Coda: Hilbert’s tenth problem

Abstract

At the turn of the previous century, David Hilbert (1862-1943) was already regarded as one of the finest mathematicians of his generation1. He had forced breakthroughs in the theory of invariants, number theory and geometry2. Hilbert would, self-evidently, address the International Congress of Mathematics in 1900 on the occasion of the World’s Fair in Paris. He conferred on the subject with his friends Hermann Minkowski (1864-1909) and Adolf Hurwitz (1859-1919). They advized him to look ahead towards the future. Organizationally, the Congress was a disaster, remembered only for Hilbert’s speech. A condensed version appeared in L’Enseignement Mathématique (1900). The complete version was published in the Nachrichten (1900) of the Göttinger Wissenschaftsgeselschaft and the following year also in Archiv der Mathematik und Physik 3. The problems Hilbert proposed, and which he felt needed resolving, came from all fields of mathematics. They dealt with divergent aspects such as the cardinality of natural and real numbers, the axiomatization of mathematics and physics, algebraic number theory, geometry, algebra, and analysis.