The 1982 SAT infamously held a math question so tricky that even its creators didn’t include a correct answer. The botch required the rescoring of 300,000 exams, scholastic victims of the knotty coin ...

If you twist something — say, spin a top or rotate a robot’s arm — and want it to return to its exact starting point, intuition says you’d need to undo every twist one by one. But mathematicians ...