Unsolved Problems

Prove that Yang–Mills theory exists and has a mass gap on $\mathbb{R}^4$, meaning the quantum particles have positive masses....

Develop a mathematical framework that axiomatizes physics, particularly mechanics, thermodynamics, and probability theory....

Apply quantum and statistical field theory methods to model and potentially control pathogen evolution....

Identify governing principles for biological systems, analogous to physical laws....

Extend understanding of symmetries and action principles in biology to include robustness, modularity, evolvability, and variability....

Connect the Langlands program to fundamental physics symmetries....