19th-century Mathematician Quotes
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.
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.
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.
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.