The SIAM 100-Digit Challenge: A Decade Later Inspirations, Ramifications, and Other Eddies Left in Its Wake

摘要

In 2002, L.N. Trefethen of Oxford University challenged the scientific community by ten intriguing mathematical problems to be solved, numerically, to ten digit accuracy each (I was one of the successful contestants; in 2004, jointly with three others of them, I published a book-Bornemann et al.: The SIAM 100-Digit Challenge, SIAM, Philadelphia, 2004-on the manifold ways of solving those problems). In this paper, I collect some new and noteworthy insights and developments that have evolved around those problems in the last decade or so. In the course of my tales, I will touch mathematical topics as diverse as divergent series, Ramanujan summation, low-rank approximations of functions, hybrid numeric-symbolic computation, singular moduli, self-avoiding random walks, the Riemann prime counting function, and winding numbers of planar Brownian motion. As was already the intention of the book, I hope to encourage the reader to take a broad view of mathematics, since one lasting moral of Trefethen's contest is that overspecialization will provide too narrow a view for one with a serious interest in computation.