Work
Borcherds is best known for his work connecting the theory of finite groups with other areas in mathematics. In particular he invented the notion of vertex algebras, which Igor Frenkel, James Lepowsky and Arne Meurman used to construct an infinite-dimensional graded algebra acted on by the monster group. Borcherds then used this, and methods from string theory, to prove the monstrous moonshine conjecture by Conway and Norton, relating the monster group to the coefficients of the q-expansion of the j-invariant. The result was not only a great increase in understanding of the monster group, a very large finite simple group whose structure was previously not well understood, but tied the monster to various aspects of mathematics and mathematical physics. In recent years, Borcherds has been attempting to construct quantum field theory in a mathematically rigorous manner.
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“Gustav Aschenbach was the writer who spoke for all those who work on the brink of exhaustion, who labor and are heavy-laden, who are worn out already but still stand upright, all those moralists of achievement who are slight of stature and scanty of resources, but who yet, by some ecstasy of the will and by wise husbandry, manage at least for a time to force their work into a semblance of greatness.”
—Thomas Mann (1875–1955)
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—Phyllis Dain (b. 1930)
“Nearly all our powerful men in this age of the world are unbelievers; the best of them in doubt and misery; the worst of them in reckless defiance; the plurality in plodding hesitation, doing, as well as they can, what practical work lies ready to their hands.”
—John Ruskin (1819–1900)