David Hilbert

1. David Hilbert Juan Ramirez

2. Fact 1 • David Hilbert was born on January 23, 1862 in Konigsberg, Prussia, now Kaliningrad, Russia. His father, Otto Hilbert, was a city judge, a very respectable position in a small city. Constance Reid indicates that Hilbert largest influence came from his mother Maria, "an unusual woman... interested in philosophy and astronomy and fascinated by prime numbers." As a young boy, Hilbert quickly found that mathematics came very easily to him. Since the gymnasium he attended emphasized language, particularly Latin, over math and science, he put aside his love for mathematics temporarily and concentrated on his weaker subjects, vowing to return to mathematics as soon as possible.

3. Fact 2 • He attended the university in Konigsberg, studying under Heinrich Weber, the only full professor of mathematics in Konigsberg. He visited the university in Heidelberg for a semester to hear lectures on differential equations by Leonard Fuchs. In 1882, Hermann Minkowski, a fellow student at Konigsberg, won the prestigious Grand Prix des Sciences Mathmatiques of the Paris Academy at the age of 17. Hearing of this unprecedented accomplishment, Hilbert quickly became friends with the shy Minkowski. In 1884, Adolf Hurwitz became an Extraordinarius, or assistant professor, at Konigsberg. They developed the habit of taking daily walks "to the apple tree... precisely at five" to discuss philosophy, literature, women, and, above all, mathematics. The three had formed a friendship that would last to their graves.

4. Fact 3 • In 1884, Hilbert completed his oral examination and completed his thesis on invariant properties for certain algebraic forms under the supervision of Ferdinand Lindemann. In 1885, he publicly defended two theses and received his degree of Doctor of Philosophy. At the suggestion of Hurwitz, Hilbert toured Europe to meet the great mathematicians of the time. After an uninspiring visit with Felix Klein in Leipzig, Hilbert went to Paris to learn from the great, although somewhat overrated in Hilbert's opinion, Henri Poincar. He then went to Berlin to study under Leopold Kronecker. Hilbert found Kronecker very disagreeable, since the older mathematician was very rigid in his beliefs. Kronecker is famous for his statement that "God made the natural numbers, all else is the work of man." Kronecker's inflexibility and refusal to accept new ideas had a profound effect on Hilbert, inspiring the young German to be more open-minded and creative in his studies.

5. Fact 4 • There was a gap of twenty years between the periods Hilbert concentrated on the foundations of geometry and the foundations of mathematics in general. During this time, he focused on integral equations and mathematical physics. Hilbert's first contributions to analysis involved homogenous integral equations and the problem of determining eigenvalues of an integral equation. Hilbert also developed a method of analysis using infinitely many vectors in an infinitely-dimensioned space. This space is now known as Hilbert space and is crucial to functional analysis. The study of transforms in Hilbert space has become very important to the studies of integral and differential equations, partial differential equations, quantum mechanics, optimization problems, bifurcation theory, approximation theory, stability problems, variational inequalities, and control problems for dynamical systems. Hilbert's work in integral equations also had a more immediate effect, namely it encouraged his student Richard Courant to delve into analysis. The study of integral equations naturally led into Hilbert's fascination with mathematical physics.