths and computer science, now works as a computer engineer for Google Australia.

'All along, we tend to emphasise the joy of learning,' Dr Billy Tao said. 'The fun is doing something, not winning something.'

Terry completed his undergraduate degree in two years, earned a master's degree a year after that, then moved to Princeton for his doctoral studies.

Dr Tao said a future project would be to try to teach more non-mathematicians how to think mathematically - a skill that would be useful in everyday tasks such as comparing mortgages.

'I believe you can teach this to almost anybody,' he said.

New York Times