# Exponentiating Mathematics (expMath)

Source: https://welltoldgrants.com/grants/hr001125s0010-exponentiating-mathematics-expmath/  
Official notice: https://www.grants.gov/search-results-detail/358789

> DARPA - Information Innovation Office offered grants to the applicants described in the notice. Applications closed on July 15, 2025.

| Field | Value |
|---|---|
| Opportunity number | HR001125S0010 |
| Agency | DARPA - Information Innovation Office |
| Status | Forecast |
| Deadline | July 15, 2025 |
| Award ceiling | not stated |
| Award floor | not stated |
| Expected awards | not stated |
| Total funding | not stated |
| Cost sharing | not required |
| Assistance Listings | 12.910 |

## Who can apply

- 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.

## 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

## Questions people ask

### Is HR001125S0010 still open?

No. It closed on July 15, 2025. A newer notice is open: DARPARA2701, closes January 13, 2027 (67 days left).

### Who can apply for Exponentiating Mathematics (expMath)?

DARPA - Information Innovation Office accepted applications from the applicants described in the notice. The notice adds further conditions, so read its eligibility section.

### What is the deadline for Exponentiating Mathematics (expMath)?

Closed July 15, 2025. Applications are no longer accepted; the program's newer notices are on this page when there are any.

### Who has won Research and Technology Development grants before?

The largest recipients over five fiscal years were University of Southern California, Clemson University, Massachusetts Institute of Technology. The program made 739 awards worth $1.5 billion in that time.