Carl Friedrich Gauss Quotes
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It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.
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It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.
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Life stands before me like an eternal spring with new and brilliant clothes.
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I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.
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I believe you are more believing in the Bible than I. I am not, and, you are much happier than I. I must say that so often in earlier times when I saw people of the lower classes, simple manual laborers who could believe so rightly with their hearts, I always envied them, and now tell me how does one begin this?
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When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.
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If the object of all human investigation were but to produce in cognition a reflection of the world as it exists, of what value would be all its labor and pains, which could result only in vain repetition, in an imitation within the soul of that which exists without it?
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We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
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The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.
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There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.
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I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.
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To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.
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Mathematicians stand on each other's shoulders.
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If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.
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Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.
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God does arithmetic.
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To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.
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The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
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I have had my results for a long time: but I do not yet know how I am to arrive at them.
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Dark are the paths which a higher hand allows us to traverse here... let us hold fast to the faith that a finer, more sublime solution of the enigmas of earthly life will be present, will become part of us.
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I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.
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The study of Euler's works will remain the best school for the different fields of mathematics and nothing else can replace it.
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You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.
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Yes! The world would be nonsense, the whole creation an absurdity without immortality.