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It’s Been Said
A systematic treatment of all possible properties of limits was contained in a manuscript by Chevalley on category theory; the manuscript was unfortunately lost by some shipping company.
Before functors, people lived in caves.
The introduction of the digit 0 or the group concept was general nonsense, too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.
Do not be seduced by the lotus-eaters into infatuation with untethered abstraction.
Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.
As long as algebra and geometry traveled separate paths their advance was slow and their applications limited. But when these two sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection.
The advancement and perfection of mathematics is intimately connected with the prosperity of the state.
We [Kaplansky and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.
Profound study of nature is the most fertile source of mathematical discoveries.
Calculus is the outcome of a dramatic intellectual struggle which has lasted for twenty-five hundred years.