Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.
I enjoyed like nothing else working in pure math, discovering new formulas.
For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.
Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.
Cancel me not - for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain.
The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.
The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.
The study of mathematics is the indispensable basis for all intellectual and spiritual progress.
I have found a very great number of exceedingly beautiful theorems.
In my paper the fact the XY was not equal to YX was very disagreeable to me. I felt this was the only point of difficulty in the whole scheme...and I was not able to solve it.
We may as well cut out group theory. That is a subject that will never be of any use in physics.
Algebra is the metaphysics of arithmetic.
Galois read the geometry from cover to cover as easily as other boys read a pirate yarn.
You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too.
Mathematics is written for mathematicians.
The elements of justice are identical with those of algebra.
Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation.
What is algebra exactly; is it those three-cornered things?
