AI Cracks 87-Year-Old Math Mystery, Disproves Jacobian Conjecture | Education and Career News
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As per the Jacobian conjecture, under certain conditions, if a mathematical function works in one direction, it should also work in reverse.
The Jacobian conjecture was proposed by German mathematician Ott-Heinrich Keller in 1939. (AI Image)
A mathematician has solved an 87-year-old mathematics problem with the help of artificial intelligence (AI). Experts say this is the toughest maths problem AI has helped solve so far.
Levent Alpöge from Harvard University announced on X that the famous Jacobian conjecture is false. To prove it, he shared a very short mathematical example, called a counterexample, that showed the idea does not always work.
What Is The Jacobian Conjecture?
The Jacobian conjecture was proposed by German mathematician Ott-Heinrich Keller in 1939. It said that under certain conditions, if a mathematical function works in one direction, it should also work in reverse. For decades, mathematicians believed this idea was true and tried to prove it. Instead, Alpöge showed that it is not always correct.
In his post, Alpöge thanked his “close friend fable,” which is believed to be Anthropic’s AI model, Claude Fable 5. He suggested that the AI helped him find the solution.
Many mathematicians have already checked Alpöge’s counterexample and confirmed that it is correct. The result also surprised experts because most mathematicians had spent years trying to prove the conjecture, not disprove it. A single counterexample was enough to show that the statement was false, reported NewScientist.
However, Alpöge’s result only disproves the version of the conjecture with three variables. A simpler version with two variables could still be true.
Experts say AI is becoming more powerful in mathematics. However, they also believe human mathematicians are still needed to create new ideas and theories. AI may help solve difficult problems, but human creativity remains an important part of mathematical research.
This is not the first major mathematical breakthrough involving AI. In May, OpenAI announced that one of its research models had found a counterexample to the Erdős Unit Distance Conjecture, a decades-old problem in mathematics. The problem asks how many pairs of points on a plane can be exactly one unit apart and is considered a major challenge in combinatorial geometry.
AI is increasingly influencing mathematical research by helping solve complex, long-standing problems and offering new perspectives.
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