OpenAI paper claims proof that pi's irrationality exponent is exactly 2
TinfoilTricorn · x · 2026-10-12
A repost highlights a paper attributed to OpenAI (dated September 24, 2026) claiming to prove that π's irrationality exponent is exactly 2.
- The irrationality exponent measures how closely fractions p/q can approximate an irrational number; the main theorem states that for every ν > 2 there is a threshold Q(ν) with |π − p/q| ≥ q^-ν for all q ≥ Q(ν).
- The classic approximation 355/113 misses π by less than three ten-millionths, illustrating the tight limit.
- A corollary resolves the classical Flint-Hills series Σ 1/(n³ sin²n) as convergent, which previously required μ(π) ≤ 5/2.
- Caveat: this is an unverified claim circulating via repost; mathematical acceptance is not yet established.
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