Richard Baxter (1615–1691) English Puritan church leader, poet, and hymn-writer
Reported in Josiah Hotchkiss Gilbert, Dictionary of Burning Words of Brilliant Writers (1895), p. 36.
“The very possibility of the science of mathematics seems an insoluble contradiction.”
— Henri Poincaré, book Science and Hypothesis
Source: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead <br class="br">Context: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6
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Henri Poincaré49
French mathematician, physicist, engineer, and philosopher … 1854–1912Related quotes
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Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: William Stanley Jevons (1887) The Principles of Science: : A Treatise on Logic and Scientific Method. p. 155
Immanuel Kant book Metaphysical Foundations of Natural Science
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Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist
As quoted in Gauss zum Gedächtniss (1856) by Wolfgang Sartorius von Waltershausen; Variants: Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
Mathematics is the queen of the sciences and number theory is the queen of mathematics. [Die Mathematik ist die Königin der Wissenschaften und die Zahlentheorie ist die Königin der Mathematik.]
“It is clear that economics, if it is to be a science at all, must be a mathematical science.”
William Stanley Jevons The Theory of Political Economy
Source: The Theory of Political Economy (1871), Chapter I, Introduction, p. 38.