::::::Historically this term originated to describe proofs in number theory which did not use complex analysis, a usage which now falls under either umbrella. Selberg's Fields Medal was for a variety of contributions (like the Nobel prize, it is given not for a single result, but for overall contributions to mathematics), the primary of which (according to the official citation) was his extension of Brun's work on the zeta function (showing that a positive proportion of zeroes lie on the critical line), decidedly non-elementary work! --[[User:MarkGall|MarkGall]] 12:55, 25 August 2009 (EDT) | ::::::Historically this term originated to describe proofs in number theory which did not use complex analysis, a usage which now falls under either umbrella. Selberg's Fields Medal was for a variety of contributions (like the Nobel prize, it is given not for a single result, but for overall contributions to mathematics), the primary of which (according to the official citation) was his extension of Brun's work on the zeta function (showing that a positive proportion of zeroes lie on the critical line), decidedly non-elementary work! --[[User:MarkGall|MarkGall]] 12:55, 25 August 2009 (EDT) |