| # The irrationality exponent of <i>π</i> is 2 | |
| The following describes the scope of the Lean formalization related to the following accompanying paper(s): | |
| - [The irrationality exponent of $\pi$ is 2](../../preprints/The-irrationality-exponent-of-pi-is-2-September-24-2026/paper.pdf) | |
| ## Scope | |
| The formalization proves that the irrationality exponent of $\pi$ is exactly two. For every $\nu>2$, all sufficiently large positive denominators $q$ satisfy $|\pi-p/q|\ge q^{-\nu}$ for every integer numerator $p$. It also states the exact supremum characterization using infinitely many rational approximations. | |
| The paper's convergence consequence for the Flint–Hills series is outside this selected statement. | |
| ## Comparator links | |
| | Result | Comparator statement | | |
| | --- | --- | | |
| | The irrationality exponent of $\pi$ equals two | [PiExponent.lean](../ComparatorChallenges/PiExponent.lean) | | |