Machine Rediscovers Formulas That Took Physicists Years to Derive express

Original: "Learning the S-matrix from data: Rediscovering gravity from gauge theory via symbolic regression"
· Nathan Moynihan
arXiv:2602.15169 · 2026-02-16 · CC BY 4.0 · 1 min
A neural network found connections between different descriptions of particle collisions on its own — without hints from theory.

When two particles collide and scatter, physicists record the outcome as a complex mathematical formula. There are many such formulas, and invisible connections exist between them, like different recipes for the same dish: change the order of steps, and the taste stays the same. Previously, these connections were derived by hand, taking months or years.

Now a program has taken on this task, searching for patterns in numbers. It was given only the results of collision calculations — with no explanations. The program rediscovered famous relations that link different descriptions of the same collision. One of them connects the theory of gravity with the theory of strong interactions inside the nucleus.

The program found a minimal set of formulas from which all others follow, as if one basic pattern could be used to sew every dress in a collection.

The method works for five particles in a collision. For more particles, technical difficulties still stand in the way, but the authors already see how to overcome them. The main takeaway is simple: a machine can search for hidden rules in physics without human hints. This means it could also be used to test new, unexplored theories.

This approach is like a detective reconstructing a crime scene from scattered clues — except here the clues are numerical.

One of the discovered relations connects the strength of gravity with the force that holds quarks inside a proton — two seemingly completely different worlds.

In the series Foundation, Hari Seldon used mathematics to predict the future — here, a machine seeks mathematical rules hidden in data about the past.

Scientists
Erwin SchrödingerHugh Everett IIIEmmy NoetherWolfgang PauliEnrico FermiPaul Dirac
Concepts
symbolic regression linear regression syk model