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- On Grothendieck's own view there should be almost no history of schemes, but only a history of the resistance to them: ... There is no serious historical question of how Grothendieck found his definition of schemes. It was in the air. Serre has well said that no one invented schemes . The question is, what made Grothendieck believe he should use this definition to simplify an 80 page paper by Serre into some 1000 pages of Éléments de géométrie algébrique? (en)
- Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this domain. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. ... The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axiomatic spirit, which then determined the development of mathematics. ... Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics. (en)
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