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AI Solves Major Math Problems, Shaking Up the Field
Confirmed
In Short: Mathematicians are struggling to process a wave of new results from artificial intelligence, which has thrown up a repository of over 370 mathematical proofs, including potential solutions to some of the most challenging problems in the field.
Mathematicians are struggling to process a wave of new results from artificial intelligence, which has thrown up a repository of over 370 mathematical proofs, including potential solutions to some of the most challenging problems in the field.
Among these is a proof that may have solved one of the seven Millennium Prize Problems, a set of complex mathematical challenges selected by the Clay Mathematics Institute in 2000, each offering a $1 million prize.
The Navier-Stokes Millennium Prize problem, which deals with the behavior of fluid dynamics, is among those reportedly resolved by AI.
Geoff Brumfield of NPR reported that mathematicians around the world are in a state of shock, facing a lot of extra homework as they verify these AI-generated proofs.
OpenAI, the company behind the AI, has announced the formation of an independent Advisory Group on Mathematics and Artificial Intelligence to address the implications of these findings.
Mathematicians are divided on the validity of these results. Andrew Sutherland of MIT told Scientific American that until the results are replicated, claims about solving these problems should be treated with skepticism.
Tristan Buckmaster, a mathematician, compared the feat to the Deep Blue-Kasparov moment in chess, signaling a significant shift in the perception of machine intelligence.
Charles Fefferman of Princeton University, who wrote the official description of the Navier-Stokes problem for the Clay Institute, expressed excitement about the potential solution.
The results are structured into 372 'families' of related proofs, each bundling a main theorem with companion arguments, consequences, or alternative proofs.
Mathematicians are also concerned about the negative externalities of solving open problems as a benchmark for new AI systems, as highlighted in an open letter by mathematicians.
The field of mathematics will never be the same, as these results challenge traditional methods and raise questions about the future of mathematical research.
What this adds
The BACKGROUND notes that one of the most notable claims is that the AI may have solved one of the seven Millennium Prize Problems, a set of complex mathematical challenges selected by the Clay Mathematics Institute in 2000, each offering a $1 million prize.
Background
One of the most notable claims is that the AI may have solved one of the seven Millennium Prize Problems, a set of complex mathematical challenges selected by the Clay Mathematics Institute in 2000, each offering a $1 million prize.
What's confirmed
- Mathematicians are struggling to process a wave of new results from artificial intelligence, which has thrown up a repository of over 370 mathematical proofs, including potential solutions to some of the most challenging problems in the field.
- Among these is a proof that may have solved one of the seven Millennium Prize Problems, a set of complex mathematical challenges selected by the Clay Mathematics Institute in 2000, each offering a $1 million prize.
- The Navier-Stokes Millennium Prize problem, which deals with the behavior of fluid dynamics, is among those reportedly resolved by AI.
- Geoff Brumfield of NPR reported that mathematicians around the world are in a state of shock, facing a lot of extra homework as they verify these AI-generated proofs.
- OpenAI, the company behind the AI, has announced the formation of an independent Advisory Group on Mathematics and Artificial Intelligence to address the implications of these findings.
- Mathematicians are divided on the validity of these results. Andrew Sutherland of MIT told Scientific American that until the results are replicated, claims about solving these problems should be treated with skepticism.
- Tristan Buckmaster, a mathematician, compared the feat to the Deep Blue-Kasparov moment in chess, signaling a significant shift in the perception of machine intelligence.
- Charles Fefferman of Princeton University, who wrote the official description of the Navier-Stokes problem for the Clay Institute, expressed excitement about the potential solution.
- The results are structured into 372 'families' of related proofs, each bundling a main theorem with companion arguments, consequences, or alternative proofs.
- Mathematicians are also concerned about the negative externalities of solving open problems as a benchmark for new AI systems, as highlighted in an open letter by mathematicians.
- The field of mathematics will never be the same, as these results challenge traditional methods and raise questions about the future of mathematical research.
What's still developing
- GEOFF BRUMFIEL, BYLINE: Earlier this month, OpenAI threw up a repository filled with more than 370 results for longstanding problems in mathematics.
- Among them was one mathematician Dana Moshkovitz at UT Austin had been working on for years.
- It's considered among the most challenging in her area of study.
- It's a hard problem about approximating solutions to other hard math problems.
- “This is a Deep Blue–Kasparov moment,” wrote mathematician Tristan Buckmaster, referring to the sea change in thinking about machine intelligence that occurred when a supercomputer beat world champion Garry Kasparov at chess in the 1990s, in a statement released late on Monday.
- The field will never be the same A mathematician compared the feat to the history-making chess competition in which IBM’s Deep Blue computer beat Garry Kasparov in 1997 By Joseph Howlett edited by Clara Moskowitz & Claire Cameron Today may go down as the biggest day in math in at least two decades, if not far longer.
- 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.
- 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.
- They are disputing whether anyone outside OpenAI has actually finished checking them, and whether the field has the bandwidth to try.
- 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.