Autoformalization and the Future of Math Research (www.neelsomaniblog.com)

In a recent initiative involving a group of undergraduate students, the autoformalization process was applied to solve open Erdős problems using advanced language models like GPT-5.2 Pro and Deep Research. This effort yielded three accepted solutions, three partial results, and four rediscoveries, all made open-source. The project revealed deeper insights into the concept of novelty in mathematical research, highlighting that failures often stem from underspecified concepts around progress and correctness, rather than outright errors. The distinction of what constitutes a "novel" result remains contentious among leading mathematicians, emphasizing the subjective nature of intellectual contribution. The implications of this autoformalization work extend beyond mathematics, proposing that formal methods can enhance various fields by providing clarity on which informal concepts underlie research and problem-solving. The authors suggest that better frameworks for assessing mathematical results—such as measures of "closeness" to a solution—could optimize research processes and lead to stronger verifications of proofs. As AI systems refine their abilities to conduct complex proofs and handle existing literature, the future of mathematical research and related disciplines could see significant transformations through these formal methods.