19th-century Mathematician Quotes

It would be rash to say that nothing remains for discovery or improvement even in the elements of mathematics; but it may be safely asserted that the ground has been so long and so thoroughly explored as to hold out little hope of profitable return for a casual adventurer.

Isaac Todhunter

My optimistic enthusiasm about the disinterested search for truth has been severely shaken..

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

The infinite time of the geologists is in the past; and most of their speculations regarding this subject seem to imply the absolute infinity of time, as if the human imagination was unable to grasp the period of time requisite for the formation of a few inches of sand or feet of mud, and its subsequent consolidation into rock.

Samuel Haughton

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

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

Federigo Enriques

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.

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

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

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

Mathematics is the codified body of all logical thought.

George David Birkhoff

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

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.

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.

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

Karl Weierstrass

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

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

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

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 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.

The recognition of the fact that infinite series fall into two classes (according to whether the limit is independent of the ordering of the terms or not) constitutes a turning-point in the conceptualization of the infinite in mathematics.

Bernhard Riemann

Figures may not lie, but statistics compiled unscientifically and analyzed incompetently are almost sure to be misleading, and when this condition is unnecessarily chronic the so-called statisticians may be called liars.

Edwin Bidwell Wilson

It is impossible to be a mathematician without being a poet in soul.

Sofia Kovalevskaya

The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.

L. E. J. Brouwer

The oxygen atom has the shape of a ring, and the sulphur atom, the shape of a clot.

Ferdinand von Lindemann