Special Projects

IPAM Special Projects are overseen by the Special Projects Director, Terence Tao.

These projects aim to make advances in the following areas:

  1. Empowering Research with Usable AI Tools. Increasingly powerful and general purpose AI tools are now available for various research tasks, but many of their use cases are unreliable due to issues such as hallucinations. There are many narrower use cases of such tools that are more reliable and already useful in current research, but such applications are not immediately obvious to the casual user. IPAM will develop a spectrum of user-friendly tools for specific research tasks, such as literature review or scientific calculation, that are powered by AI (or other modern data management tools) “under the hood”, but can be used by the working mathematician or scientist without any particular training. These tools will range from low-capability products powered by open source models that can be offered for free on the IPAM web site, to high-capability products requiring proprietary model access.
  2. Integrating Formalization into Research Workflows. One of the most promising ways to compensate for AI “hallucinations” — particularly in the area of mathematical research — is to use formal proof assistants to verify AI-generated output. Such assistants enable much larger scale collaborations than previously possible, removing the need to trust or carefully check correctness of participant contributions. However, formalization is currently an extremely tedious and requires significant expertise. Advances in AI, automated formalization, and collaboration platforms have now made large scale formalization possible — not just at the level of an individual result, but at the level of subfields. With IPAM’s strong network of expertise in mathematics, CS, and AI, we will develop new workflows that formalize mathematics at scale and automatically combine formal and informal mathematical results to improve over the existing state of the art. We will build upon Tao’s collaboration with Google Deepmind using AlphaEvolve to systematically improve known bounds on optimization problems by combining it with automatic formalization and literature review. Once mathematics formalization workflows are established, analogous workflows will be developed for other sciences, where the role of formalization is replaced by simulation or experiment, leading into other existing IPAM core projects in areas such as materials science and self-propelled laboratories.
  3. Enhancing Science Education.   AI tools, when used properly, have the potential to significantly enhance the traditional math and science education process at all levels. At their best, such tools can provide tailored assistance to students that does not simply supply answers to assigned coursework, but can nurture and encourage the student’s own problem solving skills and curiosity. However, there are also significant risks in improper use of such tools, as indiscriminate use of AI technology can make students so reliant on AI assistance that they lose the ability to solve these problems on their own. One promising approach is to introduce rigorous formal frameworks to automate (or “gamify”) some portions of the problem solving process, while leaving other key components for the student to solve on their own. At the undergraduate and graduate level, Tao has already successfully formalized several textbooks in the proof assistant language Lean, and plans to work with IPAM to expand these formalization projects and deploy them in classrooms. There are also innovative experiments at UCLA’s Olga Radko Math Circle (ORMC) at the K-12 level which IPAM plans to collaborate with to develop age-appropriate responsible AI instructional assistance that is both enjoyable for the student and genuinely educational.

Our team:

Current projects: