German mathematician who set forth the first rigorous set of geometrical axioms in Foundations of Geometry (1899). He also proved his system to be self-consistent. He invented a simple space-filling curve known as the hilbert curve, and demonstrated the "basis theorem" in invariant theory. His many contributions span number theory (Zahlbericht), mathematical logic, differential equations, and the three-body problem. He also proved Waring's theorem.

At the Paris International Congress of 1900, Hilbert proposed 23 outstanding problems in mathematics to whose solutions he thought twentieth century mathematicians should devote themselves. These problems have come to be known as Hilbert's problems, and a number still remain unsolved today. After Hilbert was told that a student in his class had dropped mathematics in order to become a poet, he is reported to have said "Good--he did not have enough imagination to become a mathematician" (Hoffman 1998, p. 95).

Additional biographies: MacTutor (St. Andrews), Bonn