From Pythagoras to Plato, we think that maths can reveal objective truth and uncover the nature of reality. But the majority of mathematics does not describe reality - from countless spatial dimensions to actual infinities. In the words of mathematician Sir Roger Penrose, maths is "full of things that have almost nothing to do with the physical world." But if this is the case, how can we know which of our mathematical theories describe reality and which are just, again in the words of Penrose, "playing around with mathematics for its own sake"?

Should we treat maths as a tool, rather than an insight into ultimate reality? Should we consider maths as demonstrating human reasoning in its most exact form - nothing more, nothing less? Or might we one day prove mathematics really does have a special metaphysical standing and grasp on truth?

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