19th-century Mathematician Quotes

David Hilbert

Henri Poincaré

Alfred North Whitehead

Niels Henrik Abel

John Herschel

Bernhard Riemann

Georg Cantor

Mathematics deals mainly with realities and stern facts, and it arms those whose life work is beset with physical difficulties. Hence it appeals especially to the leaders of the common people, and it performs a fundamental function in the education of those who aim to excel in overcoming material difficulties.

George Abram Miller

The doctrines of pure geometry often, and in many questions, give a simple and natural way to penetrate to the origin of truths, to lay bare the mysterious chain which unites them, and to make them known individually, luminously and completely.

Mathematics, like a millstone, grinds everything placed under it and, just as you won't get wheat flour by grinding Deadly Nightshade, you won't get the truth from the false premises even if you cover the page with formulae...

The theory that has had the greatest development in recent times is without any doubt the theory of functions.

An experiment is a question which man asks of nature; one result of the observation is an answer which nature yields to man.

Ferdinand Gonseth

To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.

Hilda Phoebe Hudson

A mathematician who is not also something of a poet will never be a complete mathematician.

Karl Weierstrass

Mathematicians have never been in full agreement on their science, though it is said to be the science of self-evident verities — absolute, indisputable and definitive. They have always been in controversy over the developing aspects of mathematics, and they have always considered their own age to be a period of crisis.

The application will then, sometimes directly, but more frequently through a chain of intermediate stages, have significant bearing upon the content of human experience and furnish results which may be called true. Their truth then gives, retroactively, a sound basis for belief in the validity of the conclusions of mathematics.

Truth is an absolute notion that science, which is not concerned with any such permanency, had better leave alone.

Mathematics is the codified body of all logical thought.

George David Birkhoff

What is mathematics? It has so many different aspects that the difficulties in trying to give a definition are similar to those encountered in trying to determine whether some living organisms are animal or vegetable.

Louis J. Mordell

A mere catalogue of facts, however well arranged has never led to any important scientific generalisation.

As a professor of mathematics I am practically required by the ethics of the profession to be absent-minded, unmethodical, and inconsistent in many ways fatal to bibliographical excellence.

Louis Charles Karpinski

The purely formal sciences, logic and mathematics, deal with those relations which are, or can be, independent of the particular content or the substance of objects. To mathematics in particular fall those relations between objects which involve the concepts of magnitude, of measure and of number.

How can we doubt that of which every man is most certain even from his earliest infancy?

Federigo Enriques

Logic is invincible because in order to combat logic it is necessary to use logic.

Pierre Boutroux

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

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

Nikolai Ivanovich Lobachevsky

To have a good memory the first thing you have to do is to trust your memory.

Paul Sophus Epstein

We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.

The conclusion seems inescapable: that formal logic has to be taken over by the mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so.

The different branches of algebra and analysis which have been investigated are so numerous that it would be quite impossible to give an approximately exhaustive representation even only of the most important problems, within the limits of the time allowed to me. I, therefore, have confined myself to the minimum admissible number, namely one.

Heinrich Maschke

I am an old man now, and when I die and go to Heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. And about the former I am rather more optimistic.

Relativity without mathematics may be compared with "Painless Dentistry," or "Skiing without Falling," or "Reading without Tears."