Galois theory has a special place in mathematics, because it is about something fundamental as solving a polynomial equation in one variable. When most people know how to use the quadratic formula, fewer would be able to remember formulas for solving cubics and quartics. Things get even more interesting when the degree is $\geq 5$, since such formulas do not exist for a generic polynomial, even though they do exist for special polynomials (i.e. polynomials such that their Galois group is solvable).  

For the experts it is clear how to make the jump from a solvable Galois group of the polynomial to the formulas.  The solvable group provides a solvable tower of subgroups which corresponds to a solvable tower of subfields of the splitting field of the polynomial.  This solvable tower of subfields has cyclic extensions in every step and therefore corresponds to algebraic substitutions of the form $u=x^n$.  This process is known as solving the polynomial by radicals. It is  a rather complicated process when one tries to  work out all the cases explicitly even for small degrees.

One of the  goals of this paper is to suggest a machine learning approach to find such formulas for higher degree polynomials.  Then such formulas could be verified using Lean or some other format method.  

Of course, the scope of Galois theory is much wider and deeper than figuring out formulas by radicals.  Hence this use of machine learning in Galois theory can be used in a  wide variety of methods and open questions.  This project is envisioned as a start of a large and long project of using data science in Galois theory.; see here for further details.