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.
Paul Erdos, perhaps more than any other mathematician in modern times, has epitomized the strength and breadth of mathematical collaboration. Born more than 80 years ago in Hungary, Erdos has traveled the world for decades in search of new mathematics and new collaborators. Over the years, Erdos has written hundreds of research papers on a wide range of mathematical topics. What's especially astonishing is the extent to which he has worked with other mathematicians to produce joint papers. Mathematicians assign Erdos the number 0.