MIT Affiliates Awarded Prestigious AI for Math Grants to Propel Mathematical Discovery

AI for Math Grants to Accelerate Mathematical Discovery

In a significant development for the field of mathematics, several affiliates of the Massachusetts Institute of Technology (MIT) have been awarded grants from the prestigious AI for Math Fund. This initiative, designed to propel mathematical discovery through artificial intelligence, has recognized the innovative work of MIT researchers David Roe and Andrew Sutherland, alongside four distinguished MIT alumni. The grants are expected to significantly advance the capabilities of automated theorem proving and enhance the process of mathematical research.

Advancing Automated Theorem Proving

David Roe and Andrew Sutherland, both affiliated with MIT's Department of Mathematics, are set to utilize their grants to further develop automated theorem provers. These sophisticated systems are crucial for verifying mathematical proofs, but their development has historically been under-resourced. Sutherland notes that the rapid advancements in AI technologies, particularly large language models (LLMs), are rapidly lowering the barrier to entry for these formal tools. This democratization of formal verification frameworks promises to make them more accessible to a broader range of mathematicians.

Bridging Mathematical Databases and Formal Systems

A core focus of Roe and Sutherland's project involves creating a crucial bridge between the L-Functions and Modular Forms Database (LMFDB) and the mathlib formal mathematics library. The grant will fund efforts to make the LMFDB's extensive results available within mathlib as assertions that are yet to be formally proven. Concurrently, precise formal definitions of the numerical data housed within the LMFDB will be established. This integration is anticipated to benefit both human mathematicians and AI agents, establishing a robust framework for connecting other mathematical databases to formal theorem-proving systems.

Overcoming Obstacles in Mathematical Discovery

The automation of mathematical discovery and proof faces several significant hurdles. These include the limited availability of formalized mathematical knowledge, the substantial cost associated with formalizing complex mathematical results, and the inherent gap between what is computationally accessible and what is practically feasible to formalize. The funding from the AI for Math Fund will be instrumental in addressing these challenges by developing tools that facilitate access to the LMFDB from within mathlib. This will make a vast repository of unformalized mathematical knowledge accessible to a formal proof system, enabling proof assistants to pinpoint specific targets for formalization without the need to process the entire LMFDB corpus upfront.

Leveraging Computational Power and Existing Knowledge

David Roe highlights the strategic advantage of this approach, stating, "Making a large database of unformalized number-theoretic facts available within mathlib will provide a powerful technique for mathematical discovery, because the set of facts an agent might wish to consider while searching for a theorem or proof is exponentially larger than the set of facts that eventually need to be formalized in actually proving the theorem." This method circumvents the need to re-perform extensive computations, leveraging the thousands of CPU-years already invested in creating databases like the LMFDB. This not only saves resources but also makes it feasible to explore examples or counterexamples without predefined search parameters. Furthermore, mathematical databases, being curated repositories, offer a structured and reliable source of information.

The Role of Computation in Proofs

The researchers emphasize that proving theorems at the cutting edge of mathematical knowledge often involves steps that rely on non-trivial computations. A notable example is Andrew Wiles' proof of Fermat's Last Theorem, which utilized a critical step known as the "3-5 trick." Sutherland explains that this trick depends on specific properties of the modular curve X_0(15), facts that, while verifiable with computational tools, are not easily proven by hand or readily formalized. The integration of formal theorem provers with computer algebra systems, and the leveraging of computational outputs from mathematical databases, offers a more efficient pathway for verification and discovery.

Future Directions and Community Engagement

Roe outlines the immediate next steps for the project, which include building a dedicated team, engaging with both the LMFDB and mathlib communities, and beginning the formalization of definitions related to elliptic curves, number fields, and modular forms within the LMFDB. The ultimate goal is to enable LMFDB searches directly from within mathlib. Roe also extends an invitation to interested MIT students to get involved in this groundbreaking research.

Broader Impact of AI in Mathematics

The AI for Math Fund, with its commitment of $18 million to 29 projects, underscores a growing recognition of AI's potential to revolutionize mathematical research. The fund supports projects that are crucial for the field but may lack the incentive for development within traditional academic or industry settings. These include the creation of open-source tools, the expansion of datasets for AI model training, and the enhancement of tool usability for mathematicians. The ultimate aim is to accelerate the pace and impact of mathematical discovery, potentially leading to new fundamental theorems, strengthening the security of hardware and software, and improving the reasoning capabilities of AI models themselves. The involvement of MIT affiliates in this initiative highlights the institution's continued leadership in pioneering the intersection of artificial intelligence and fundamental scientific research.

Four Additional MIT Alumni Honored

In addition to the work of Roe and Sutherland, four other MIT alumni were recognized for their distinct projects: Anshula Gandhi ’19, Viktor Kunčak SM ’01, PhD ’07; Gireeja Ranade ’07; and Damiano Testa PhD ’05. Their inclusion further underscores the significant contributions of the MIT community to the advancement of mathematics and AI.

The AI for Math Fund Ecosystem

Launched with an initial commitment from XTX Markets, which later doubled its funding to $18 million due to the high quality of submissions, the AI for Math Fund received 280 proposals. Renaissance Philanthropy plays a key role in administering the fund and supporting the grantees. The fund