“For math to thrive, it has to connect to nature. There is no other way.” — Van Vu
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I wouldn't say that point set topology has thrived, not as a self-contained area of research. It explored all kinds of pathological dead ends and ran out of steam. One semester is useful, but after that everyone moves on.
yes! haha that's what i was trying to get at with awfully confusing meme .. my understanding is that point set topology didn't thrive for these very reasons you pointed out
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of course i *do* think pure mathematics can thrive independent of reference to a physical object, so i do disagree with the quote on some level
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I think math can diverge from application for only so long before it becomes self-absorbed and isolated. It may develop independently for decades, but eventually it feeds back into application and draws inspiration from application, or it withers.
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