In the movie "Good Will Hunting," an impoverished South Boston kid who scrapes by mopping floors at MIT astonishes prize-winning professors with his ability to solve--at a glance--math problems that have stumped the experts.
How likely is this scenario? Could a person with no specialized education instantaneously see his way through intellectual thickets impenetrable to the top people in the field? Even if he is a natural-born genius?
Conventional wisdom has it that science today is the province of experts bedecked with degrees and weighty with wisdom acquired through experience. It may come as a surprise, therefore, to learn that amateurs and outsiders have made substantial contributions in fields ranging from chemistry to astronomy:
* A San Diego homemaker working at her kitchen table discovered dozens of new geometric patterns that experts had thought were impossible.
* A Texas banker came up with a formal conjecture (a kind of mathematical hypothesis) that amounts to an expansion, or "sequel," to the famous Fermat's Last Theorem, which defied proof for more than 300 years.
* An electrical engineer in Anaheim discovered two new exploding stars in one night.
Amateurs can't compete with professionals when it comes to high-tech equipment, university connections, academic prestige and funding. But in some ways, their status as nonprofessionals can be a plus.
"Amazingly, lack of formal education can be an advantage," says mathematician Doris Schattschneider of Moravian College in Pennsylvania, who helped "discover" the San Diego homemaker now hailed by mathematicians for her work. "We get stuck in our old ways," Schattschneider said. "Sometimes, progress is only made when someone from the outside looks at it with new eyes."
There was nothing unusual about amateur scientists 200 years ago when science was something people did in their parlors and backyards. Science was not yet sequestered in its own private world, with obscure language and strict academic requirements barring all but highly trained experts.
"If you go back far enough, everybody was an amateur," said UCLA chemist Charles Knobler, who uses methods developed by amateur Agnes Pockels in his work (see accompanying box). "John Priestly, who discovered oxygen, was a minister." Benjamin Franklin was perhaps the ultimate amateur. The 18th century statesman not only discovered that lightning is electricity, he also invented the heat-efficient stove and bifocal eyeglasses.
However, as science has become more specialized, the occasional breakthrough by an amateur has become much more surprising.
'You Need People Who Don't . . . Have All the Wrong Assumptions'
That's one reason the work of San Diego homemaker Marjorie Rice caused such a stir.
A mother of five, Rice made a habit of getting her hands on Scientific American magazine, to which her son subscribed, before the rest of the family. She was a particular fan of Martin Gardner's long-running column, "Mathematical Games."
In July 1975, Gardner, an author and perhaps the best-known mathematical amateur of all, published a column about tiling patterns. A branch of mathematics that lives up to its name, tiling is concerned with determining what kinds of shapes can fit together perfectly without any overlaps or gaps. Since all solid matter, from brains to crystals, is made of tightly packed clusters of molecules, studying the possible ways that shapes can arrange themselves has many scientific applications.
In his column, Gardner mentioned that only certain types of pentagons could perfectly tile a plane, or flat surface, and that all of them were known--or so the mathematicians thought. After reading the piece, however, an amateur named Richard James III thought he found some pentagons that the experts had overlooked. As it turned out, he was right, and Gardner published James' results in his December 1975 column.
The minute Rice saw that, she was off and running. "It made me wonder," she said recently from her home in San Diego. "If he could find one, maybe I could." Since she had no formal training in mathematics, Rice developed her own notation, listing various combinations of sides and angles of pentagons on 3-by-5 cards.
She worked on the problem all through Christmastime 1975, drawing diagrams on the kitchen table when no one was around and hiding them when her husband and children came home, or when friends stopped by.
By February 1976 she was confident she had found new kinds of pentagons that could tile. She sent them off to Gardner. "I'd never written to anyone who wrote articles in magazines," she said, still somewhat awed.
Gardner forwarded Rice's drawings to Schattschneider, an expert in tiling patterns. Schattschneider at first was skeptical. Rice's peculiar markings seemed odd, like "hieroglyphics," the professor recalled. "I was probably condescending."