A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars.

It is known that the expected number of zeros in the interval (-1, 1) of the sum a0ψ0(t) + a1ψ1(t) + ⋯ + anψn(t), in which ψk(t) is the normalized Legendre polynomial of degree k and the coefficients ...