Replicating Wigner’s Insight

I was introduced to the notion of experimental mathematics–where one uses computation (and a lot of heuristics?) to investigate and eventually derive properties of mathematical objects–by my friend Grigory Sarnitsky. Even after using it to compute infinite powers of large matrices, I remained skeptical of its usefulness in physics (sorry Grigory).

To continue familiarizing myself with the toolkit of experimental mathematics, I wanted to look into Symbolic Regression. Symbolic regression is similar to function fitting. However, unlike traditional fitting where a function is specified up to some unknown parameters which are tweaked to fit some data, symbolic regression does not require a specific function beforehand. Instead, one specifies a set of elementary operations and functions which are then combined to construct an expression modeling the data. It’s like fitting without knowing the fitting function itself!

The aim of this post is to see if a computer can rediscover Wigner’s celebrated surmise using Julia’s SymbolicRegression.jl.

Wigner’s surmise

See if I can add executable Julia code