At a time when we constantly hear that artificial intelligence (AI) will soon replace human thinking, researchers from the Faculty of Information Technology at the Czech Technical University in Prague (FIT CTU) have achieved a remarkable success. In an international benchmark in Leipzig, where the world's leading AI models attempted to solve one hundred challenging mathematical problems, humanity came out ahead. Specifically, researchers from FIT CTU's Department of Theoretical Computer Science recently solved a problem that current AI systems are still unable to tackle.
The Leipzig benchmark was designed to evaluate how well today's AI models perform in advanced mathematics. Its authors compiled a set of one hundred problems with known human solutions and tested whether AI could independently arrive at those solutions as well.
The result? AI demonstrated the extraordinary capabilities of today's most advanced models—but it did not achieve a clean sweep. Out of the 100 problems, AI successfully solved 98. One of the two remaining unsolved problems had been solved by a team of researchers from our faculty. It is a simplified version of the well-known open problem of shattering triples with permutations, a longstanding question in combinatorics.
"The problem of shattering triples with permutations has long been one of my favorite open problems. Although the original problem remains unsolved, our attempts to tackle it led us to formulate a simpler variant, which my research group has managed to solve," explains Mgr. Jan Volec, Ph.D., from the Department of Theoretical Computer Science at FIT CTU.
This simplified variant was later included among the one hundred problems in the Leipzig benchmark. The fact that current AI models were unable to derive its solution independently highlights that, despite their ability to process vast amounts of knowledge, mathematical creativity and abstract reasoning remain areas where humans still have the upper hand.
The result was achieved by Dr. Alexander Clifton, Ing. Daniela Černá, and Mgr. Jan Volec, Ph.D., from the Department of Theoretical Computer Science at FIT CTU, in collaboration with Dr. Bartołomiej Kielak from the University of Leipzig.
