Recently AI (alphazero) was used to improve practical matrix multiplications by around 10 to 20 percent. Alphageometry and ramanujan machines all came into existence in the recent years as well. Seems like it might time AI gets used to further improve algorithms for pi like this one? If so, is there a sketch of a solution?


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All of the improved algorithms that Alphazero found are basically the same idea: there is a combinatorial search space of solutions which is hard to navigate through, but it's possible to prove that you've found a solution when you propose one.

There are definitely algorithms for computing $\pi$ that live in spaces like this. Machin-like formulas are an example that are relatively easy to understand: there are an infinite number of possible algorithms, it's straightforward to prove that one is correct or not, and the goal is to find the most efficient of them.

The Chodnovsky and Borwein algorithms are both examples of Ramanujan-Sato series. Again, these form a large search space that is feasible to search and prove correctness. So it's certainly possible that alphazero could indeed produce new algorithms of that type.


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