34 quotes
I have had my results for a long time: but I do not yet know how I am to arrive at them.
The Mind and the Eye (1954)
All the measurements in the world do not balance one theorem by which the science of eternal truths is actually advanced.
The study of Euler's works will remain the best school for the different fields of mathematics and nothing else can replace it.
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.
But in our opinion truths of this kind should be drawn from notions rather than from notations.
About the proof of Wilson's theorem. Disquisitiones Arithmeticae (1801)
The way I have taken seems not to lead to the goal, but much rather to make the truth of geometry doubtful.
But of all these principles ours is the most simple; by the others we should be led into the most complicated calculations.
Theoria motus corporum coelestium in sectionibus conicis solem ambientum (1809)
The centre and the radius of this auxiliary sphere are here quite arbitrary.
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.
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.
Gauss-Schumacher Briefwechsel (1862)
You say that faith is a gift; this is perhaps the most correct thing that can be said about it.
Carl Friedrich Gauss: Titan of Science (1955)
If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.
The World of Mathematics (1956)
Mathematics is the queen of the sciences.
Gauss zum Gedächtniss (1856)
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.
Yes! The world would be nonsense, the whole creation an absurdity without immortality.
Carl Friedrich Gauss: Titan of Science (1955)
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.
Theoria motus corporum coelestium in sectionibus conicis solem ambientum (1809)
Procreare jucundum, sed parturire molestum ["to beget is pleasant, but to give birth is painful"]
Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.
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?
Carl Friedrich Gauss: Titan of Science (1955)