19th-century Mathematician Quotes

The highest reach of human science is the scientific recognition of human ignorance...

William Rowan Hamilton

One thing at least they have not forgotten, that geometry is nothing if it be not rigorous, and that the whole educational value of the study is lost, if strictness of demonstration be trifled with. The methods of Euclid are, by almost universal consent, unexceptionable in point of rigor. Opening Address by the President, Section A

Henry John Stephen Smith

With the exception of the geometric series, there does not exist in all of mathematics a single infinite series whose sum has been determined rigorously.

Niels Henrik Abel

If "poetry is unfallen speech," then geometry is undebased thought, and if "architecture is frozen music" then it is also the crystallized science of form.

David Eugene Smith

Scientific theory and its application to the growing needs of mankind advance hand in hand.

Cargill Gilston Knott

To [the scientific man] the discovery of a new law of nature, or even of a new experimental fact, or the invention of a novel mathematical method, no matter who has been the first to reach it, is an event of an order altogether different from, and higher than, those which are so profusely chronicled in the newspapers.

Peter Guthrie Tait

The general phenomenon [total eclipse] is perhaps the most awfully grand which man can witness.

George Biddell Airy

As a boy of six I could understand the proof of a mathematical theorem more readily than that meat had to be cut with one's knife, not one's fork.

Ferdinand Eisenstein

Nature has raised the curtain of futurity, and displayed before him [Man] the succession of her decrees, so far as they effect the physical universe, for countless ages to come; and the revelations of which she has made him the instrument, are supported and verified by a never-ceasing train of predictions fulfilled.

Dionysius Lardner

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.

Julian Coolidge

The great problem of the day is, how to subject all physical phenomena to dynamical laws. With all the experimental devices, and all the mathematical appliances of this generation, the human mind has been baffled in its attempts to construct a universal science of physics.

Joseph Lovering

I am almost inclined to coin a word and call the appearance fluorescence, from fluor-spar, as the analogous term opalescence is derived from the name of a mineral.

Sir George Stokes, 1st Baronet

What is familiar to professional scientists highly needs to be placed in the public domain.

Jacques Babinet

A mathematical science is any body of propositions which is capable of an abstract formulation and arrangement in such a way that every proposition of the set after a certain one is a formal logical consequence of some or all the preceding propositions. Mathematics consists of all such mathematical sciences.

John Wesley Young

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.

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

Pierre Boutroux

All good teaching must flow from copious sources of knowledge. The shallow fountain cannot emit a vigorous stream.

Charles Davies (professor)

He who discovers a fact or makes known a new law or adds a novel beauty to truth in any way makes every one of us his debtor. How beautiful upon the highway are the feet of him who comes bringing in his hands the gift of a new truth to mankind.

Robert Daniel Carmichael

If the sun were created expressly to light and heat the earth, what a waste of energy!

Forest Ray Moulton