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I'm not sure I entirely follow what he's saying. My understanding is that Von Neumann is saying that at its core, mathematics is about describing nature, so the
by pesmhey 8y ago
I'm not sure I entirely follow what he's saying. My understanding is that Von Neumann is saying that at its core, mathematics is about describing nature, so the mathematician should prioritize keeping those descriptions useful over rigorous. This isn't an attempt to summarize the whole article, just to see if I'm in the ballpark on what he's saying.
- breck 8y agoYeah you've got it. My read is he's saying for the most part mathematics arises in empiricism, in real world problems. Once the problem is translated into mathematics useful tools develop, but then over time branches will spawn that become increasingly abstract/aesthetic and are generally a waste of time. I also liked the beginning bit where he says you generally can't understand something until you have "assimilated it in an instinctive and empirical way". You need that muscle memory, even for intellectual subjects.