The Shaw prize

Author's comments: The following three documents were composed on the receipt of the Shaw Prize in 2007. They have appeared or will appear in publications of the Shaw Foundation. The first two, a very brief autobiography and a slightly longer memoir, need no explanation. They are informal. So is the third, an attempt to explain clearly the nature of what is often referred to as the Langlands program. It is still uncertain that I succeeded, partly because the program remains in good part just that---a program and not a mature theory, although I have been cheered by the reaction to this essay, which contains a dangerously large speculative element.

Programs, if that is the correct word, are a combination of insights, partial results and conceptual constructions, whose value depends to a very large extent on the quality and vigor of those who understand their purpose and are convinced of their pertinence. This particular program has found many friends, to whom its strength is due, but in some respects it went against the grain of a good number mathematicians. There are elements in it sufficiently foreign to them that even with good will they were unable to grasp its nature. The misunderstanding and resistance that ensue can, I hope, be overcome by patience and time. The occasional frank discussion or candid admission of cherished, even if somewhat veiled, goals may also be of some value. I hope that this essay is blunt enough to be clear, but not so blunt that it is ineffective.