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His work was mainly on projective and algebraic geometry. Fano was a pioneer in finite geometry and one of the first people to try to set geometry on an abstract footing. Before Hilbert was to make such abstract statements Fano said
As basis for our study we assume an arbitrary collection of entities of an arbitrary nature, entities which, for brevity, we shall call points, and this quite independently of their nature.
References (6 books/articles)