# Exponentiating Mathematics (expMath)

Canonical: https://abierto.us/opportunities/hr001125s0010

- Solicitation number: HR001125S0010
- Notice type: Solicitation
- Status: Awarded to University of California, Los Angeles
- 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
- County: Los Angeles County (FIPS 06037). https://abierto.us/counties/los-angeles-county-ca-06037
- City: Los Angeles. https://abierto.us/cities/los-angeles-ca-0644000
- First posted: April 30, 2025
- Last posted: June 10, 2025
- SAM.gov: https://sam.gov/workspace/contract/opp/fb8136c6d9cf41e3bd1f87fb519e7551/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 mathematic

## Award on USAspending

- Recipient: University of California, Los Angeles (UEI RN64EPNH8JC6)
- Contract: HR001126CE054, definitive contract
- Obligated: $442,857.00, current value $5,046,736
- Competition: Full and Open Competition, 43 offers received
- Link: solicitation number HR001125S0010 equals the FPDS solicitation identifier; same awarding office HR0011 (high confidence)
- Record: https://www.usaspending.gov/award/CONT_AWD_HR001126CE054_9700_-NONE-_-NONE-/


## Publications

- April 30, 2025: Solicitation, due July 8, 2025. Notice 869c8d7351c04234be43c45e2082b846. https://sam.gov/workspace/contract/opp/869c8d7351c04234be43c45e2082b846/view
- May 13, 2025: Solicitation, due July 8, 2025. Notice 5ad415466dbb4054ae905009ec501343. https://sam.gov/workspace/contract/opp/5ad415466dbb4054ae905009ec501343/view
- June 10, 2025: Solicitation, due July 15, 2025. Notice fb8136c6d9cf41e3bd1f87fb519e7551. https://sam.gov/workspace/contract/opp/fb8136c6d9cf41e3bd1f87fb519e7551/view

## Points of contact

- BAA Coordinator, expMath@darpa.mil

---
Source: SAM.gov Contract Opportunities bulk extract and USAspending.gov award data. Confirm deadlines on SAM.gov before responding. Cite https://abierto.us/opportunities/hr001125s0010.