Symbolic regression is a method that discovers mathematical formulas from data without assumptions on what those formulas should look like. Given a set of input variables x1, x2, x3, etc, and a target variable y, it will use trial and error find f such that y = f(x1, x2, x3, …).
Introduced in 2009, the Eureqa software gained great popularity with the promise that it could potentially be used to derive new physical laws from empirical data in an automatic way. Details of this reasoning can be found in the original paper, called Distilling Free-Form Natural Laws from Experimental Data.
Given a sequence of numbers, finding an explicit mathematical formula that computes the nth term of the sequence can be challenging, except in very special cases like arithmetic and geometric sequences.