Nikolai Ivanovich Lobachevsky Quotes

There is no royal road to geometry.

Euclid Alone Has Looked on Beauty Bare.

Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

I've always been passionate about geometry and the study of three-dimensional forms.

The shortest distance between two points is a straight line.

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.

The early study of Euclid made me a hater of geometry.

Plane geometry is sort of the key course where you learn about proving things and abstraction.

Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

Those ignorant of geometry shall not enter.

At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.

The ludicrous state of solid geometry made me pass over this branch.

Geometry draws the soul towards truth.

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

Where there is matter, there is geometry.

If Euclid's point, though incapable of being drawn by any human agency, has an imperishable value, my picture has its own for mankind to live.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

All things are literally better, lovelier, and more beloved for the imperfections which have been divinely appointed, that the law of human life may be effort, and the law of human judgment, mercy.

Geometry is the only science that it hath pleased God hitherto to bestow on mankind.

Extracurricular Parallel to none I am perpendicular

She's not perfect, but she tries so hard for me. And I thank God, that she isn't, cause how boring that would be.

At the age of eleven, I began Euclid, with my brother as my tutor. ... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.

Euclid for children is barbarous.

There are no sects in geometry.

Proofs of the Euclidean [parallel] postulate can be developed to such an extent that apparently a mere trifle remains. But a careful analysis shows that in this seeming trifle lies the crux of the matter; usually it contains either the proposition that is being proved or a postulate equivalent to it.