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.

Alexander Abian, Solvability of Infinite Systems of Polynomial Equations Over the Field of Complex Numbers, The American Mathematical Monthly, Vol. 92, No. 2 (Feb., 1985), pp. 94-98 ...

R. Creutzburg, M. Tasche, Parameter Determination for Complex Number-Theoretic Transforms Using Cyclotomic Polynomials, Mathematics of Computation, Vol. 52, No. 185 ...