Grants / Department of Defense / DARPA - Information Innovation Office

HR001125S0010: Exponentiating Mathematics (expMath)

Closed Closed July 15, 2025 Opportunity HR001125S0010 ☆ Save

This grant is closed. A newer notice from the same program is open now: Young Faculty Award (YFA) 2027 (DARPARA2701). Status: Closes January 13, 2027 (67 days left). It is in our archive of DARPA - Information Innovation Office notices from 2025.

• Award amountsNot given on Grants.gov
• Cost sharingNot required
• Funding typeCooperative Agreement, Other, Procurement Contract

Key dates

Who can apply

This opportunity was open to the applicants described in the notice.

• Others (see text field entitled "Additional Information on Eligibility" for clarification)

All responsible sources capable of satisfying the Government's needs may submit a proposal that shall be considered by DARPA. See the Eligibility Information section of the BAA for more information.

Is this a realistic fit?

• Most of the program's money (93% over five years) went to colleges and universities.
• No cost sharing or match is required.

What the grant funds

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

Category: Science and Technology and other Research and Development.

Applying now

This notice no longer takes applications. Apply under the newer notice, DARPARA2701, which is open now.

The notice on Grants.gov keeps its full text and attachments, which is useful for planning a resubmission.