Article ID: CBB001211748

Intuition and Rigor and Enriques's Quest (2011)

unapi

Mumford, David (Author)


Notices of the American Mathematical Society
Volume: 58, no. 2
Issue: 2
Pages: 250-260


Publication Date: 2011
Edition Details: Part of a special issue on the history of algebra
Language: English

In the preceding article we have seen that Enriques and, indeed, the whole Italian school of algebraic geometry in the rst half of the twentieth century were frustrated by one glaring gap in their theory of algebraic surfaces. This magni cent theory answered essentially all the basic questions about algebraic surfaces and had been constructed using purely geometric tools. But one of its central theorems seemed to defy all their attempts to give it a geometric proof. It had been proven by analytic means by Poincaré with his theory of normal functions,1 so the theory was sound---but this approach was alien to their intuitions. It was much like the need for analysis in proving the prime number theorem before Selberg found his elementary proof. In my own education, I had assumed they were irrevocably stuck, and it was not until I learned of Grothendieck's theory of schemes and his strong existence theorems for the Picard scheme that I saw that a purely algebrogeometric proof was indeed possible. I say here algebro-geometric, not geometric, because the rst requirement in moving ahead had been the introduction of new algebraic tools into the subject rst by Zariski and Weil and subsequently by Serre and Grothendieck.

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Article Brent, Richard P.; Zimmermann, Paul (2011) The Great Trinomial Hunt. Notices of the American Mathematical Society (pp. 233-239). unapi

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Authors & Contributors
Pompeo Faracovi, Ornella
Speranza, Francesco
Nurzia, Laura
D'Agostino, Salvatore
Enriques, Federigo
Israel, Giorgio
Journals
Physis: Rivista Internazionale di Storia della Scienza
Revue d'Histoire des Mathématiques
Organon: International Review
Historia Mathematica
Theoria (0495-4548)
Notices of the American Mathematical Society
Publishers
Guaraldi
Bollati Boringhieri
Belforte
Springer Nature
Pensa Multimedia
Franco Angeli
Concepts
Mathematics
Intuitionistic mathematics
Proof
Logic
Geometry
Algebraic geometry
People
Enriques, Federigo
Hilbert, David
Castelnuovo, Guido
Archimedes
Poincaré, Jules Henri
Einstein, Albert
Time Periods
20th century
20th century, early
19th century
21st century
Early modern
Ancient
Places
Italy
Europe
France
North America
China
Japan
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