Event № 625

In 1687 Sir Isaac Newton discovered that the area cut off from an oval in the plane by a straight line never depends algebraically on the line (the question was motivated by           celestial mechanics). In 1987 V. I. Arnold proposed to generalize Newton's observation to higher dimensions and conjectured that all smooth bodies, with the exception of        ellipsoids in odd-dimensional spaces, have an analogous property. The talk is devoted to the current status of this conjecture.