Read Carl Friedrich Gauss biography

But in our opinion truths of this kind should be drawn from notions rather than from notations.

Carl Friedrich Gauss— About the proof of Wilson's theorem.

The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it. But when a person of that sex, that, because of our mores and our prejudices, has to encounter infinitely more obstacles and difficulties than men in familiarizing herself with these thorny research problems, nevertheless succeeds in surmounting these obstacles and penetrating their most obscure parts, she must without doubt have the noblest courage, quite extraordinary talents and superior genius.

Carl Friedrich Gauss— Letter to Sophie Germain (30 April 1807) ([...]

Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems.

Carl Friedrich Gauss— "Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in

Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.

Carl Friedrich Gauss— "Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in

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 ½ proof = 0, and it is demanded for proof that every doubt becomes impossible.

Carl Friedrich Gauss— In a letter to Heinrich Wilhelm Matthias Olbers (14 May 1826), defending Chevalier d'Angos against presumption of guilt (by Johann Franz Encke and others), of having falsely claimed to have discovered a comet in 1784; as quoted in

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.

Carl Friedrich Gauss— Letter to Friedrich Wilhelm Bessel (1830)

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.

Carl Friedrich Gauss— Letter to Farkas Bolyai, on his son János Bolyai's 1832 publishings on non-Euclidean geometry.

Mathematics is the queen of the sciences.

Carl Friedrich Gauss— As quoted in

The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases confined within certain limits, the probability of errors exceeding those limits ought always to be zero, while our formula always gives some value. However, this defect, which every analytical function must, from its nature, labor under, is of no importance in practice, because the value of our function decreases so rapidly... that it can safely be considered as vanishing. Besides, the nature of the subject never admits of assigning with absolute rigor the limits of error.

Carl Friedrich Gauss—

Ask her to wait a moment — I am almost done.

Carl Friedrich Gauss— When told, while working, that his wife was dying, as attributed in

I have had my results for a long time: but I do not yet know how I am to arrive at them.

Carl Friedrich Gauss—

If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

Carl Friedrich Gauss—

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.

Carl Friedrich Gauss— A reply to Olbers' 1816 attempt to entice him to work on Fermat's Theorem. As quoted in

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.

Carl Friedrich Gauss— As quoted in

I believe you are more believing in the Bible than I. I am not, and, you are much happier than I.

Carl Friedrich Gauss— A reply to Rudolf Wagner's on his religious views as quoted in

A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

Carl Friedrich Gauss— On higher arithmetic.

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. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

Carl Friedrich Gauss— As quoted in

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.

Carl Friedrich Gauss— As quoted in

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. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. 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.

Carl Friedrich Gauss—