In which, without lapse into solipsism, your correspondent defends mathematical formalism in the face of deep connections between mathematics and the physical universe.

In response to a comment of mine at Ars Math the unapologetic John Armstrong challenges me thus:

So, Matt, you’re a formalist? You seem to have a similar underlying belief that mathematics is a formal system, and a product of the activities of human minds (brains).

Not to claim a Platonic position here, but I challenge you with the same response as I’d give to a hardcore formalist: how do you explain the “unreasonable effectiveness” of mathematics in the physical sciences? Why should the output of human brains have anything to do with physical law, and how is it that truly well-formed sciences are invariably expressed in mathematics? Escapes into radical solipsism will be discarded as the jokes they are.

My response is after the jump.

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