In 1969, Eugene Wigner wrote what has become a famous paper, titled “The unreasonable effectiveness of mathematics in the natural sciences.” There’s a pretty good summary of the related issues in the Wikipedia article of the same name.

As you might guess from the title of this blog post, I disagree with Wigner. In my view, the effectiveness of mathematics is entirely reasonable. And it has long seemed reasonable to me. I thought about it either in high school or as a graduate student in mathematics (I’m not sure which), and came up with what I found to be a satisfactory explanation.

**Perspective on mathematics**

I’ll start with my broad perspective, which I have probably mentioned before on this blog. I often say that mathematics is not about reality. The mathematician Kronecker famously said “God gave us the natural numbers. All else is the work of man.” I almost agree, except that I think Kronecker gave God too much credit. As I see it, the natural numbers are also the work of man. That’s part of why I am a mathematical fictionalist.