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David Hilbert (1862&ndash1941), a German mathematician considered along with Henri Poincaré to be one of the foremost mathematicians of his day, contributed greatly to an even more diverse areas of mathematics than that worthy.
Famously introduced the "Paris Problems", a selection of outstanding mathematical questions he felt deserved attention from the mathematical community, during his plenary address to the second World Congress of Mathematics held in 1900 in Paris, France. The first such congress was held in 1896 in Zurich, Switzerland.
There were 23 problems covering a variety of areas of mathematics:
- Set Theory
- Philosophy of Mathematics
- Analysis (e.g. Calculus of Variations)
- Function Analysis
- Banach Spaces
To get an idea of the mathematics of the day, also see the work of Henri Poincaré. Both men (unsurprisingly) failed to predict the emergence of areas that would become important in the following century of mathematics, e.g. mathematical statistics.
Was a proponent of Cantor's set theory:
- Continuum Theory
- Well-Ordered Hypothesis
This was a controversial idea at the time is was propounded.