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For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear.

— Leonhard Euler

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Source: introduction to De Curvis Elasticis, Additamentum I to his Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes 1744; translated on pg10-11, "Leonhard Euler's Elastic Curves", Oldfather et al 1933
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It would be a considerable invention indeed, that of a machine able to mimic speech, with its sounds and articulations. … I think it is not impossible.

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The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error.

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Madam, I have come from a country where people are hanged if they talk.

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Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.

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Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.

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To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.

Fundamentals of Teaching Mathematics at University Level (2000)

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Quote text and notes from Wikiquote: Leonhard Euler (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.