  According to two remarkable theorems of Nyman and B\'aez-Duarte, the Riemann
hypothesis is equivalent to a simply-stated criterion concerning least-squares
approximation. In carrying out computations related to this criterion, we have
observed a curious phenomenon: for no apparent reason, at least the first
billion entries of a certain infinite triangular matrix associated to the
Riemann zeta function are all positive. In this article we describe the
background leading to this observation, and make a conjecture.
