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Exponentiating Mathematics (expMath)

ID: HR001125S0010 • Type: Posted

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.
Background
The Defense Advanced Research Projects Agency (DARPA), through its Information Innovation Office (I2O), is issuing a Broad Agency Announcement (BAA) for the Exponentiating Mathematics (expMath) program. The goal of this initiative is to develop an AI collaborator that can significantly accelerate the rate of progress in pure mathematics. This program aims to address the slow advancement in mathematics, which is critical for technological innovation and national security.

The expMath program seeks to leverage recent advances in artificial intelligence to automate the decomposition of mathematical problems and formalization processes, thereby enhancing productivity in mathematical research.

Grant Details
The expMath program will consist of two technical areas (TAs):

- TA1 focuses on automation of decomposition and formalization/informalization. Proposals for TA1 should aim to develop technologies that assist mathematicians by positing collections of lemmas that prove theorems and translating natural language into theorem-proving languages like Lean. Proposals must demonstrate a technical approach that enables rapid iteration between abstraction and code execution, with potential methods including recursion planning, curriculum learning, and program synthesis.

- TA2 emphasizes evaluation methods for AI capabilities in professional mathematics. Proposals for TA2 should focus on developing evaluation methods using appropriate datasets, specifically addressing subfields such as partial differential equations, number theory, and computational complexity. Evaluations will be conducted every six months across diverse areas of mathematics.

Eligibility Requirements
All responsible sources capable of satisfying the Government's needs may submit proposals. Historically Black Colleges and Universities, Small Businesses, Small Disadvantaged Businesses, and Minority Institutions are encouraged to participate; however, no portion of this announcement is set aside for these organizations due to impracticality. Non-U.S. organizations may also participate under compliance with necessary regulations.

Period of Performance
The period of performance for the expMath program is thirty-six (36) months, starting from January 1, 2026. Progress evaluations will occur every six months.

Grant Value
Multiple awards are anticipated under this BAA; however, specific total values for individual grants have not been disclosed.

Place of Performance
The geographic locations for performance will be specified by the Government during program execution.
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Overview

Agency
Defense Advanced Research Projects Agency (DARPA) [DoD]
Category of Funding
Science and Technology and other Research and Development
Funding Instruments
Cooperative Agreement
Other
Procurement Contract
Grant Program (CFDA)
12.910 - Research and Technology Development
Grant Category
Discretionary
Cost Sharing / Matching Requirement
False
Source
Grants.gov
On 4/30/25 Defense Advanced Research Projects Agency posted grant opportunity HR001125S0010 for Exponentiating Mathematics (expMath). The grant will be issued under grant program 12.910 Research and Technology Development.

Timing

Posted Date
April 30, 2025, 12:00 a.m. EDT
Closing Date
July 8, 2025, 12:00 a.m. EDT Due in 55 Days
Closing Date Explanation
See Full Announcement for details.
Last Updated
April 30, 2025, 1:51 p.m. EDT
Version
1
Archive Date
Aug. 7, 2025

Eligibility

Eligible Applicants
Others (see text field entitled "Additional Information on Eligibility" for clarification)
Additional Info
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.

Contacts

Contact
DARPA - Information Innovation Office
Contact Email
expmath@darpa.mil   Profile
Email Description
None
Contact Phone
(703) 696-2258
Additional Information
SAM.gov Contract Opportunities
Additional Information Site
https://sam.gov/opp/869c8d7351c04234be43c45e2082b846/view

Documents

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