This scientist discovered structures where the stable and unstable manifolds of a fixed point intersect infinitely called homoclinic tangles. Élie Cartan (“ay-LEE car-TAWN”) used differential forms to express this scientist’s integral invariants, one of which requires the sum of the oriented areas of projections onto canonical planes to be preserved. After discovering an error in his own work, this scientist paid to recall his paper that had won a prize awarded by (10[1])King Oscar (-5[1])II (“the second”). This scientist proved that a Hamiltonian system with a finite phase space volume will return arbitrarily (10[1])close (10[2])to its initial state (10[2])infinitely (10[2])many times. (10[2])The state space of a dynamical system can be visualized with this scientist’s namesake (10[1])sections. (-5[1])This scientist names the group (10[1])of isometries of Minkowski (10[1])(“min-KOF-skee”) spacetime. (10[1])For 10 points, (10[1])every simply connected, closed 3-manifold is homeomorphic to the 3-sphere by (10[1])what (10[1])French mathematician’s (10[2])conjecture? ■END■ (10[1])