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In my opinion, the Mathematical Universe Hypothesis is putting the cart before the horse. To me, mathematical theories offer a descriptive account of physical data - physical data is not somehow generated by or determined by mathematical laws which underly reality.

Moreover, I would say that much of what mathematics really is can be analysed in terms of psychology and sociology. There is not some mathematical world of ideas (numbers etc.) - numbers are psychological constructs, and therefore the place they exist is within the human brain.

Of course, there is one tricky point which is hard to explain in this way. Why does mathematics do such a good job of describing the physical world?