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Why does the universe being bounded imply mathematics is finite?

Because the bounded universe creates bounds on what the intelligences within it can conceive of as mathematics.

We can conceive of lots of mathematics that our own universe doesn't necessarily support. But only that much and no more: we're still made of stuff inside the universe, and so are our tools, so there are upper limits on our conception.

Bounds do not imply bounds. There are an infinite number of numbers between zero and one. Heck, with our finite minds in finite time we have created uncountable infinities!

Mathematics that our universe does not support is still mathematics. Also you're viewing this through a human lens. How do you know it doesn't support what you think it doesn't support? Mathematics after all is a very human pursuit. Some alien species may have started off with ternary or even continuous logic. We have no counterexamples to show that that is beyond our universe.

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