"... there are two kinds of generalization, one facile and one valuable. One is generalization by dilution, the other is generalization by concentration. Dilution means boiling the meat in a large quantity of water into a thin soup; concentration means condensing a large amount of nutritive material into an essence. The unification of concepts which in the usual view appear to lie far removed from each other is concentration. Thus, for example, group theory has concentrated ideas which formerly where found scattered in algebra, number theory, geometry and analysis and which appeared to be very different. Examples of generalization by dilution would be still easier to quote, but this would be at the risk of offending sensibilities."
Tomado del prefacio a la primera edición del Problems & Theorems in Analysis de G. Pólya y G. Szegö (las negritas son mías).
Friedrich Hirzebruch (1927-2012)
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