Editing Mathematical proof (section)

==Heuristic mathematics and experimental mathematics==
{{Main|Experimental mathematics}}
While early mathematicians such as [[Eudoxus of Cnidus]] did not use proofs, from [[Euclid]] to the [[foundational mathematics]] developments of the late 19th and 20th centuries, proofs were an essential part of mathematics.<ref>{{cite book|title=[[Indra's Pearls (book)|Indra's Pearls: The Vision of Felix Klein]] |publisher=[[Cambridge University Press]] |last1=Mumford |first1=David B. |author1-link=David Mumford |last2=Series |first2=Caroline |author2-link=Caroline Series |last3=Wright |first3=David  |author3-link=David Wright (arranger) |year=2002 |isbn=978-0-521-35253-6 |quote=What to do with the pictures? Two thoughts surfaced: the first was that they were unpublishable in the standard way, there were no theorems only very suggestive pictures. They furnished convincing evidence for many conjectures and lures to further exploration, but theorems were coins of the realm and the conventions of that day dictated that journals only published theorems.}}</ref> With the increase in computing power in the 1960s, significant work began to be done investigating [[mathematical object]]s beyond the proof-theorem framework,<ref>{{cite web|url=https://home.att.net/~fractalia/history.htm |title=A Note on the History of Fractals |archive-url=https://web.archive.org/web/20090215114618/https://home.att.net/~fractalia/history.htm |archive-date=February 15, 2009 |url-status=dead |quote=Mandelbrot, working at the IBM Research Laboratory, did some computer simulations for these sets on the reasonable assumption that, if you wanted to prove something, it might be helpful to know the answer ahead of time.}}</ref> in [[experimental mathematics]]. Early pioneers of these methods intended the work ultimately to be resolved into a classical proof-theorem framework, e.g. the early development of [[fractal geometry]],<ref>{{cite book |title=Introducing Fractal Geometry |last=Lesmoir-Gordon |first=Nigel |publisher=[[Introducing... (book series)|Icon Books]] |year=2000 |isbn=978-1-84046-123-7 |quote=...brought home again to Benoit [Mandelbrot] that there was a 'mathematics of the eye', that visualization of a problem was as valid a method as any for finding a solution. Amazingly, he found himself alone with this conjecture. The teaching of mathematics in France was dominated by a handful of dogmatic mathematicians hiding behind the pseudonym 'Bourbaki'... |url-access=registration |url=https://archive.org/details/introducingfract0000lesm }}</ref> which was ultimately so resolved.