Cours de géométrie descriptive by Xavier Antomari
By Xavier Antomari
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Indeed, it is not enough “to get convicted, as it were, rather than convinced of a mathematical truth by a long chain of formal inferences and calculations leading us blindfolded from link to link” [Weyl 1985, p. 14]. 15 A mathematical proof is not just an instrument of persuasion. It is the guise in which a mathematical experience haunts the world hoping to live anew in receptive minds. In Dewey’s model at least, this new life requires a re-creation of creative experience. Re-creation may not measure up to creation but, then again, it ain’t bad!
Re-creation may not measure up to creation but, then again, it ain’t bad! I remember vividly the moment I was able to hold in my mind, all at once, a proof that every finitary closure space has a minimal closed basis. It would have been even more glorious if it had been my proof. But it was glorious nonetheless. There is a drive to own an insight, to grasp a solution in a grasping way. Puzzle drive, though, asks only that we come to understand, to survey the inner mechanism, to get at the why. It is wonderful just to see even when someone else shows us where to look and even when, to return to an earlier point, we have no idea how our insight might 10 Stephen Pollard land us a job or cure a disease.
I love them just the same, Fred I mean and the children, but it’s as though it wasn’t me at all—as though I were looking on at someone else” [Coward 1935, p. 25]. In the end, it just ends. I mention all this because of its relevance to the doctrine of mathematical platonism: the view that mathematical objects are causally inert, supernatural beings with no coordinates in space or time. Whatever one may think of this as metaphysics, one must acknowledge a certain moral insight: mathematics provides a static nowhere, a refreshment room of the mind where, as long as the cat is fed and the children tucked in, we can enjoy voluptuous experiences without harm to any living creature.