Hilbert's Contributions to Mathematics
- In his book, The Foundations of Geometry, Hilbert described a set of axioms that removed the flaws of Euclidean Geometry. These axioms unify plane geometry with the solid geometry of Euclid into a single system. Hilbert is considered to be one of the most influential mathematician in the field of Geometry.
- Proposed a list of 23 unsolved problems to the International Congress of Mathematics in Paris. Since their presentation in 1900, several of the problems have been solved, though others remain a mystery today. Hilbert's 23 problems are the most influential lists of open problems of all time
- Hilbert's problems led to development of the formalist school of mathematics. Hilbert started a research program that came to be called Hilbert's Program in which he aimed to formulate math on a solid logical foundation. Hilbert believed this would be possible by showing that all of math follows a finite system of axioms which could be proved. This came to be called Formalism.
- Hilbert proved the finite basis theorem for multiple variables. Paul Gordon had been able to prove the theorem earlier, but only for two variables. Hilbert approached the problem in a different way, advancing algebraic number theory.