From the age of seven, Erik Demaine travelled with and was taught by his father - until Erik took over, aged nine. Jon Marcus met him at MIT, where the 21-year-old is an assistant professor on the cutting edge of mathematics and map folding

Most of the students in the "introduction to algorithms" course Erik Demaine taught at the Massachusetts Institute of Technology last semester were older than he was. It is also likely that their route to this place was radically different from his.

Demaine, who turned 21 at the end of February, is not only MIT's youngest assistant professor ever, he has already helped solve some of today's most confounding mathematical problems. He got there after quitting school at the age of seven and being schooled by his father, a silversmith and glassblower with no more than a high-school education. Together they travelled around North America to craft shows, stopping at university campuses, where his father would knock on doors and ask questions of faculty members. Most obliged. "The academic environment is really open in that sense," Demaine says now, though he concedes that many faculty were probably just curious about this obvious child prodigy.

The pair stayed in rented rooms, ate cheap meals and travelled mainly by bus from eastern Canada to the southern United States. In addition to spending an hour a day on home schooling, they visited museums and libraries and borrowed textbooks or browsed in bookshops. When he was nine, Erik took over the home-schooling manual and started teaching himself. He occasionally enrolled in school, but found the pace too slow. Because of this, he says, public education "misses out on a lot of potential. A lot of students could do what I did. It shouldn't be that difficult. But the system is set up so that it is difficult, and that's not easy to change. It's possible to circumvent the system, and that's what we did, but there should be a system that works for everyone."

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Home schooling was faster, he says, and uninterrupted by long summer holidays. "You don't forget everything you've learned and have to spend the next term reviewing it. A lot of it I would do just by myself, reading about computers or mathematics, and sometimes I would do things with my dad, like a puzzle."

When he was 12, Demaine wandered into the computer science department of Dalhousie University in Nova Scotia, Canada, and asked to enrol. Even though he lacked any formal qualifications, he was allowed to take programming and algebra classes in which he excelled.

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Two years later, he took a seat in a graduate class at the University of Waterloo in Ontario. "I did not know how young Erik was when I first met him," says Anna Lubiw. "Since I met him as a student in my graduate classes, I just assumed he was a very youthful-looking graduate student."

But his work stood out. "He was already a good scholar, in the sense that he would always do a thorough job in the library looking things up. But many of the assignments required original thought, and Erik's thinking was just not in the same channel as everyone else's. It was somehow freer. He had not put walls between different areas, as the rest of us had."

By the time Erik was 15, he and Lubiw were writing papers together. When Lubiw discovered that Erik's father was also attending her classes, she hired him as a research assistant. It was the senior Demaine, with his background in art, who introduced his son to the obscure field of origami mathematics. "He mentioned it as something interesting he had read in a maths article," says his son, who made origami maths - in essence the study of how things fold - the subject of his doctoral thesis. "He has some great ideas that seem to come out of nowhere. We're both learning together."

Origami mathematics has become a resurgent field and has been applied to everything from the folding of proteins in human DNA to the folding of air bags in cars. Demaine was one of three scholars who developed an algorithm that causes the distance between all points of an arc to increase constantly, solving, among other things, a 40-year-old puzzle of keeping robot arms from tangling.

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But the good-natured scientist has also applied his skills to more frivolous problems, such as how to fold maps.

After he finished his doctorate at Waterloo at the age of 19, Demaine began to be recruited by top institutions, including Stanford, New York and Carnegie Mellon universities. He took the job at MIT, which made his father an unpaid visiting scholar with an office one floor above his son's.

Demaine has already been granted a semester's leave from teaching to co-write a book called Folding and Unfolding in Computational Geometry . But even when he returns to a classroom in the autumn, most of his students will still be older than he is - something, he says, that has not appeared to present a problem. "As far as I know, it didn't come up," he says. "It shows their maturity. It shouldn't matter."