"How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!" (Archimedes, "On Spirals", cca. 225 BC)
“It is essential that the treatment [of geometry] should be rid of everything superfluous, for the superfluous is an obstacle to the acquisition of knowledge; it should select everything that embraces the subject and brings it to a focus, for this is of the highest service to science; it must have great regard both to clearness and to conciseness, for their opposites trouble our understanding; it must aim to generalize its theorems, for the division of knowledge into small elements renders it difficult of comprehension.” (Proclus, cca. 5th century)
"It is very difficult to write mathematics books today. If one does not take pains with the fine points of theorems, explanations, proofs and corollaries, then it won’t be a mathematics book; but if one does these things, then the reading of it will be extremely boring." (Johannes Kepler, Astronomia Nova, 1609)
“The Excellence of Modern Geometry is in nothing more evident, than in those full and adequate Solutions it gives to Problems; representing all possible Cases in one view, and in one general Theorem many times comprehending whole Sciences; which deduced at length into Propositions, and demonstrated after the manner of the Ancients, might well become the subjects of large Treatises: For whatsoever Theorem solves the most complicated Problem of the kind, does with a due Reduction reach all the subordinate Cases.” (Edmund Halley, “An Instance of the Excellence of Modern Algebra in the resolution of the problem of finding the foci of optic glasses universally”, Philosophical Transactions, 1694)
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