19th-century Mathematician Quotes

[Science] advances by leaps; and the impulse for each leap is either some new observational resource, or some novel way of reasoning about the observations. Such novel way of reasoning might, perhaps, be considered as a new observation means, since it draws attention to reactions between facts which would previously have been passed by unperceived.

Charles Sanders Peirce

In repeating an argument that I have learned, I could readily have discovered it myself: or rather, even if this is an illusion, if I were not clever enough to have created it myself, I rediscover it myself, to the extent that I repeat it.

Henri Poincaré

My method to overcome a difficulty is to go round it.

Each atom of the Holy Spirit is intelligent, and like all other matter has solidity, form, and size, and occupies space.

The more progress physical sciences makes, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.

Adolphe Quetelet

To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship...

Srinivasa Ramanujan

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

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

Perhaps I may without immodesty lay claim to the appellation of Mathematical Adam, as I believe that I have given more names (passed into general circulation) of the creatures of the mathematical reason than all the other mathematicians of the age combined.

James Joseph Sylvester

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 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.

As far as I can see, all a priori statements in physics have their origin in symmetry.

Logic is the olive branch from the old to the young, the wand which in the hands of youth has the magic property of creating science.

Alfred North Whitehead

By slow degrees, the minds of men were cut adrift from their old scholastic moorings and sent forth on the wide sea of scientific inquiry, to discover new islands and continents of truth.

The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to geometry, mechanics, physics and even statistics involve these processes directly and indirectly.

Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.

Antoine Augustin Cournot

Mathematics must take its motivation from concrete specific substance and aim again at some layer of "reality." The flight into abstraction must be something more than a mere escape; start from the ground and reentry are both indispensable, even if the same pilot cannot handle all phases of the trajectory.

Richard Courant

Mathematics is the science of the connection of magnitudes. Magnitude is anything that can be put equal or unequal to another thing. Two things are equal when in every assertion each may be replaced by the other.

Hermann Grassmann

'My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?'

W. W. Rouse Ball

No number of facts or aphorisms learned by heart makes a man a thinker, or does him much intellectual service.

Joshua Girling Fitch

A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range.

That a formal science like algebra, the creation of our abstract thought, should thus, in a sense, dictate the laws of its own being, is very remarkable. It has required the experience of centuries for us to realize the full force of this appeal.

George Ballard Mathews

Man is what he is, because a spiritual element has entered into, and taken possession of, animal consciousness. This spiritual element is not, according to Christian teaching, divine: but it is capable of entering into relations with God. It can perceive Him: in thought, it can reason as to His nature and actions: in will and feeling, it can serve and love Him, or disobey and fear Him. Such activity shows itself in what we call the working of conscience.

The problems of statistical physics are of the greatest in our time, since they lead to a revolutionary change in our whole conception of the universe.

Richard von Mises

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