Content deleted Content added
Arthur Rubin (talk | contribs) Revert "property" addition; seems misplaced, at best. |
m fix |
||
Line 56:
During the [[19th century]], mathematicians started to formalize all the different branches of mathematics. [[Karl Weierstrass|Weierstrass]] advocated building calculus on [[arithmetic]] rather than on [[geometry]], which favoured Euler's definition over Leibniz's (see [[arithmetization of analysis]]).
At first, the idea of a function was rather limited. [[Joseph Fourier]], for example, claimed that every function had a [[Fourier series]], something no mathematician would claim today. By broadening the definition of functions, mathematicians were able to study "strange" mathematical objects such as continuous functions that are [[nowhere differentiable]]. These functions were first thought to be only theoretical curiosities, and they were collectively called "monsters" as late as the turn of the 20th century. However, powerful techniques from [[functional analysis]] have shown that these functions are in some sense "more common" than differentiable functions. Such functions have since been applied to the modeling of physical phenomena such as [[Brownian motion]].
Towards the end of the 19th century, mathematicians started to formalize all of mathematics using [[axiomatic set theory|set theory]], and they sought to define every mathematical object as a [[set]]. [[Johann Peter Gustav Lejeune Dirichlet|Dirichlet]] and [[Nikolai Ivanovich Lobachevsky|Lobachevsky]] independently and almost simultaneously gave the modern "formal" definition of function.
| |||