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Hilbert's Problems

  In 1900, one of the most distinguished mathematicians of the day, David Hilbert (1862 - 1943), gave a lecture in Paris looking ahead to the new century in mathematics and attempting to define the areas in which future developments would lie. ‘We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. If we would obtain an idea of the probable development of mathematical knowledge in the future, we must … look over the problems which the science of today sets and whose solution we expect from the future.’ Hilbert went on to list twenty-three such problems. Some were specific mathematical problems, others more general questions (such as the sixth, the application of the method of axiomatization to physics). The remarkable things about these problems were the breadth of mathematics covered (from set theory to number theory to algebra to topology to mathematical physics), and the effect they have had on modern mathematics. A couple were trivial, but the others generated whole new branches of the subject in the efforts made to solve them or to show that they were insoluble (as some were). SMcL  



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