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

Nicholas Murray Butler Analytical Geometry Calculus Carl Friedrich Gauss Descartes Gauss Geometry Gottfried Leibniz Gottfried Wilhelm Leibniz Isaac Newton Leibniz Lobachevsky Mathematics Newton Philosophers Philosophy Reason René Descartes Riemann Science Scientists Supremacy Sylvester

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

Eric Temple Bell Clifford Copernicus Geometry Impact Lobachevskian Lobachevsky Math Mathematics Nicolaus Copernicus Nikolai Ivanovich Lobachevsky Nikolai Lobachevsky Science Thought William Clifford William Kingdon Clifford