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Historical Context

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David Hilbert was born in Königsberg, Germany, on January 23, 1862. He obtained his doctorate from the University of Königsberg in 1885, where he remained until 1895 when he took up the professorship at Göttingen he was to hold until his death in 1943.

Hilbert's contributions to mathematics have been vast and far-reaching. His early work was concerned with the theory of invariants, while later he moved into the foundations of geometry and the theory of algebraic number fields. At the turn of the century Hilbert's research efforts broadened yet further, encompassing potential theory, the calculus of variations and various areas of mathematical physics. In his later years Hilbert became primarily involved with the foundations of mathematics, and he is now remembered as one of the greatest mathematicians of the twentieth century. Indeed, it is staggering how many deep results and profound conjectures Hilbert produced across the wide spectrum of his mathematical interests. He also wrote monumental texts on the foundations of mathematics, geometry, logic and algebraic number theory. By the end of the nineteenth century Hilbert's achievements had already lifted him to a point from which he dared to chart out the most promising avenues for research in the twentieth century. In 1900 Hilbert gave life to his vision through the formulation of twenty-three problems that he presented at the International Congress of Mathematicians in Paris. These problems have inspired and guided the minds of mathematicians throughout the last century. Out of the original twenty-three problems eight were of a purely investigative nature. To date twelve of the remaining fifteen have been completely resolved. Quite remarkably, only one problem, the so-called Riemann Hypothesis remains as mysterious and challenging as ever, being now widely regarded as the most important open problem in pure mathematics.

The CMI Millennium Prize Problems are not intended to shape the direction of mathematics in the next century. Rather these problems focus attention on a small set of long-standing mathematical questions, each central to mathematics, that also have resisted many years of serious attempts by experts to solve them. The Riemann hypothesis is one of Hilbert's original questions.

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