The irrationality exponent of pi is 2
We prove the conjecture that the irrationality exponent of π is 2. As a consequence, the classical Flint–Hills series $\sum_{n\ge1}1/(n^3\sin^2 n)$ converges, with angles in radians.
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A Brief Digest of Some New OpenAI Results | Persiflagegaloisrepresentations.orgPersiflage
the close similarity between the arguments here and Roth’s argument for algebraic irrationals. Again, this is something that I hope we shall address at our upcoming conference. Broadly speaking, for the problems in the Langlands program that I am interested in, while OpenAI did an amazing job,…