Harvard mathematician Levent Alpöge has used Anthropic's Fable 5 to disprove the Jacobian conjecture, a long-standing open problem in algebraic geometry. The achievement highlights the potential of advanced AI models in mathematical research, though its broader implications remain uncertain.
TL;DR
- Harvard mathematician Levent Alpöge used Anthropic's Fable 5 to disprove the Jacobian conjecture, a 90-year-old open problem in algebraic geometry.
- The disproof is a significant achievement for AI in mathematics, but its broader implications for the field are still being evaluated.
- This follows OpenAI's recent disproof of the Erdős unit distance conjecture, which had more productive outcomes for the mathematical community.
What happened
On Sunday evening, mathematician Levent Alpöge announced on X that he had used Anthropic's Fable 5 to disprove the Jacobian conjecture. This conjecture is a long-standing open problem in algebraic geometry that has puzzled mathematicians for nearly 90 years. It was included in 'Smale's problems,' a list of unresolved math problems presented by mathematician Stephen Smale in 1998.
Alpöge, who is part of Harvard's Society of Fellows and has an affiliation with Anthropic, used Fable 5, Anthropic's latest frontier AI model, to find a counterexample that disproves the conjecture. Fable 5 is the public version of Claude Mythos Preview, which Anthropic previously described as having advanced cybersecurity capabilities that were too dangerous for public release.
Why it matters
The disproof of the Jacobian conjecture by Fable 5 is a significant achievement for AI in mathematics. It demonstrates the potential of advanced AI models to tackle complex mathematical problems that have evaded human mathematicians for decades. However, the broader implications of this achievement for the field of mathematics are still being evaluated.
Professor and mathematician Andrew Blumberg from Columbia University noted that while providing a counterexample is a notable accomplishment, it does not necessarily provide new insights into the structure of nature or advance the field in a meaningful way. He compared it to finding a cure for cancer without understanding the underlying mechanisms. In contrast, OpenAI's disproof of the Erdős unit distance conjecture in May provided a more productive outcome, as experts were able to unpack the disproof and use it to make further advancements.
Key facts
- Mathematician Levent Alpöge used Anthropic's Fable 5 to disprove the Jacobian conjecture.
- The Jacobian conjecture is a 90-year-old open problem in algebraic geometry.
- Fable 5 is the public version of Claude Mythos Preview, Anthropic's advanced AI model.
- Alpöge is part of Harvard's Society of Fellows and has an affiliation with Anthropic.
- Professor Andrew Blumberg noted that the disproof is significant but does not necessarily provide new insights.
- OpenAI's disproof of the Erdős unit distance conjecture had more productive outcomes for the mathematical community.
- The Jacobian conjecture was included in 'Smale's problems,' a list of unresolved math problems presented by Stephen Smale in 1998.
Context
The use of AI in mathematical research is not new, but recent advancements in AI models like Fable 5 and OpenAI's internal models have shown promising results in tackling complex mathematical problems. These achievements highlight the potential of AI to augment human intelligence and accelerate discoveries in various fields, including mathematics.
However, the broader implications of these achievements for the field of mathematics and the scientific community at large are still being explored. While AI models can provide counterexamples and disprove long-standing conjectures, the deeper understanding and insights that drive scientific progress may still require human expertise and intuition.