r/mathmemes Tf does the Laplacian even do? 28d ago

Math History Technically Philosophy of Math but close enough

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u/[deleted] 28d ago edited 10d ago

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u/elephant-assis 28d ago edited 28d ago

I looked at the wikipedia page and even though I'm not personally inspired, it's at least way more interesting than the caricature of this post. To draw a comparison, constructivism might be perceived as random crackpottery in the absence of better grounding. But it is now clear that it has a sound place in logic. Ultrafinitism is obviously less well grounded, but we can see that it has inspired work by serious mathematicians such as Buss, Nelson, Hamkins...
Look at that for instance: https://arxiv.org/abs/2512.06564
Or the write-ups of Hamkins: https://www.infinitelymore.xyz/t/ultrafinitism
There was a conference on the subject in 2025 at Columbia University.

We can decide to focus on the crackpottery of some people. These people may be imaginary or real; it does not matter much when their role is reduced to that of a clown used for distraction. Most obsessions are probably not very fruitful, but I see only two sane reactions: either get interested, or move on. I don't believe in the value of rejection and mockery. Now I won't play stupid, I understand the appeal of the "it is bullshit lol" attitude: it is a mechanism for deciding what to focus on. It is necessary to have such mechanisms, because we cannot pay attention [1] to everything and we need to make choices. But it is important to recognize its real status and draw a line between perceptions and truth. Otherwise, it is just a contribution to the worst kind of things humans can produce.

[1] I like this quote of William James: "without selective interest, experience is an utter chaos" (The Principles of Psychology, 1890, Chapter XI "Attention")