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AI is shaking up the field of mathematics. But what comes next?
Confirmed
In Short: Mathematicians are grappling with a flood of new results from artificial intelligence, including potential solutions to longstanding Millennium Prize Problems.
Mathematicians are facing a new challenge as artificial intelligence (AI) has produced a repository of over 370 results for longstanding problems in mathematics, according to NPR.
Among these results is a potential solution to one of the most challenging problems Dana Moshkovitz at UT Austin has been working on for years, a problem that involves approximating solutions to other hard math problems.
OpenAI's repository includes a solution to the Navier-Stokes Millennium Prize problem, one of the seven complex mathematical challenges set by the Clay Mathematics Institute in 2000, each offering a $1 million prize.
Mathematicians are in a state of shock, with some comparing the feat to the moment IBM’s Deep Blue computer beat Garry Kasparov in 1997, marking a significant shift in the perception of machine intelligence.
The field of mathematics will never be the same, as mathematician Tristan Buckmaster noted, referring to the historical chess competition that changed the landscape of machine intelligence.
OpenAI’s internal model reportedly solved over 100 longstanding mathematical problems, including the Navier-Stokes problem, leading to the formation of an independent Advisory Group on Mathematics and Artificial Intelligence.
The results are grouped into 372 “families” of related results, each containing a main theorem with companion arguments, consequences, or alternative proofs.
However, mathematicians are disputing whether anyone outside OpenAI has actually finished checking these results, and whether the field has the bandwidth to try.
Charles Fefferman of Princeton University, who wrote the Clay Institute’s official description of the Navier-Stokes problem, expressed his excitement over the potential solution.
Andrew Sutherland, a mathematician at MIT, advised treating any claims about solving problems with a single agent as unverified until the model and results can be replicated.
The mathematicians' concerns are echoed in an open letter titled “A Severe Misalignment of AI in Mathematics,” which highlights the negative externalities of solving open problems as a benchmark for new AI systems.
What this adds
The mathematicians' shock and the comparison to Deep Blue's victory at chess underscore the transformative impact of AI in mathematics.
The formation of the Advisory Group on Mathematics and Artificial Intelligence suggests a proactive approach to addressing the challenges and opportunities presented by AI in the field.
What's confirmed
- Mathematicians are facing a new challenge as artificial intelligence (AI) has produced a repository of over 370 results for longstanding problems in mathematics, according to NPR.
- Among these results is a potential solution to one of the most challenging problems Dana Moshkovitz at UT Austin has been working on for years, a problem that involves approximating solutions to other hard math problems.
- OpenAI's repository includes a solution to the Navier-Stokes Millennium Prize problem, one of the seven complex mathematical challenges set by the Clay Mathematics Institute in 2000, each offering a $1 million prize.
- Mathematicians are in a state of shock, with some comparing the feat to the moment IBM’s Deep Blue computer beat Garry Kasparov in 1997, marking a significant shift in the perception of machine intelligence.
- The field of mathematics will never be the same, as mathematician Tristan Buckmaster noted, referring to the historical chess competition that changed the landscape of machine intelligence.
- OpenAI’s internal model reportedly solved over 100 longstanding mathematical problems, including the Navier-Stokes problem, leading to the formation of an independent Advisory Group on Mathematics and Artificial Intelligence.
- The results are grouped into 372 “families” of related results, each containing a main theorem with companion arguments, consequences, or alternative proofs.
- However, mathematicians are disputing whether anyone outside OpenAI has actually finished checking these results, and whether the field has the bandwidth to try.
- Charles Fefferman of Princeton University, who wrote the Clay Institute’s official description of the Navier-Stokes problem, expressed his excitement over the potential solution.
- Andrew Sutherland, a mathematician at MIT, advised treating any claims about solving problems with a single agent as unverified until the model and results can be replicated.
- The mathematicians' concerns are echoed in an open letter titled “A Severe Misalignment of AI in Mathematics,” which highlights the negative externalities of solving open problems as a benchmark for new AI systems.
What's still developing
- JUANA SUMMERS, HOST: Mathematicians are struggling to figure out what to do with a flood of new results from artificial intelligence.
- GEOFF BRUMFIEL, BYLINE: Earlier this month, OpenAI threw up a repository filled with more than 370 results for longstanding problems in mathematics.
- AI-written mathematical proofs have saddled the community with a lot of extra homework.
- It's considered among the most challenging in her area of study.
- Tiep helped to prove part of the conjecture in 2013, and has worked “intensively” on the rest since then, he said in a Rutgers statement.
- Brauer, Tiep said, was a “rare intellect” as though “from another world,” and Tiep was surprised when he did eventually manage to solve the immensely complicated problem.
- Buckmaster and Alpöge focused on a set of equations called the Euler (pronounced like “oiler”) equations.
- The new result, on one of mathematics’ most important problems, is “the spectacular culmination of the arc we have seen over the last 12 months,” OpenAI researcher Sébastien Bubeck said during a September 8 news conference.
- “Ten years ago, nobody believed there was a singularity for Navier-Stokes,” said Córdoba — though many believed that the Euler equations did admit a singularity.
- Born in Indiana in 1936, Hamilton studied mathematics before moving to Boston and joining an MIT laboratory in 1965.
- MIT praised her for guiding software development when the field was in its infancy.
- Those results were bundled into 722 individual manuscripts and sorted into 372 “result families,” a structure OpenAI uses to group related proofs and lemmas under a single research thread rather than publishing each one in isolation.