OpenAI Proves Pi's Irrationality Exponent is 2

2026-10-07

OpenAI has published a mathematical proof showing that the irrationality exponent of pi is 2. This finding suggests pi behaves typically among real numbers regarding approximation by rational numbers. The irrationality exponent quantifies how well a number can be approximated by fractions, and while most numbers have an exponent of 2, some constants like Cahen's constant have higher exponents.