Eduardo quotes Mac Lane as saying (paraphrased) If it hasn't been proved, it isn't mathematics
Much as I admire Mac Lane and owe much to him, that's rather at odds with what most of us do even those who insist on getting a proof ultimately.
case in point:
http://www.oxfordtoday.ox.ac.uk/2005-06/v18n2/04.shtml
if that isn't math, what is it? (perjorative adjective of your choice) mathematics?
Was Newton doing *only* physics?
jim
In fact standards of proof and rigor have undergone quite some transformation in time, so why could they not change drastically in future? Again lacking proper knowledge I want to ask those who know more history to confirm or reject something I've been told. Namely, seemingly in times of Euler and Bernoullis, to be able to prove one's statements was just a matter of honour, but nobody was obliged to accompany announcement of a theorem with a proof - you could keep the latter to yourself and should only present it if somebody would challenge you by expressing doubt; which probably did not happen that often. So how do we know that what we consider a rigorous proof today will not be viewed as something insufficient or even irrelevant in a couple of centuries? For example, if mathematics would develop my way, I would give a fact the status of being established only after seeing its validity does not require any serious effort or expertise from an average mathematician (maybe even a student). This would not necessarily mean waiting much more time - in case mathematicians would continue to learn *seeing* more and more. I mean, if you have to explain to a person in the street how to reach some place, the amount and kind of explanation you need depends critically on whether the person is blind or not. Mamuka