Artificial intelligence models are beginning to demonstrate an ability to solve complex mathematical problems, marking a potential shift in the capabilities of these systems. Software engineer and startup founder Neel Somani discovered this unexpectedly while testing OpenAI's latest model.

Somani pasted a high-level math problem into ChatGPT and, after allowing the model 15 minutes to process, found a complete solution. He then rigorously evaluated the proof using the Harmonic tool, confirming its validity. "I was curious to establish a baseline for when LLMs are effectively able to solve open math problems compared to where they struggle," Somani said. "The surprise was that, using the latest model, the frontier started to push forward a bit."

The AI's problem-solving approach involved a chain of reasoning, citing mathematical axioms such as Legendre's formula, Bertrand's postulate, and the Star of David theorem. The model identified a Math Overflow post from 2013, where Harvard mathematician Noam Elkies had provided a solution to a similar problem. However, ChatGPT's final proof diverged from Elkies' work, offering a more comprehensive solution to a version of a problem originally posed by mathematician Paul Erdős. Erdős is known for his collection of unsolved problems that have become a benchmark for testing AI capabilities.

Large Language Models (LLMs) like ChatGPT are trained on vast amounts of text data, enabling them to identify patterns and relationships within the information. This allows them to generate human-like text, translate languages, and, as this instance demonstrates, tackle complex mathematical challenges. The ability of AI to solve these problems could have implications for various fields, including scientific research, engineering, and finance, where complex calculations and problem-solving are essential.

The development highlights the rapid advancements in AI and its potential to contribute to mathematical research. While AI is not yet capable of independently formulating new mathematical theories, its ability to analyze existing problems and generate solutions is a significant step forward. Further research is needed to understand the limitations and potential biases of AI in mathematical problem-solving. The ongoing developments in AI's mathematical capabilities suggest a future where AI could become a valuable tool for mathematicians and researchers.