"A mathematical truth is neither simple nor complicated in itself, it is." (Émile Lemoine)
"Beauty in mathematics is seeing the truth without effort." (George Pólya)
"Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion." (André-Marie Ampère)
"Geometrical truths are in a way asymptotes to physical truths, that is to say, the latter approach the former indefinitely near without ever reaching them exactly." (Jean le Rond D’Alembert)
"[It used to be that] geometry must, like logic, rely on formal reasoning in order to rebut the quibblers. But the tables have turned. All reasoning concerned with what common sense knows in advance, serves only to conceal the truth and to weary the reader and is today disregarded." (Alexis C Clairaut)
"Math is the only place where truth and beauty mean the same thing." (Danica McKellar)
"Mathematics connect themselves on the one side with common life and the physical sciences; on the other side with philosophy, in regard to our notions of space and time, and in the questions which have arisen as to the universality and necessity of the truths of mathematics, and the foundation of our knowledge of them." (Arthur Cayley)
"Mathematics is a form of poetry which transcends poetry in that it proclaims the truth, a form of reasoning which transcends reasoning in that it wants to accomplish the truth it proclaims, a form of action, ritual behavior, which finds fulfillment in the act, but must proclaim and elaborate a poetic form of truth." (Salomon Bochner)
"Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional." (Charles P Steinmetz)
"Show all these fanatics a little geometry, and they learn it quite easily. But, strangely enough, their minds are not thereby rectified. They perceive the truths of geometry, but it does not teach them to weigh probabilities. Their minds have set hard. They will reason in a topsy-turvy wall all their lives, and I am sorry for it." (Voltaire)
"The character of necessity ascribed to the truths of mathematics and even the peculiar certainty attributed to them is an illusion." (John S Mill)
"There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation." (Charles Hermite) [in The Mathematical Intelligencer, Vol. 5, No. 4, 1983)
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