Carl Friedrich Gauss

Bei Gegenstdnden mit denen ich mich noch nicht lange beschaftigt habe, bin ich gegen meine eigenen Ansichten, zumal wenn sie einem Laplace widersprechen, misstrauisch und nehme gern die von anderen entgegen. ["I am suspicious of my own …

Procreare jucundum, sed parturire molestum ["to beget is pleasant, but to give birth is painful"]

Pauca sed matura ["few, but ripe"]

A good building should not show its scaffolding when completed

That this subject [of ] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If for instance, +1, -1, √-1 had been called direct, …

In such apparent accidents which finally produce such a decisive influence on one s whole life, one is inclined to recognize the tools of a higher hand. The great enigma of life never becomes clear to us here below.

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.

All the measurements in the world do not balance one theorem by which the science of eternal truths is actually advanced.

Finally, a few days ago, it has been achieved - but not by my cumbersome search, rather through God’s good grace, I am tempted to say. As the lightning strikes the riddle was solved; I myself would be unable to point to a guiding thread …

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.

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.

But of all these principles ours is the most simple; by the others we should be led into the most complicated calculations.

The principle that the sum of the squares of the differences between the observed and computed quantities must be a minimum may, in the following manner, be considered independently of the calculus of probabilities.

it will no longer be possible to satisfy exactly all the observations by a purely elliptic motion

when the planet has been observed for a longer time

the motion would differ so little from motion exactly described, according to the laws of Kepler, in a perfect ellipse, that observations cannot show the difference.

The perturbations which the motions of planets suffer from the influence of other planets, are so small and so slow that they only become sensible after a long interval of time; within a shorter time

the nature of the subject never admits of assigning with absolute rigor the limits of error

Mathematics is the queen of the sciences.

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.

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.

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.

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

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