1. By:David Smith

2.  The first steps of Hilbert’s career occurred at the University of Königsberg, at which, in 1884, he finished his Inaugurel-dissertation (Ph.D.); he remained at Königsberg as a Privatdozent (lecturer, or assistant professor) in 1886–92, as an Extraordinarius (associate professor) in 1892–93, and as an Ordinarius in 1893–95.

3.  Hilbert was preeminent in many fields of mathematics, including axiomatic theory, invariant theory, algebraic number theory, class field theory and functional analysis. His examination of calculus led him to the invention of "Hilbert space," considered one of the key concepts of functional analysis and modern mathematical physics. He was a founder of fields like metamathematics and modern logic.

4.  Hilbert ' s basis theorem Hilbert ' s axioms Hilbert ' s problems Hilbert ' s program Einstein – Hilbert action Hilbert space Hilbert ' s basis theorem Hilbert ' s axioms Hilbert ' s problems Hilbert ' s program Einstein – Hilbert action Hilbert space  And mainly all of his mathematical problems.