Real quadratic fields and finite quantum dilogarithms I

Danylo Radchenko and Campbell Wheeler have posted an extraordinary new paper in which they prove that Stark units for real quadratic fields are algebraic numbers. (Not yet a Shimura reciprocity law that shows these generate abelian extensions but hey, this is only part I.) This, to me, is arguably the most significant mathematical result of the past month. There is a lot of rich mathematics going on here, and I apologize for not having the time to even summarize it. But I didn’t want it to go unmentioned!