Evolution of the Mapping/Function Concept - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T02:54:38Z http://mathoverflow.net/feeds/question/92702 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/92702/evolution-of-the-mapping-function-concept Evolution of the Mapping/Function Concept Yrogirg 2012-03-30T18:02:51Z 2012-12-30T05:25:33Z <p>Hello! I'm looking for a survey (of the history) of the concept of mapping/function. How the concept was <em>evolving</em>. Especially I'm interested in what it turned into during the last 50 years.</p> <p>So actually what are the modern views on this entity and how they emerged, the motivation behind.</p> http://mathoverflow.net/questions/92702/evolution-of-the-mapping-function-concept/92805#92805 Answer by Ronnie Brown for Evolution of the Mapping/Function Concept Ronnie Brown 2012-04-01T11:07:33Z 2012-04-01T11:07:33Z <p>For the early history of the function concept, and the confusions, see the delightful book </p> <p>J.E. Littlewood, "A mathematician's miscellany" Methuen, London, 1953. Republished as <em>Littlewood's Miscellany</em>, Edited B. Bollobas, Cambridge University Press, 1986.</p> http://mathoverflow.net/questions/92702/evolution-of-the-mapping-function-concept/117568#117568 Answer by Peter Michor for Evolution of the Mapping/Function Concept Peter Michor 2012-12-29T22:26:59Z 2012-12-29T22:26:59Z <p>For Euler a function was something that was given by a formula (that you had to find ...). Also, for sequences \$a_0,a_1,a_2,\dots\$ he sometimes tried to find \$a_{1/2}\$. This forebodes holomorphic or analytic functions. The general notion of a function as associating a value to each argument is due to Dedekind and Weierstrass. I think that they were deeply influenced by developments in physical measurements at the same time which took place in Berlin (Helmholtz etc) where long lists of values of physical measurements were produced and discussed. </p>