# Who invented the first Geometry Axiomization

Brief biography of mathematician David Hilbert, who introduced the concepts of formalism into mathematics and the Invariant Theory. Mathematician David Hilbert is famous for his axiomatization of geometry and his Paris speech, “The Problems of Mathematics.” To him, mathematics is concerned with formal symbolic systems, an activity that uses a series of symbols and rearranges them according to formal rules.

Speaking in Paris in 1900, Hilbert caused a stir by presenting 23 mathematical problems, some of which have been solved through the years.

## Early Life of David Hilbert

David Hilbert was born in Königsberg, Prussia (now Kaliningrad, Russia) on January 23 1862. He worked for his Ph.D. at the University of Königsberg and completed in 1885. After graduation, he was taken as a member of staff at the university and eventually given a professorship in 1893. Hilbert worked on invariant theory and proved his famous basis theorem, then began work on algebraic number theory.

He moved to Göttingen, Germany in 1895, taking the prestigious post of professor of mathematics. It was during these years that he published two of his books, Zahlbericht, a synethesis of the work of Kummer, Kronecker and Dedekind; and Grundlagen der Geometrie, putting geometry on a formal axiomatic setting.

## Hilbert’s Invariant Theory

Part of his contribution to science, and mathematics in particular, is that Hilbert introduced an original approach to ways of considering mathematical invariants. An “invariant” is something that is left unchanged by some class of functions. In terms of a geometrical transformation, an it would be an object that does not alter its shape or size while it is being moved.

Hilbert spent 20 years of the 20th century proving that all invariants could be expressed in terms of a finite number – a number that can actually be counted. His theory was in later years, 1931, contradicted by the “Incompleteness Theorem” of Czech-born American mathematician and logician Kurt Gödel. The theorem showed that every consistent theory must contain propositions that are undecidable.

## Mathematics and Problems

Hilbert’s fame sits mainly on the list of 23 problems he presented at the Second International Congress of Mathematicians in Paris. In 1900, he presented this in a speech in Paris entitled “The Problems of Mathematics.” Many of them have now been solved.

He thought of mathematics as a living subject with a great future, while he saw the problems as opportunities for further exploration.

## Hilbert Contribution and Legacy

David Hilbert reduced branches of mathematics such as geometry to a series of axioms, therefore, removing mathematics from any relationship to a physical reality. It was all about symbols on paper and rules for manipulating those symbols.

He retired in 1930, and was made and honorary citizen of Königsberg. He died on February 14, 1943, aged 81. His acquaintances include Albert Einstein, Norbert Wiener and Hermann Minkowski.