Mathematics that unifies
Understanding the relations between different branches of pure mathematics, and creating overarching theories that bind them together.
Using machine learning methods to search the vast space of Calabi-Yau manifolds for ones that predict the Standard Model from string theory.
Exploring the spectral properties of subgraphs of the hypercube and Hamming graphs for insights into coding theory and models of evolution.
Generalizing the divisor function to find a new kind of number that can be recursively divided into parts, for use in design and technology.