 Both Kronecker, with his divisor theory, and Dedekind, with his ideal theory, were able to obtain important results. Each theory also had a strong influence on later developments—Dedekind’s by shaping the approaches to modern algebra (field theory, ring theory, etc.) of Hilbert, Emmy Noether, B.L. van der Waerden, Emil Artin, Nicolas Bourbaki, and others (Alten et al. 2003, Corry 2004, McLarty 2006, Gray 2008, 2018); Kronecker’s by influencing Hilbert’s work as well, and by being revived later in, among others, André Weil’s and Alexander Grothendieck’s work (class field theory, algebraic geometry) (Weil 1950, Edwards 1990, Reed 1995, Corfield 2003). The contrast between their approaches provides a clear example—historically the first significant example—of the opposition between “classical” and “constructivist” conceptions of mathematics.