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“Night is a time of rigor, but also of mercy. There are truths which one can see only when it’s dark”
― Isaac Bashevis Singer, Teibele and her demon

“Objectivity cannot be equated with mental blankness; rather, objectivity resides in recognizing your preferences and then subjecting them to especially harsh scrutiny â€� and also in a willingness to revise or abandon your theories when the tests fail (as they usually do).”
― Stephen Jay Gould, The Lying Stones of Marrakech: Penultimate Reflections in Natural History

“Rigor alone is paralytic death, but imagination alone is insanity.”
― Gregory Bateson, Mind and Nature: A Necessary Unity

“If someone were to propose that the planets go around the sun because all planet matter has a kind of tendency for movement, a kind of motility, let us call it an ‘oomph,â€� this theory could explain a number of other phenomena as well. So this is a good theory, is it not? No. It is nowhere near as good as the proposition that the planets move around the sun under the influence of a central force which varies exactly inversely as the square of the distance from the center. The second theory is better because it is so specific; it is so obviously unlikely to be the result of chance. It is so definite that the barest error in the movement can show that it is wrong; but the planets could wobble all over the place, and, according to the first theory, you could say, ‘Well, that is the funny behavior of the ‘oomph.”
― Richard P. Feynman, The Meaning of It All: Thoughts of a Citizen-Scientist

“The test of real and vigorous thinking, the thinking which ascertains truths instead of dreaming dreams, is successful application to practice.”
― John Stuart Mill, Considerations on Representative Government

“A book isn’t rigorous if students aren’t reading it.”
― Penny Kittle, Book Love: Developing Depth, Stamina, and Passion in Adolescent Readers

“The Greek thinkers was no way of bridging the gap between the rectilinear and the curvilinear which would at the same time satisfy their strict demands of mathematical rigor and appeal to the clear evidence of sensory experience.”
― Carl B. Boyer, The History of the Calculus and Its Conceptual Development

“Such attempts lacked all semblance of mathematical rigor because of the lack at that time of satisfactory definitions of either the infinite of the infinitesimal. Arithmetic had not become sufficiently abstract and symbolic to free itself of spatial interpretations, for number was still interpreted metrically as a ratio of geometrical magnitudes.”
― Carl B. Boyer, The History of the Calculus and Its Conceptual Development

“Cournot protested that concepts exist in the understanding, independently of the definition which one gives to them. Simple ideas sometimes have complicated definitions, or even none. For this reason he felt that one should not subordinate the precision of such ideas as those of speed or the infinitely small to logical definition. This point of view is diametrically opposed to that which analysis since the time of Cournot has been toward ever-greater care in the formal logical elaboration of the subject. This trend, initiated in the first half of the nineteenth century and fostered largely by Cauchy, was in the second half of that century continued with notable success by Weierstrass.”
― Carl B. Boyer, The History of the Calculus and Its Conceptual Development

“Newton had considered the calculus as a scientific description of the generation of magnitudes, and Leibniz had viewed it as a metaphysical explanation of such generation. The formalism of the nineteenth century took from the calculus any such preconceptions, leaving only the bare symbolic relationships between abstract mathematical entities.”
― Carl B. Boyer, The History of the Calculus and Its Conceptual Development

“O tempo é um juiz rigoroso.”
― Victor Bello Accioly