In the beginning of the twentieth century, Hilbert asked mathematicians to look for a general algorithm to determine whether or not a Diophantine equation has integer solutions in a finite amount of time A twenty-two-year-old Russian proved that this famous problem in number theory was unsolvable
A generalized Euclidean space in which mathematical functions take the place of points; crucial to the understanding of quantum mechanics and other applications
born Jan. 23, 1862, Königsberg, Prussia died Feb. 14, 1943, Göttingen, Ger. German mathematician whose work aimed at establishing the formalistic foundations of mathematics. He finished his Ph.D. at the University of Königsberg (1884) and moved to the University of Göttingen in 1895. In 1900 at the International Mathematical Congress in Paris, he laid out 23 research problems as a challenge to the 20th century. Many have since been solved, in each case to great fanfare. Hilbert's name is prominently attached to an infinite-dimensional space called a Hilbert space (see inner product space), a concept useful in mathematical analysis and quantum mechanics