MIT mathematicians David Roe and Andrew Sutherland have been named recipients of the AI for Math grants, an inaugural funding scheme launched by Renaissance Philanthropy and XTX Markets. As members of MIT’s Department of Mathematics, they’re going to take this opportunity to blend artificial intelligence with groundbreaking mathematical research.
This new initiative aims to propel mathematical discovery by funding 29 pioneering projects, each tasking AI to reshape the field of mathematics. It’s all about giving mathematicians the tools to develop AI systems that boost discovery speed and enhance formal reasoning in a wide array of mathematical areas.
Im Rahmen dieser beeindruckenden Einführung planen Roe und Sutherland in Zusammenarbeit mit Chris Birkbeck von der University of East Anglia, ihren Zuschuss zu nutzen, um zwei wichtige mathematische Ressourcen miteinander zu verbinden: die Datenbank für L-Funktionen und modulare Formen (LMFDB) und die Lean4-Mathematikbibliothek (mathlib).
On one hand, the mathlib, a comprehensive library driven by a massive international community, uses the Lean theorem prover to verify the validity of each logical step in a proof. With about 100,000 mathematical results, it’s basically a goldmine of mathematical findings.
On the other hand, there’s the LMFDB, a mammoth digital encyclopedia of modern number theory. Housing over a billion mathematical statements and data points, it’s a go-to-resource for professional and aspiring mathematicians alike. Making sense of this colossal data mountain is a daunting task, but with Roe and Sutherland serving as the LMFDB’s managing editors, they’re just the right people for the job.
Der traditionelle Lernweg zum Verständnis automatischer Theorembeweiser ist steil, räumt Sutherland ein. Aufgrund der zunehmenden Verfügbarkeit und Effektivität von großen Sprachmodellen (LLMs) und anderen KI-Tools ist der Lernprozess jedoch weniger einschüchternd geworden und lädt ein breiteres Publikum von Mathematikern ein, diese Systeme zu nutzen.
The primary goal here is to avail the LMFDB’s vast number-theoretic facts to mathlib. This integration would open up unrestricted exploration of the mathematical universe to both AI agents and human mathematicians. To achieve this, the team is not planning on formalizing the whole LMFDB – which would be extremely labor-intensive – rather, they aim to develop tools that selectively tap into its contents. The tactic, expected to cut costs, implies that not all of the information required for establishing new theorems has to be formally proved.
Modern mathematical theorems, such as Andrew Wiles’ proof of Fermat’s Last Theorem, lean heavy on computational steps which are not so simple to formalize by hand. This is exactly why mathematical databases like the LMFDB are invaluable and serve as crucial resources to mathematicians.
The importance of curation in mathematical databases can’t be overstated. For instance, the LMFDB’s focus on the conductor in elliptic curves was pivotal in the recent identification of elliptic curve murmurations, a phenomenon discovered using machine learning techniques.
Roe and his team intend to start the whole endeavor by formalizing the definitions that underpin the LMFDB’s elliptic curve, number field, and modular form sections and allow execution of LMFDB searches within mathlib. Their plan opens up opportunities for students at MIT to be part of this grand mathematical adventure.
Neben Roe und Sutherland wurden vier weitere Pioniere der Mathematik vom MIT - Anshula Gandhi, Viktor Kunčak, Gireeja Ranade und Damiano Testa - in Anerkennung ihrer innovativen Arbeit auf diesem Gebiet mit den AI for Math-Stipendien ausgezeichnet.
Weitere Informationen über die KI für Mathematik-Stipendien finden Sie im vollständigen Artikel hier.
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