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Ivars Peterson's MathLand June 10, 1996 Groups, Graphs, and Paul Erdos Many people have the impression that mathematical research is largely a solitary pursuit. They imagine a mathematician squirreled away in some dingy garret, lonely wilderness cabin, or sparsely furnished cubicle, oblivious to everyday concerns and focused on a single problem, scribbling inscrutable equations across scraps of paper, and thinking long and hard before emerging with a eureka and a proof. The dramatic announcement in 1993 by Andrew Wiles that he had proved Fermat's Last Theorem appeared to belong to this category of discovery. He had virtually separated himself from the rest of the mathematical community for nearly eight years to work on this problem. Only a select few were aware of what he was trying to accomplish. Yet, Wiles had relied heavily on the previous work of other mathematicians who had tackled the same problem. He had occasionally tested his ideas on a few trusted experts in areas of mathematics relevant to his approach. And when reviewers later discovered a flaw in his original chain of logic, he obtained help from one of his former graduate students, Richard Taylor, to fill in the gap and complete the proof. At the same time, the relative isolation that Wiles sought is certainly not the rule in mathematical research. Doing mathematics is really a remarkably social process. The abundance of meetings, conferences, workshops, colloquia, seminars, and other gatherings of mathematicians attests to the importance of collaboration. Electronic communication speeds and facilitates such interaction. | |
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