Breakthrough on tetrahedra
Collaboration PI Bjorn Poonen and affiliated researcher Kiran Kedlaya, with Alexander Kolpakov and Michael Rubinstein, have classified all tetrahedra with rational dihedral angles. This resolves a 1976 question of J.H. Conway and A.J. Jones. The solution is a tour-de-force of computational arithmetic geometry and requires solving a polynomial equation with 105 terms! Their preprint “Space vectors forming rational angles” is now on the arXiv; see their press release for more details.