How AI Cracked a 60-Year-Old Math Puzzle: The Unlikely Hero

In a surprising turn of events, a 23-year-old named Liam Price solved a complex mathematical problem that had puzzled experts for six decades, thanks to modern AI tools. Despite lacking an advanced background in mathematics, Price achieved this feat by using the ChatGPT Pro service, succeeding where many renowned mathematicians had failed.

AI and the Challenge of Mathematical Problems

Erdős problems, named after the famous mathematician Paul Erdős, have long been a benchmark for testing AI’s capabilities in mathematics. However, these problems vary in significance and difficulty, making them an imperfect standard for measuring AI’s prowess.

Price’s solution, using the latest version of ChatGPT, stands out. The tool employed a novel approach previously unknown in this type of question. While it’s too early to draw definitive conclusions, this new method could have broader applications in the future.

Understanding Primitive Sets

The problem Price solved involved special sets of integers where no number can evenly divide another. These are known as “primitive sets” due to their connection to prime numbers, which can only be divided by themselves and one.

The core concept in this problem is the “Erdős sum,” a value that can be calculated for any primitive set. Erdős proved that the maximum sum reaches about 1.6, a value that should also apply to the infinite set of prime numbers. This prediction was confirmed in 2022.

Human Errors and AI Success

According to Terence Tao, a mathematician at the University of California, researchers typically followed standard steps to solve this problem, but AI chose a different path. The AI used a formula known in other areas of mathematics, but no one had thought to apply it to this specific question.

Although the AI’s initial outputs were unclear, experts managed to analyze and refine the proof to clarify the main idea.

Conclusion

The contribution of AI in solving this problem is not just a technical achievement; it marks the beginning of a new understanding of how to handle large numbers and their structures. Jared Lichtman from Stanford University believes this shift confirms his intuition that these problems share a unified approach. This development opens up new possibilities in mathematics and highlights the growing role of AI in previously unexpected fields.