Reflections on the Future of Mathematics

Avner Friedman
1998 Mitteilungen der DMV  
Imagine Arehirnedes (287-212 BC) , one of the most distinguished mathematicians of all times, being asked: What do you see in the future for mathematics? Perched on the beach of his hometown, Syracuse, on t he eastern shore of Sicily, the ancient mathematician, having just computed t he surface and volume of spheres, or the area of a parabolic section, straightens up his back and Iooks intently into the horizon. He wonders: What else could he or anyone else do with mathematics? One of his great
more » ... s? One of his great ambitions was to be able to compute volumes and surfaces of any geometric object; yet he had no idea how to go about it. His tools were purely geometrical, based on several hundred years of research by Greek mathematicians, edited several decades before his birth by Euclid in his famous book, Elements. Being quite limited in his mathematical tools, Arehirnedes was undoubtedly also limited in his vision. He did not have a quick way of adding or multiplying fractions. For it would take more than a thousand years before t he decimal system would be developed and transported to Europe by the Hindus and Arabs. The simplification of notation introduced by the decimal system was revolutionary in its enabling power .
doi:10.1515/dmvm-1998-0212 fatcat:7ayqppse5vglnnamoe3apx3lbi