Child prodigy Ruth tells why she's all tied up in knots

Perhaps 100 years from now, Ruth Lawrence may again become world- famous, just as she was nearly 14 years ago as the mathematical prodigy who entered Oxford University when just 12 years old. But then it will be for her equations rather than for her age.

It will take until then, she thinks, because the branch of mathematics she is now researching as an assistant professor in the US is so advanced, so abstruse, so mind-bogglingly complicated for the non-mathematician that it will be years before technology and science advance enough to make any practical use of it.

Knot theory is the broad term for the rarefied branch of maths Ruth is now studying and teaching at the University of Michigan in Ann Arbor, near Detroit. Broadly speaking, it is about, well, knots - their geometry and behaviour, the more complicated they get. But try to narrow it down and you will find yourself in a dense thicket of phrases like "partition functions of a topological quantum field theory".

"Maths is in the end a tool which can be used," she says. "But you shouldn't expect that deep fundamental research will be applicable to anything in the next 50 years."

Ruth was the girl who, aged nine, won the top maths A-level mark; who went to study mathematics at Oxford in 1983 before she was even in her teens, accompanied for all three years by her father, Harold; and who graduated with a first in 1985.

After that, she seemed to disappear from view, though in fact nothing really changed. She simply carried on working, pursuing a brilliant career in mathematics that in 1993 led to her appointment at Michigan.

Nobody there, she says, has any problems with being taught by a 25-year- old. "I don't think they notice after the first day."

Like others her age, she has embraced the Internet with enthusiasm, using it to meet other mathematicians and scientists; she has her own Web page, offering links mostly to mathematical resources, but also to an exhibition of Chagall pictures and a florist. If a Web page indicates a person's character, one would judge that Professor Lawrence is intensely wrapped up in her work. That, certainly, makes no change from the past.

And her personal life does not appear to have changed significantly, either. When you call her home near the university, in Ann Arbor outside Detroit, it is her father, now 57, who answers. It was he who almost obsessively taught her maths from the earliest days. Is he visiting now, or living there? She pauses. "He's ... he does help with typing up papers. But we don't collaborate on them, on research. He helps with proofreading."

She has a word of advice for Sufiah Yusof, the Northampton girl who later this year will, just like her, go to Oxford to read mathematics at the age of 12.

"Enjoy the subject, the beauty of the subject, " she says. "My father brought me up with maths always around me. I always thought it was very beautiful."

Her chosen topic was topology, or the study of surfaces and interconnections. The language of it is complete gibberish to the layman. Her CV says: "My main research interests are in the vast area which has come to be known as Jones-Witten theory." This is where knots and those topological quantum field theories come in. Putting it into words is virtually impossible. Even pictures don't really do it justice. Like all high maths, only equations will do.

"Paraphrase it? Mmmmm," she says, sounding mistrustful of the idea. "Any reader would probably get the wrong impression. It's not like a piece of biology that you can put on a microscope slide. Knot theory is about the very beautiful connections that exist between the invariance of knots" - that is, how some knots just can't be untied or simplified - "and manifolds" (not engine parts, but multi-dimensional constructs).

Surely that's about as abstruse, and unapplicable to anything in real life, as they come? She systematically squashes the suggestion, citing the theory, developed at the beginning of this century, of infinite-dimensional complex spaces. Abstruse? Then, certainly.

"But it led in the 1920s to the possibility of quantum theory; and that made it possible to understand the idea of energy levels of quantum objects. Which led, in time to the laser.

"And even when lasers were invented, people were saying, 'What use is that?' Now, of course, it's everywhere, in compact disc players, laser printers... That's what maths is like: it has always shown itself to be useful in the end."

So somewhere in the future there lies a physical use for phrases she uses with carefree abandon, such as the Jones-Witten theory, and the Yang-Baxter equation, and braid groups, and the Iwahori-Hecke algebra. But it lies somewhere ahead - at a time when Ruth Lawrence will be remembered for her work, not her name.