Lobachevsky Quotes & Sayings

In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain. — Nikolai Lobachevsky

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought. — Eric Temple Bell

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. — Nikolai Lobachevsky

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world. — Clifford A. Pickover

I am never forget the day I first meet the great Lobachevsky.
In one word he told me secret of success in mathematics:
Plagiarize!
Plagiarize!
Let no one else's work evade your eyes!
Remember why the good Lord made your eyes!
So don't shade your eyes,
But plagiarize, plagiarize, plagiarize -
Only be sure always to call it please 'research'.
[Lobachevsky] — Tom Lehrer

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason. — Nicholas Murray Butler

Many statements about God are confidently made by theologians on grounds that today at least sound specious. Thomas Aquinas claimed to prove that God cannot make another God, or commit suicide, or make a man without a soul, or even make a triangle whose interior angles do not equal 180 degrees. But Bolyai and Lobachevsky were able to accomplish this last feat (on a curved surface) in the nineteenth century, and they were not even approximately gods. — Carl Sagan