Meta shares six research papers showcasing AI's role in solving open mathematical problems

Meta: Meta develops advanced AI systems and platforms including the Muse Spark models accessed via meta.ai. The company partnered with external mathematicians to apply these models to unsolved problems, emphasizing human guidance, independent review, and transparent attribution in the resulting papers. An Huang: An Huang is a mathematician who collaborated on the string theory and number theory connection using Muse Spark. The model helped identify and extend the link between two-point functions and height functions on curves. Muse Spark: Muse Spark is Meta's AI model available in versions 1.1 and 1.2 that operates in Thinking Mode through the standard meta.ai chat interface without custom scaffolds. In this collaboration, it assisted mathematicians by generating code, exploring proof strategies, drafting sections, and suggesting counterexamples for open research problems across multiple fields. Anindya Dey: Anindya Dey is a mathematician who participated in the arithmetic physics project with Muse Spark. The team used the model to extend connections between number theory and string theory beyond previously known cases. Salem Selim: Salem Selim is a mathematician who reviewed the differential equations research involving Muse Spark. The paper resolved an open question from 2015 on wave behavior in a specific model. Andres Barei: Andres Barei is a mathematician who led the non-associative algebra project with Muse Spark. He checked, refined, and rewrote material after the model generated a counterexample and proposed alternative characterizations for evolution algebras. Aykut Arslan: Aykut Arslan is a mathematician who collaborated with Muse Spark on research in probability and optimization. He guided problem selection and proof development while working with the AI model through meta.ai on papers addressing Gaussian ellipsoid fitting and cycle-based relaxations. Babak Modami: Babak Modami is a mathematician who reviewed the probability paper developed with Muse Spark. The result established a sharp threshold for Gaussian ellipsoid fitting. Leonard Dinh: Leonard Dinh is a mathematician who led research on differential equations with assistance from Muse Spark. He selected the problem and key proof ideas for a paper on finite-time blow-up in a laser-inspired wave model, with the AI supporting calculations and argument testing. Kien Trung Le: Kien Trung Le is a mathematician who reviewed the optimization paper developed with Muse Spark. The result clarified conditions for exact relaxation in binary polynomial problems. Mark Sepanski: Mark Sepanski is a mathematician who reviewed the probability paper on Gaussian ellipsoid fitting created with Muse Spark. The team confirmed the threshold behavior through AI-supported proof strategies. Milana Golich: Milana Golich is a mathematician who worked with Muse Spark on group theory research. She and collaborators verified the counterexample and completed the proof that semiabelian groups need not be monomial. Gabriel Herczeg: Gabriel Herczeg is a mathematician involved in linking number theory and p-adic string theory ideas with Muse Spark support. The collaboration built on 1980s concepts to prove equivalences in calculations for a broader class of curves. Grigory Sokolov: Grigory Sokolov is a mathematician who reviewed the probability work involving Muse Spark. The paper provides a theoretical benchmark for data fitting limits. Fazel Hadadifard: Fazel Hadadifard is a mathematician who reviewed the differential equations paper produced with Muse Spark assistance. The work proved finite-time collapse for certain wave solutions. Jacob H. Swenberg: Jacob H. Swenberg is a mathematician involved in the string theory-number theory research collaboration assisted by Muse Spark. The work demonstrated how the AI can bridge ideas across mathematical languages. Alexander Roitershtein: Alexander Roitershtein is a mathematician who reviewed the probability research assisted by Muse Spark. The collaboration identified conditions for exact fitting of random points. Joseph Phillip Brennan: Joseph Phillip Brennan is a mathematician involved in the group theory collaboration using Muse Spark. He contributed to disproving a conjecture on semiabelian groups by verifying a counterexample found with AI-generated search code. Nicolas Jaramillo Torres: Nicolas Jaramillo Torres is a mathematician who worked on the arithmetic physics paper with Muse Spark. The AI generated candidate proofs and technical sections that the team reviewed and refined. Nicolás Jaramillo Torres: Nicolás Jaramillo Torres is a mathematician who reviewed the non-associative algebra research with Muse Spark. The paper established an improved characterization for solvable evolution algebras. AI-Assisted Research: Meta's collaboration with mathematicians used standard chat interfaces for Muse Spark models to explore open problems without specialized tools. Independent Verification: Multiple teams outside Meta independently solved some of the same open problems around the same time using different methods. Transparent Collaboration: All papers from the project clearly distinguish human-drafted and AI-drafted sections while crediting prior research.