Monday, April 16, 2007

Euler's 300th birthday

celebration is drawing several articles particularly about his beautiful equation:
http://www.sciencenews.org/articles/20070414/mathtrek.asp
He was one of those who could work on any area of mathematics on any day and in the days when proofs were not always sound could feel his way through most complicated concepts and computations. Some say that he and Jacobi were the only two comparable to Srinivasa Ramanujam for their feel for astonishing formulae and he was probably the first to realize the many valuedness of the logarithmic function. He was also a religious man and there is this 'story' of his proof for the existence of god. If you sum the series 1-1+1-1+1-1+1... by one grouping (1-1)+(1-1)+...you get 0 and if you sum it 1+(-1+1)+(-1+1)+..., you get 1. Apparently this was how god created something out of nothing. The precise notion of infinite sums, called convergence, became clearer only with Cauchy but Euler got away with playing around with non-convergent series.