One of the names found in history of mathematics from the 20th century is that of David Hilbert. Born on January 23, 1862 in Prussia, Russia, this famous mathematician had developed his interest and skill in mathematics through his mother who was a mathematician and astronomer herself. His father was a judge named as Otto Hilbert.
Hilbert received high school education from Friedrichskollegium Gymnasium (a secondary level school for advanced studies). In the final year his outstanding command in mathematics granted him with the opportunity of studying at a higher level school by getting transferred to the Wilhelm Gymnasium. After graduating, he took admission in the University of Königsberg to study mathematics from where he received a doctoral degree in 1885. The following year he was made assistant professor at the University of Königsberg, got promoted to associate professor 1892 and to Professor in 1893. After nine years of services, he left this university to work as professor for his entire remaining life at the University of Gottingen. Many prominent mathematicians of the past have also been a part of this university as professors.
Utilizing his interest in mathematics, Hilbert contributed to various disciplines. Some of his major contributions are;
- Theorems of invariants
Hilbert published a report in 1897 titled as Zahlbericht (Commentary on Numbers). In this report he proved the theorem of invariants and discussed its further applications.
- Hilbert’s axiom
Hilbert presented his set of axioms in his book Grundlagen der Geometrie (The Foundations of Geometry) in 1899. The flaws found in Euclidean Geometry were removed through these axioms that combined one and two dimensional geometry.
- Hilbert space
Hilbert also did a lot of work in calculus and vector algebra and discovered a new concept which was names as ‘Hilbert Space’. It served as the basis for functional analysis, quantum mechanics and mathematical physics
- Hilbert’s 23 problems
Hilbert discovered many mathematical issues which he considered as essential to be addressed. He shared them in his lecture The Problems of Mathematics, at the International Mathematical Congress in Paris in 1900. There, he presented 23 problems that are famously known as the Hilbert’s 23 Problems. In this way, he set a stage for mathematicians of the 20th century to bring revolution in mathematics by solving the identified problems. In the following few years, mathematicians solved many of those problems, yet some still remain unsolved.
- Mathematical physics
Hilbert believed that without applying concepts of math many of the physical problems could not be solved. Along with his colleague Hermann Minkowski who was also a mathematician and professor at the University of Gottingen, Hilbert did a lot work in mathematical physics and from 1907 to 1912, most of his researches were related to this field only. Some of his research topics include theory of radiations, kinetic gas theory, number theory etc.
After years of contributions in the field of mathematics, Hilbert retired from the University of Gottingen in 1930. His memorable address Naturerkennen und Logik (The Understanding of Nature and Logic) reflected his passion for mathematics and deep concern for its future. Hilbert and a French mathematician received a joint Mittag-Leffler prize by the Swedish Academy in 1939.
In late 1930s, David Hilbert raised his voice for the Jewish professors and mathematicians in Austria and Germany that were becoming victim of the Nazi Regime. Unfortunately, he couldn’t do much but see the assassinations and destruction of a popular mathematical center.
He died after thirteen years of his retirement on February 14, at 81 years of age. By that time, the mathematical community at Gottingen had reduced to very less mathematicians. He couldn’t receive the honor he deserved as only around 12 people attended his funeral, but his discoveries and contributions played major role in molding the future of mathematics.