"There is nothing more pleasant for man than the certainty of knowledge; whoever has once tasted of it is repelled by everything in which he perceives nothing but uncertainty. This is why the mathematicians who always deal with certain knowledge have been repelled by philosophy and other things, and have found nothing more pleasant than to spend their time with lines and letters." (Christian Wolff, 1741)
"In mathematics it [sophistry] had no place from the beginning: Mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly we find no parties among mathematicians, and hardly any disputes." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"Mathematicians have, in many cases, proved some things to be possible and others to be impossible, which, without demonstration, would not have been believed […] Mathematics afford many instances of impossibilities in the nature of things, which no man would have believed, if they had not been strictly demonstrated. Perhaps, if we were able to reason demonstratively in other subjects, to as great extent as in mathematics, we might find many things to be impossible, which we conclude, without hesitation, to be possible." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"Mathematical studies […] when combined, as they now generally are, with a taste for physical science, enlarge infinitely our views of the wisdom and power displayed in the universe. The very intimate connexion indeed, which, since the date of the Newtonian philosophy, has existed between the different branches of mathematical and physical knowledge, renders such a character as that of a mere mathematician a very rare and scarcely possible occurrence." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)
"Whoever limits his exertions to the gratification of others, whether by personal exhibition, as in the case of the actor and of the mimic, or by those kinds of literary composition which are calculated for no end but to please or to entertain, renders himself, in some measure, dependent on their caprices and humours. The diversity among men, in their judgments concerning the objects of taste, is incomparably greater than in their speculative conclusions; and accordingly, a mathematician will publish to the world a geometrical demonstration, or a philosopher, a process of abstract reasoning, with a confidence very different from what a poet would feel, in communicating one of his productions even to a friend." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)
"Mathematicians have, in many cases, proved some things to be possible and others to be impossible, which, without demonstration, would not have been believed […] Mathematics afford many instances of impossibilities in the nature of things, which no man would have believed, if they had not been strictly demonstrated. Perhaps, if we were able to reason demonstratively in other subjects, to as great extent as in mathematics, we might find many things to be impossible, which we conclude, without hesitation, to be possible." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)
"Mathematical studies […] when combined, as they now generally are, with a taste for physical science, enlarge infinitely our views of the wisdom and power displayed in the universe. The very intimate connexion indeed, which, since the date of the Newtonian philosophy, has existed between the different branches of mathematical and physical knowledge, renders such a character as that of a mere mathematician a very rare and scarcely possible occurrence." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)
"Whoever limits his exertions to the gratification of others, whether by personal exhibition, as in the case of the actor and of the mimic, or by those kinds of literary composition which are calculated for no end but to please or to entertain, renders himself, in some measure, dependent on their caprices and humours. The diversity among men, in their judgments concerning the objects of taste, is incomparably greater than in their speculative conclusions; and accordingly, a mathematician will publish to the world a geometrical demonstration, or a philosopher, a process of abstract reasoning, with a confidence very different from what a poet would feel, in communicating one of his productions even to a friend." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)
"So-called professional mathematicians have, in their reliance on the relative incapacity of the rest of mankind, acquired for themselves a reputation for profundity very similar to the reputation for sanctity possessed by theologians." (Georg C Lichtenberg, "Aphorisms", 1765-1799)
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