[coolsdude2282]

This is only tangentially related but I hope it provokes discussion. One thing that I don't understand is why Platonism remains extremely popular throughout Mathematics departments the world over and Finitism/Ultra-finitism is so unpopular with them. Combinatorics and Discrete topics are often very unpopular topics to work on in my experience.

Finitism in an analogous way to functional programming seems like the best way to move the field forward, but it is rarely used by Mathematicians in practice. Why on earth is this? (My understanding of mathematics is lacking, so I hope this doesn't come off as a silly comment)

[teraflop]

I'm having a hard time understanding this comment. Are you talking about mathematics or philosophy?

I don't understand why finitism would ever be expected to lead to new mathematical insights, since it basically amounts to closing off research directions because they don't have some nebulous quality of "real-ness". I also don't see how finitism has any connection to functional programming.

[xelxebar]

Ultra-finitist logic is a perfectly rigorous field of study in its own right. I think OP is making a point that this logic and us related branches are quite understudied.

It's encouraging to note that with things like Homotopty Type Theory, we're finally starting to come to grips with Fundamentals that aren't tied to the ZFC implementation.

[eastWestMath]

But ultrafinitism isn't actually interesting as a mathematical theory. As the previous poster said, its appeal lies in its "realness". Intuitionistic and linear logic are substantially more interesting.

[coolsdude2282]

But this was why I posed it as a question, everyone says this is somehow 'more interesting' but is that because it is actually qualitatively more interesting or are more interesting things coming out of it simply due to the fact that it is more popular quantitatively with researchers? If it is qualitatively more interesting, what about it makes it so?

I likened it to functional programming because finitism makes things interesting via its purity and restriction in an analogous way.

[eastWestMath]

But it's not similarly interesting, linear and intuitionistic logic are. Finitism is just kind of stupid.

[posterboy]

philosophy of mathematics? The argument to closing off areas goes both ways. FP, I guess, was really just used as analogy.