Levent Alpoge, a researcher at Anthropic, reported an interesting achievement in the field of algebraic geometry. With the help of the advanced language model Claude Fable 5, he managed to find a counterexample to the famous Jacobian hypothesis. This fundamental mathematical problem was formulated back in 1939 by the German scientist Ott-Heinrich Keller. The essence of the hypothesis was that if a certain formula converts one set of numbers into another without losing information at each individual point, then this process can always be reversed. However, artificial intelligence has built a formula that successfully passes local verification, but at the same time converts three different sets of numbers into the same result. This makes it impossible to restore the original data and definitively refutes the statement that mathematicians have been struggling with for 87 years.

An important feature of this discovery is its absolute verifiability. Unlike many statements by technology companies that rely on closed internal tests, this counterexample is a specific mathematical formula. Any specialist can substitute the values and independently recalculate the result, for example, using the publicly available Wolfram Alpha service. Leading representatives of the mathematical community have already praised this breakthrough. Mathematician Qiaochu Yuan noted that this is the most famous open problem ever solved by a language model. He also ironically noted that the Jacobian hypothesis is notorious for the large number of erroneous proofs that have been published even by recognized scientists in the past. His colleague Jared Duker Lichtman called the result truly outstanding, recalling that special cases of this hypothesis have become topics of serious academic dissertations.

This success has become a vivid example of the growing role of artificial intelligence in solving fundamental scientific problems. Earlier this year, models from OpenAI and Google DeepMind have already demonstrated the ability to solve complex problems from the list of the famous mathematician Pal Erdos. However, many of those achievements concerned tasks that can be solved using standard algorithmic methods. The refutation of the Jacobian hypothesis represents a qualitatively new level, since it is a famous problem that had no direct analogues in the existing literature. Levent Alpoge himself has a serious academic background, having defended his doctoral thesis at Princeton under the supervision of a Fields Prize winner. His result is currently awaiting formal academic review, which will be the final step in recognizing this historic achievement of artificial intelligence.