Exponentiating Mathematics (expMath)
Closed Posted
- Opportunity number
- HR001125S0010
- Agency
-
Defense Advanced Research Projects Agency
Department of Defense
- Applications due
- Award size
- Not on record
Opportunity facts
- Assistance listings
- Funding instrument
- Cooperative Agreement, Procurement Contract
- Category
-
- Science and Technology and other Research and Development
- Eligible applicants
-
- Other
- Points of contact
-
- BAA Coordinator expmath@darpa.mil
- Full announcement
Opportunity details come from Grants.gov. Updated .
About this opportunity
The Defense Advanced Research Projects Agency (DARPA) is seeking innovative proposals for the Exponentiating Mathematics (expMath) program, aimed at developing artificial intelligence technologies to dramatically accelerate mathematical research. The program will fund teams capable of creating an AI co-author that can propose and prove mathematical abstractions by addressing two critical challenges: automated problem decomposition and auto(in)formalization of mathematical proofs. Proposers must demonstrate expertise in both mathematics and artificial intelligence, with a focus on developing technologies that can predict and prove lemmas in 90% of evaluation problems while reducing solution time by 100x. Evaluation will emphasize the potential to fundamentally reshape mathematical research practices, with particular attention to technical approach, team capabilities, and potential impact across mathematical subfields like partial differential equations, number theory, and computational complexity. Key dates include a proposal abstract due on May 15, 2025, and full proposals due by July 15, 2025.
The program anticipates multiple awards using various funding instruments, including procurement contracts, cooperative agreements, and other transactions, with potential funding ranges typical of DARPA's Research and Technology Development program ($125,000 to $14,997,315). The performance period is set for 36 months, with the anticipated start date of January 1, 2026. Evaluations will be conducted every six months, and the program strongly encourages open-source development and collaborative research approaches. The place of performance is not geographically restricted, allowing for diverse institutional participation from universities, research organizations, and commercial firms with demonstrated capabilities in AI and mathematical research.
Synopsis
2 versions
Update #2 · Latest ·
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 mathematic
Update #1 ·
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.
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