"One idle evening last October, Mehtaab Sawhney took up an old pastime. He began perusing the website erdosproblems.com, an updated record of the 1,179 conjectures left behind by the eccentric and indefatigable 20th-century mathematician Paul Erdos. Sawhney, a mathematician at Columbia University, had always been interested in the Erdos problems, which range from minor curiosities to central open problems in number theory and combinatorics."
"He came upon a problem, #339, that seemed too straightforward to still be open nearly two decades after Erdos's death. He'd seen similar conjectures before. There were a number of problems that kind of looked too approachable, Sawhney says. In the past, he'd turned to Google. And then eventually, with enough searching, I would find a reference to a solution."
"But recently he'd been playing with ChatGPT as a new way to check the literature. I decided to plug it in, and then it just told me there was a reference, Sawhney says. It went so well that he reached out to a fellow mathematician, Mark Sellke, who had recently gone on leave from an academic position to work for OpenAI. Together they prompted ChatGPT to dig up lost solutions to nine other Erdos problems, plus partial solutions to 11 more."
Mathematicians have used large language models to locate references and recover solutions to longstanding Erdos conjectures. Mehtaab Sawhney used ChatGPT to find a reference for problem #339 and then collaborated with Mark Sellke to prompt the model for additional answers. LLMs have performed enhanced literature searches and, in many cases, synthesized existing theorems in dialogue with mathematician prompters to form new or improved proofs. Activity on erdosproblems.com has increased sharply, and a webpage maintained by Terence Tao reports that AI tools assisted in moving roughly 100 Erdos problems into the solved column since October. These efforts range from uncovering lost solutions to assembling partial results.
Read at www.scientificamerican.com
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