Here’s an op-ed in the NYT about mathematical realism (also called “mathematical Platonism”). Do numbers and math exist out there somewhere and are real entities, or are they the product of human contrivance? Did humans invent mathematics or discover it?
My own view, and I’m hardly qualified to express one as I’m not a philosopher, is that nature can be expressed in mathematical rules because nature (or at least physics) is regular. That is, there are laws of nature most prominently the laws of physics. Now I don’t know why that is, but if there are laws and regularities, then we can always express them in math. And for the life of me I can’t see that numbers predated minds that could comprehend them—that’s almost a religious view (note the title of Wilkinson’s book, though I have no idea whether he’s religious). And you’ll never convince me that the Pythagorean Theorem is somehow floating out there in the cosmos, and is not just a regularity noticed and expressed in mathematical form by humans.
But on this I have little expertise. Click to read.
The beginner math mystery, available to anyone, concerns the origin of numbers. It’s a simple speculation: Where do numbers come from? No one knows. Were they invented by human beings? Hard to say. They appear to be embedded in the world in ways that we can’t completely comprehend. They began as measurements of quantities and grew into the means for the most precise expressions of the physical world — E = mc², for example.
The second mystery is that of prime numbers, those numbers such as 2, 3, 5, 7, 11 and 13 that can be divided cleanly only by one or by themselves. All numbers not prime are called composite numbers, and all composite numbers are the result of a unique arrangement of primes: 2 x 2 = 4. 2 x 3= 6. 2 x 2 x 2 = 8. 3 x 3= 9. 2 x 3 x 3 x 37 = 666. 29 x 31 = 899. 2 x 2 x 2 x 5 x 5 x 5 = 1,000. If human beings invented numbers and counting, then how is it that there are numbers such as primes that have attributes no one gave them? The grand and enfolding mystery is whether mathematics is created by human beings or exists independently of us in a territory adjacent to the actual world, the location of which no one can specify. Plato called it the non-spatiotemporal realm. It is the timeless nowhere that never has and never will exist anywhere but that nevertheless is.
Mathematics is one of the most efficient means of approaching the great secret, of considering what lies past all that we can see or presently imagine. Mathematics doesn’t describe the secret so much as it implies that there is one.
But is there a “great secret”? I can’t imagine Wilkinson is thinking of God, for he doesn’t allude to a divinity. What else could a great secret be, though? To the mystery of prime numbers, my own response would be, “Well, that’s just the way it is.”
By the way, both the existence of regular physical laws and mathematics have been used as evidence for God: see pp. 158-160 of Faith Versus Fact.