An infinite-dimensional analog of Euclidean space.
- His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space.
- He took various ideas of Hilbert on integral equations and combined these into the concept of a Hilbert space around 1905.
- In short, to have any hope of understanding what a Hilbert space is, you must learn and digest a whole hierarchy of lower-level concepts first.
Early 20th century: named after David Hilbert (1862–1943), German mathematician.
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Syllabification: Hil·bert space
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