Are mathematicians discovering algorithms by mining them with computers?

Question

Throughout history many famous equations have been intuitively derived by famous mathematicians - Einstein's discovery of mass–energy equivalence, Schrödinger's equation for the orbitals of electrons, Euler's identity, etc.

During the process of discovering equations, these famous minds pondered about their observations of the world and attempted to make the mathematical pieces fit. They juggled patterns, curvatures, attempted to isolate fixed points, and combined other mathematical shapes and operations in various ways. Ultimately, the equations that they experimented with had to be proven correct by matching outcomes of existing data.

We have many mathematical transformations and constants in our arsenal. Exponents, PI, inverse, the list is quite large. But nothing a computer couldn't churn through in a fraction of a second.

Have there been attempts to mine algorithms by having computers calculate brute-force combinations of these mathematical primitives, in an attempt to find an equation (or equations) that will accurately predict a collected dataset yet unsolved?

Answer 1

A computer cannot churn out physical theories that match experimental data in a fraction of a second, because this problem is NP-hard.

Answer 2

The title of the question mentions algorithms and mathematicians but then mostly talks about models and physics. Along that line, the following is quoted from the cosmology@home letter.

The goal of Cosmology@Home is to search for the model that best describes our Universe and to find the range of models that agree with the available astronomical and particle physics data. In order to achieve this goal, participants in Cosmology@Home (i.e. you!) will compute the observable predictions of millions of theoretical models with different parameter combinations. We will use the results of your computations to compare all the available data with these models. In addition, the results from Cosmology@Home can help design future cosmological observations and experiments, and prepare for the analysis of future data sets [...].