weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/23/86)
Amazing history flash! In the current issue of _The Mathematical Intelligencer_ and a more detailed forthcoming issue of _Historia Mathematica_ is a description of the notebook of Georg Hindenburg Wunschtraum, an extremely obscure late 19th century mathematician. The notebook was found in 1984, in an attic of some distant relative of Wunschtraum's. In it is a solution to Waring's problem that predates Hilbert's solution by twenty years. Waring's problem says every positive integer is a some of g(k) k'th powers, for some g(k). Wunschtraum's result was apparently not published because his upper bound on g(k) is extremely poor (an iterated exponential of [1 + Euler's constant] about k! times), and his proof was cavalier with divergent series (although rectifiable by standard methods), and his proof was very long and complicated. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720