An AI has just solved a 60-year-old problem. The AI’s proof has now been examined and confirmed by scientists.
Paul Erdős (1913 – 1996) was an extremely prolific Hungarian mathematician of the 20th century, considered one of the founders of modern combinatorics and graph theory. Many of his statements appear harmless but lead into deep areas of number theory, combinatorics, or analysis and still frustrate people today.
However, Liam Price, a 23-year-old person without deep mathematical knowledge, has now solved a 60-year-old problem of Erdős with the help of ChatGPT. This was reported by the English-language magazine scientificamerican.com.
ChatGPT proposes proof for a 60-year-old problem
What kind of problem is this? The Erdős problem in question concerns the divisibility of binomial coefficients. Simply put, the problem asks for numbers for which specific combinatorial numbers fulfill multiple coprime or divisible properties simultaneously; the difficulty lies in the fact that these arithmetic conditions interact very irregularly.
The AI was not used by Price as a traditional proof assistant but rather as creative support. The user entered the problem statement, and the model proposed a proof idea that was reported to be new and unusual.
The crucial point was not merely “ChatGPT knows the solution”, but: The AI generated a proof path that a human apparently had not directly come up with. Terence Tao, a mathematician at the University of California in Los Angeles, stated that every human wanted to solve the problem in the same way:
There was something like a standard sequence of steps that everyone who had previously dealt with this problem had begun with.
However, the AI took a completely different approach and utilized a formula that, while known in related areas of mathematics, had not yet been applied to this type of question.
Jared Lichtman, a mathematician at Stanford University, explained that ChatGPT’s proof was not perfect. With a colleague, he had to first verify and condense ChatGPT’s proof so that the result could even be understood. And this validation step is what makes the case mathematically so interesting:
The raw data of ChatGPT’s proof was actually quite poor. Therefore, it required an expert to sift through it and truly understand what was being said.
Many years ago, an AI revolution like in Terminator was turned into a horror story. Today, AI tools are ubiquitous, yet obeying humans does not always work. More about this can be read directly on MeinMMO: Researchers have proven that AI does not obey completely: ChatGPT prevented its own shutdown to continue operating
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