Ernest S. Croot III  Ernest S. Croot III is a mathematician and professor at the School of Mathematics, Georgia Institute of Technology. He is known for his solution of the Erdős–Graham conjecture, and for contributing to the solution of the cap set problem. Ernest Croot attended Centre College at Danville, Kentucky, where he received a B.S. in Mathematics and a B.S. in  Computer Science in 1994. In 2000, he completed a Ph.D. in Mathematics at the University of Georgia under the supervision of Andrew Granville.