Can A.I. Quicken the Pace of Math Discovery?

New York Times

3 days ago

Artificial intelligence can write a poem in the style of Walt Whitman, provide dating advice and suggest the best way to cook an artichoke. But when it comes to mathematics, large language models like OpenAI's immensely popular ChatGPT have sometimes stumbled over basic problems. Some see this as an inherent limitation of the technology, especially when it comes to complex reasoning.
A new initiative from the Defense Advanced Research Projects Agency, or DARPA, seeks to account for that shortfall by enlisting researchers in finding ways to conduct high-level mathematics research with an A.I. 'co-author.' The goal of the new grant-making program, Exponentiating Mathematics, is to speed up the pace of progress in pure (as opposed to applied) math — and, in doing so, to turn A.I. into a superlative mathematician.
'Mathematics is this great test bed for what is right now the key pain point for A.I. systems,' said Patrick Shafto, a Rutgers University mathematician and computer scientist who now serves as a program manager in DARPA's information innovation office, known as I20. 'So if we overcome that, potentially, it would unleash much more powerful A.I.' He added, 'There's huge potential benefit to the community of mathematicians and to society at large.'
Dr. Shafto spoke from his office at DARPA's headquarters, an anonymous building in Northern Virginia whose facade of bluish glass gives little indication that it houses one of the most unusual agencies in the federal government. Inside the building's airy lobby, visitors surrender their cellphones. Near a bank of chairs, a glass display shows a prosthetic arm that can be controlled by the wearer's brain signals.
'By improving mathematics, we're also understanding how A.I. works better,' said Alondra Nelson, who served as a top science adviser in President Joseph R. Biden Jr.'s administration and is a faculty member at the Institute for Advanced Study in Princeton, N.J. 'So I think it's kind of a virtuous cycle of understanding.' She suggested that, down the road, math-adept A.I. could enhance cryptography and aid in space exploration.
Started after World War II to compete with the Soviet Union in the space race, DARPA is most famous for fostering the research that led to the creation of ARPANET, the precursor to the internet we use today. At the agency's small gift store, which is not accessible to the public, one can buy replicas of a cocktail napkin on which someone sketched out the rudimentary state of computer networks in 1969. DARPA later funded the research that gave rise to drones and Apple's digital assistant, Siri. But it is also responsible for the development of Agent Orange, the potent defoliant used to devastating effect during the Vietnam War.
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