Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

A.J. VAN DER POORTEN, A NOTE ON HADAMARD ROOTS OF RATIONAL FUNCTIONS, The Rocky Mountain Journal of Mathematics, Vol. 26, No. 3 (SUMMER 1996), pp. 1183-1197 ...

Polynomial interpolation to analytic functions can be very accurate, depending on the distribution of the interpolation nodes. However, in equispaced nodes and the like, besides being badly ...