For math I’d say Exeter would be the best. One of their math teachers, Zuming Feng, coached the IMO for team USA, and published a bunch of math-related practice books. He was also Mark Zuckerberg’s favorite teacher at Exeter.
I don’t know much about politics for these schools listed, but I can tell you that Groton is certainly a great school if your daughter wants to be a politician. Many Groton graduates turn out to be politicians/diplomats (most notably FDR).