Everything. But we clean up the incorrectness, sweep any inconsistencies under the rug and then publish the corrected proof as if it sprang, fully-formed, from

Everything. But we clean up the incorrectness, sweep any inconsistencies under the rug and then publish the corrected proof as if it sprang, fully-formed, from our mind. This, much to the bewilderment and bafflement of students thereafter! mwahahaha! http://upload.wikimedia.org/wikipedia/commons/8/84/Evillaugh.ogg http://upload.wikimedia.org/wikipedia/commons/8/84/Evillaugh... If your viewpoint is the history of mathematical proof, then the answer might be "Everything up to the early Greeks." Here's a nice link: "The History and Concept of. Mathematical Proof" by Steven G. Krantz http://www.math.wustl.edu/~sk/eolss.pdf http://www.math.wustl.edu/~sk/eolss.pdf But if you want to really understand then take a look at the book Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by G. Lakoff & R. Núñez. http://www.amazon.com/Where-Mathematics-Comes-Embodied-Brings/dp/0465037712/ref=sr_1_1?s=books&ie=UTF8&qid=1313945868&sr=1-1 http://www.amazon.com/Where-Mathematics-Comes-Embodied-Bring... The introduction and first four chapters [PDF] are available at http://www.cogsci.ucsd.edu/~nunez/web/INTR-04.PDF http://www.cogsci.ucsd.edu/~nunez/web/INTR-04.PDF