Richard Borcherds

 (born 29 November 1959) is a British mathematician, known for his proof of. He was elected in 1994 and in 1998 was awarded a.

Quotes

 * The classification of s shows that every finite simple group either fits into one of about 20 infinite families, or is one of 26 exceptions, called . The is the largest of the sporadic finite simple groups, and was discovered by  and  ... Its order is        8080,17424,79451,28758,86459,90496,17107,57005,75436,80000,00000     = 246 ⋅ 320 ⋅ 59 ⋅ 76 ⋅ 112 ⋅ 133 ⋅ 17 ⋅ 19 ⋅ 23 ⋅29 ⋅ 31 ⋅ 41 ⋅ 47 ⋅ 59 ⋅ 71  (which is roughly the number of elementary particles in the earth). The smallest irreducible representations have dimensions 1, 196883, 21296876, ... The  has the power series expansion j(τ) = q−1 + 744 + 196884q + 21493760q2 +... where q = e2π iτ, and is in some sense the simplest nonconstant function satisfying the functional equations j(τ) = j(τ + 1) = j(−1/τ).  noticed some rather weird relations between coefficients of the elliptic modular function and the representations of the monster as follows:                    1 = 1          196884 = 196883 + 1       21493760 = 21296876 + 196883 + 1       where the numbers on the left are coefficients of j(τ) and the numbers on the right are dimensions of irreducible representations of the monster. At the time he discovered these relations, several people thought it so unlikely that there could be a relation between the monster and the elliptic modular function that they politely told McKay that he was talking nonsense. The term “monstrous moonshine” (coined by ) refers to various extensions of McKay’s observation, and in particular to relations between sporadic simple groups and modular functions.


 * ... if you take the s, we have a classification of them ... And then we've got a very simple explanation of why this list turns up, that they more or less correspond to finite reflection groups. And we know who to classify finite reflection groups. ... we can give single uniform construction of all the compact Lie groups. But there's nothing like that for the sporadic groups.
 * (quote at 35:35 of 1:36:06 in video)

Quotes about Richard Borcherds
Richard Borcherds has used the study of certain exceptional and exotic algebraic structures to motivate the introduction of important new algebraic concepts: vertex algebas and generalized s, and he has demonstrated their power by using them to prove the “moonshine conjectures” of and  about the Monster Group and to find whole new families of automorphic forms. A central thread in his research has been a particular Lie algebra, now known as the, which is, in a certain sense, the simplest known example of a generalized Kac-Moody algebra which is not finite-dimensional or affine (or a sum of such algebras). As the name might suggest, this algebra appears to have something to do with the Monster group, i.e. the largest sporadic finite simple group.
 * , arXiv preprint