Algebraic Structures Quotes

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Math is a language that you use to describe statistics, but really it's about collecting information and putting it in an order that makes sense.

God made integers, all else is the work of man.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

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 beauty of string theory is that it is all about mathematics. For that, you don't need resources or labs. Just sit in your room and do the maths.

Among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other, and continues to fascinate me, is the structure hidden in mathematical things.

I have found a very great number of exceedingly beautiful theorems.

Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.

When I entered Harvard, my background was mostly combinatorics and algebra.

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

There's a beauty to math. Math is so simple. It's just one step after the next.

Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation.

God Bless Theoretical Mathematics And May It Never Be Of Use To Anyone

Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.

What is algebra exactly; is it those three-cornered things?