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ActiveDARPA - Information Innovation Office · 2026

Exponentiating Mathematics (expMath)

Quick Facts

Agency: DARPA - Information Innovation Office
Funding: Varies
Deadline: Check Source
Status: Active
Eligibility: Open to all eligible applicants.

About This Grant

Exponentiating Mathematics (expMath) is sponsored by DARPA - Information Innovation Office. Aims to accelerate mathematical progress through AI by developing tools to assist in mathematical research and theorem proving.

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Official Opportunity Details

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Opportunity Listing - Exponentiating Mathematics (expMath) Exponentiating Mathematics (expMath) Agency: DARPA - Information Innovation Office Assistance Listings: 12. 910 -- Research and Technology Development Last Updated: May 13, 2026 View version history on Grants. gov 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 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. Grantor contact information File name Description Last updated HR001125S0010-Amendment-02.

pdf HR001125S0010-Amendment-02. pdf Jun 10, 2025 02:51 PM UTC HR001125S0010-Amendment-01. pdf HR001125S0010-Amendment-01.

pdf May 13, 2025 04:01 PM UTC SAMPLE_OT_P__-_Expenditure_Based_Approach_-_2025. 02. 28.

docx Baseline Model - OT for Prototype Expenditure Apr 30, 2025 05:51 PM UTC SAMPLE_OT_P__-_Cost-Share_Expenditure_Based_-_2025. 02. 28.

docx Baseline Model - OT for Prototype Cost Share Apr 30, 2025 05:51 PM UTC Baseline_Model_Contract__Large_Business__Mar_2025. pdf Baseline Model - Large Business Contract Apr 30, 2025 05:51 PM UTC Baseline_Model_Contract__Small_Business__Mar_2025. pdf Baseline Model - Small Business Contract Apr 30, 2025 05:51 PM UTC SAMPLE_OT_P__-_Fixed_Support_Nontraditional_-_2025.

02. 28. docx Baseline Model - OT for Prototype Fixed Support NT Apr 30, 2025 05:51 PM UTC P5_-_Associate_Contractor_Agreement__ACA.

docx P5 Associate Contract Agreement (ACA) Apr 30, 2025 05:51 PM UTC A1_Abstract_Instructions_and_Submission_Template. docx A1 Abstract Instructions and Submission Template Apr 30, 2025 05:51 PM UTC Baseline_Model-_Contract_Addendum_Circumstance-Driven_Additional_Clauses. docx Baseline Model - Possible Additional Contract Clauses Apr 30, 2025 05:51 PM UTC Baseline_Model-_Cooperative_Agreement_11-21-24.

docx Baseline Model - Cooperative Agreement Apr 30, 2025 05:51 PM UTC HR001125S0010. pdf HR001125S0010. pdf Apr 30, 2025 05:51 PM UTC P1_-_Proposal_Instructions_and_Volume_I_Template__Technical_and_Management.

docx P1 Proposal Instructions and Volume I Template (Technical and Management) Apr 30, 2025 05:51 PM UTC SAMPLE_OT_P__-_Fixed_Support_Traditional_Cost-Share_-_2025. 02. 28.

docx Baseline Model - OT for Prototype Fixed Support T Apr 30, 2025 05:51 PM UTC SAMPLE_OT_R__-_Streamlined-fixed_-_2025. 02. 28.

docx Baseline Model - OT for Research Streamline Fixed Apr 30, 2025 05:51 PM UTC SAMPLE_OT_R__-_Fixed_Support_Consortium_-_2025. 02. 28.

docx Baseline Model - OT for Research Fixed Support Consortium Apr 30, 2025 05:51 PM UTC SAMPLE_OT_R__-_Expenditure_Consortium_-_2025. 02. 28.

docx Baseline Model - OT for Research Expenditure Consortium Apr 30, 2025 05:51 PM UTC A2_Abstract_Summary_Slide_Instructions_and_Template. pptx A2 Abstract Summary Slide Instructions and Template Apr 30, 2025 05:51 PM UTC P2_-_Proposal_Instructions_and_Volume_II_Template__Cost. docx P2 Proposal Instructions and Volume II Template (Cost) Apr 30, 2025 05:51 PM UTC P4_-_DARPA_Standard_Cost_Proposal_Spreadsheet.

xlsx P4 DARPA Standard Cost Proposal Spreadsheet Apr 30, 2025 05:51 PM UTC SAMPLE_OT_R__-_Expenditure_Company_-_2025. 02. 28.

docx Baseline Model - OT for Research Expenditure Co Apr 30, 2025 05:51 PM UTC P3_-_Proposal_Summary_Slide_Instructions_and_Template. pptx P3 Proposal Summary Slide Instructions and Template Apr 30, 2025 05:51 PM UTC SAMPLE_OT_R__-_Articles_of_Collaboration_Model_-_2025. 02.

28. docx Baseline Model - OT for Research Articles of Collab Apr 30, 2025 05:51 PM UTC SAMPLE_OT_R__-_Fixed_Support_Company_-_2025. 02.

28. docx Baseline Model - OT for Research Fixed Support Co Apr 30, 2025 05:51 PM UTC SAMPLE_OT_P__-_Streamlined__Fixed_-_2025. 02.

28. docx Baseline Model - OT for Prototype Streamlined Fixed Apr 30, 2025 05:51 PM UTC Link to additional information SAM. gov Contract Opportunities Funding opportunity number : Cost sharing or matching requirement : Funding instrument type : Opportunity Category Explanation : Category of Funding Activity : Science technology and other research and development Your account requires additional identity verification.

Eligibility Requirements

Open to all eligible applicants.

Frequently Asked Questions

Who can apply for Exponentiating Mathematics (expMath)?

According to the current listing, eligibility includes: Open to all eligible applicants. Confirm the full requirements in the official notice before applying.

Who funds Exponentiating Mathematics (expMath)?

Exponentiating Mathematics (expMath) is funded by DARPA - Information Innovation Office. Verify program details on the funder's official page before applying.

How do I apply for Exponentiating Mathematics (expMath)?

Start from the official opportunity page linked in this listing — it carries the sponsor's submission instructions.

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