Classic paper: “The Unreasonable Effectiveness of Mathematics” by Wigner

Eugene Wigner wrote in 1960 about the surprising number of ways in which mathematics seems to correspond to natural phenomenon, with really no good reason:

“We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors.”

“The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and… there is no rational explanation for it.”

I find it extremely seductive to think that scientific theories are just made-up stories that explain the latest unexplained observations and perhaps make it possible to predict the “next” observations.  This is consistent with the observation that almost all scientific theories — no matter how useful and well-received — are eventually proven to be false.

The main problem with this way of seeing the world is that some scientific theories end up being *extraordinarily* productive in terms of predictions.  That is, they don’t just let us see 5 minutes into the future, but they let us peer decades into the future.  If they aren’t technically speaking “true,” then why would these theories work so well?

I don’t know how to explain this, and Wigner seems to be confessing that he doesn’t either.


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