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.