Archive for May 17th, 2018

May 17, 2018

The reasonable effectiveness of mathematics in the natural sciences

by Neil Rickert

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.

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