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Most of our modern conceptions of math defined in terms of a universe in which there are only three dimensions. In some advanced math classes, I have learned to generalize my math skills to any number of variables- which means more dimensions. Still, let's assume that some alternate theory of the universe, such as string theory is true. Does any of our math still hold true? How would our math need to be altered to match the true physics of the universe?

Let's start with a quick comment about string theory. My knowledge is only journalistic, but it's clear that string theory is a mathematical theory and states its hypotheses about extra dimensions using mathematics. And as your comment about additional variables already suggests, there's nothing mathematically esoteric about higher dimensions. When variables have the right sort of independence, they represent distinct mathematical dimensions in a mathematical space, though not necessarily a physical space. (Quantum theory uses abstract spaces called Hilbert spaces that can have infinitely many dimensions. But these mathematical spaces don't represent space as we usually think of it.) Of course, it might be that getting the right physics will call for the development of new branches of math. Remember, for example, that Newtonian physics called for the invention of Calculus, and though earlier thinkers had insights that helped pave the way, Calculus was something new. Just what sort of new...

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