For a president under siege, maybe this could help. In an episode of “Mythbusters” on the Discovery Channel to be shown on Dec. 8, President Obama will help determine whether the Greek scientist Archimedes really set fire to an invading Roman fleet using only mirrors and the reflected rays of the sun. Producers of the television series are not saying exactly how Mr. Obama will help prove — or disprove — that myth. But the first presidential appearance is intended to help spur interest in math and science as part of the White House effort to increase American competitiveness in...