Let S be a finite set of lines through the origin in R^3. Whenever two lines in S are orthogonal, augment S with the line orthogonal to both of them. Can the size of S increase without bound?
We'll discuss this problem and its generalizations, naturally considering factorization in the integral quaternions and octonions along the way.
Next week: Laszlo Lovasz (Wednesday) and Doron Zeilberger (Thursday)