The Exponentiating Mathematics (expMath) program aims to accelerate the rate of progress in pure mathematics by developing an AI co-author capable of proposing and proving useful abstractions. The program will focus on two main areas: auto decomposition and auto(in)formalization. The goal is to create an AI system that can assist mathematicians in their work, making it easier to explore new mathematical concepts and prove theorems. • The program will be comprised of teams focused on developing AI capable of auto decomposition and auto(in)formalization. • The teams will also focus on evaluation with respect to professional-level mathematics. • The program will engage with the math and AI communities to fundamentally reshape the practice of mathematics by mathematicians. • The opportunity is open to all responsible sources capable of satisfying the Government's needs. • The submission deadline is July 8, 2025.