# Exponentiating Mathematics (expMath) Proposers Day Canonical: https://abierto.us/opportunities/darpasn2544 - Solicitation number: DARPA-SN-25-44 - Notice type: Special notice - Status: Closed. Deadline was April 16, 2025 - Department: Department of Defense - Agency: Defense Advanced Research Projects Agency - Contracting office: Def Advanced Research Projects Agcy (HR0011) - NAICS: 541715 Research and Development in the Physical, Engineering, and Life Sciences (except Nanotechnology and Biotechnology) - Product or service code: AC12 National Defense R&D Services; Department Of Defense - Military; Applied Research - First posted: March 25, 2025 - Last posted: March 25, 2025 - SAM.gov: https://sam.gov/workspace/contract/opp/11ef0d3da9b947c693a0f4e5cee8da75/view ## Description MATHEMATICS IS THE SOURCE OF SIGNIFICANT TECHNOLOGICAL ADVANCES; HOWEVER, PROGRESS IN MATH IS SLOW. Recent advances in artificial intelligence (AI) suggest the possibility of increasing the rate of progress in mathematics. Still, a wide gap exists between state-of-the-art AI capabilities and pure mathematics research. Advances in mathematics are slow for two reasons. First, decomposing problems into useful lemmas is a laborious and manual process. To advance the field of mathematics, mathematicians use their knowledge and experience to explore candidate lemmas, which, when composed together, prove theorems. Ideally, these lemmas are generalizable beyond the specifics of the current problem so they can be easily understood and ported to new contexts. Second, proving candidate lemmas is slow, effortful, and iterative. Putative proofs may have gaps, such as the one in Wiles’ original proof of Fermat’s last theorem, which necessitated more than a year of additional work to fix. In theory, formalization in programming languages, such as Lean, could help automate proofs, but translation from math to code and back remains exceedingly difficult. The significant recent advances in AI fall short of the automated decomposition or auto(in)formalization challenges. Decomposition in formal settings is currently a manual process, as seen in the Prime number theorem and beyond and the Polynomial Freiman-Ruzsa conjecture, with existing tools, such as Blueprint for Lean, only facilitating the structuring of math and code. Auto(in)formalization is an active area of research in the AI literature, but current approaches show poor performance and have not yet advanced to even graduate-level textbook problems. Formal languages with automated theorem-proving tools, such as Lean and Isabelle, have traction in the community for problems where the investment in manual formalization is worth it. The goal of expMath is to radically accelerate the rate of progress in pure mathematics by developing an AI co-author capable of proposing and proving useful abstractions. expMath will be comprised of teams focused on developing AI capable of auto decomposition and auto(in)formalization and teams focused on evaluation with respect to professional-level mathematics. We will robustly engage with the math and AI communities toward fundamentally reshaping the practice of mathematics by mathematicians. ## Publications - March 25, 2025: Special notice, due April 16, 2025. Notice 11ef0d3da9b947c693a0f4e5cee8da75. https://sam.gov/workspace/contract/opp/11ef0d3da9b947c693a0f4e5cee8da75/view ## Points of contact - BAA Coordinator, expMath@darpa.mil --- Source: SAM.gov Contract Opportunities bulk extract. Confirm deadlines on SAM.gov before responding. Cite https://abierto.us/opportunities/darpasn2544.