"It is not possible to find in all geometry more difficult and more intricate questions or more simple and lucid explanations [than those given by Archimedes]. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearance, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required." (Plutarch, cca. 1st century)
"[...] it is my opinion that this problem is what led the ancients to attempt the squaring of the circle. For if a parallelogram can be found equal to any rectilinear figure, it is worth inquiring whether it is not possible to prove that a rectilinear figure is equal to a circular area. Indeed Archimedes proved that a circle is equal to a right-angled triangle when its radius is equal to one of the sides about the right angle and its perimeter is equal to the base. But of this elsewhere." (Proclus Lycaeus, cca 5th century)
"Euclid, Archimedes, and Apollonius brought geometry to as high a state of perfection as it perhaps could be brought without first introducing some more general and more powerful method than the old method of exhaustion. A briefer symbolism, a Cartesian geometry, an infinitesimal calculus, were needed. The Greek mind was not adapted to the invention of general methods. Instead of a climb to still loftier heights we observe, therefore, on the part of later Greek geometers, a descent during which they paused here and there to look around for details which had been passed by in the hasty ascent." (Florian Cajori, "A History of Mathematics", 1893)
"Wallis was in sympathy with Greek mathematics and astronomy, editing parts of the works of Archimedes, Eutocius, Ptolemy, and Aristarchus; but at the same time he recognized the fact that the analytic method was to replace the synthetic, as when he defined a conic as a curve of the second degree instead of as a section of a cone, and treated it by the aid of coordinates." (David E Smith, "History of Mathematics", 1923)
"Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub." (Richard J Trudeau, "Dots and Lines", 1976)
"The absolute scholar is in fact a rather uncanny being. He is instinct with Nietzsche's finding that to be interested in something, to be totally interested in it, is a libidinal thrust more powerful than love or hatred, more tenacious than faith or friendship - not infrequently, indeed, more compelling than personal life itself. Archimedes does not flee from his killers, he does not even turn his head to acknowledge their rush into his garden when he is immersed in the algebra of conic sections." (George Steiner, "The Cleric of Treason", 1980)
"The mathematician's circle, with its infinitely thin circumference and a radius that remains constant to infinitely many decimal places, cannot take physical form. If you draw it in sand, as Archimedes did, its boundary is too thick and its radius too variable." (Ian Stewart, "Letters to a Young Mathematician", 2006)
"Once a mathematical result is proven to the satisfaction of the discipline, it doesn’t need to be re-evaluated in the light of new evidence or refuted, unless it contains a mistake. If it was true for Archimedes, then it is true today." (Peter Rowlett, "The Unplanned Impact of Mathematics", Nature, 2011)
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