(Having tried to read the paper without knowing any of the physics involved, it... seems... that circles are very much involved? It sounds less like they're say

(Having tried to read the paper without knowing any of the physics involved, it... seems... that circles are very much involved? It sounds less like they're saying "we tried to calculate this QM question and it turns out the answer is Pi, how elegant!" and more like they're saying "we've tried to use these standard physics formulas to calculate something involving strictly circular orbits [I think... something about how circular the strictly circular orbits of electrons around a hydrogen atom are? But again, I don't know any of the physics here, and am guessing a lot to make up for lack of understanding], which we already know the answer to which is "Pi", but we were surprised to arrive at this specific formula for Pi first derived in 1655, so probably part of the Schroedinger and Bohr equations we used is just an encoding of this Wallis formula for Pi that nobody noticed before [which is cool in a geeky way, and maybe we could rewrite them in a way that makes that Pi factor more apparent and would help us grok the equations better]?")