Math Quotes

A bouquet of quotations:

  1. Galois theory is a showpiece of mathematical unification, bringing together several different branches of the subject and creating a powerful machine for the study of problems of considerable historical and mathematical importance.

    Ian Stewart, Galois theory

  2. Galois at seventeen was making discoveries of epochal significance in the theory of equations, discoveries whose consequences are not yet exhausted after more than a century.

    E. T. Bell

  3. It is a tribute to the genius of Galois that he recognized that those subgroups for which the left and the right cosets coincide are distinguished ones. Very often in mathematics the crucial problem is to recognize and to discover what are the relevant concepts; once this is accomplished the job may be more than half done.

    I. N. Herstein

  4. For Artin, to be a mathematician meant to participate in a great common effort, to continue work begun thousands of years ago, to shed new light on old discoveries, to seek new ways to prepare the developments of the future. Whatever standards we use, he was a great mathematician.

    R. Brauer

  5. Abel has left mathematicians enough to keep them busy for five hundred years.

    C. Hermite

  6. A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept. I make it my first job to build one.

    P. R. Halmos

  7. The only way to learn mathematics is to do mathematics.

    P. R. Halmos

  8. A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.... The mathematician's patterns, like the painter's or poet's, must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test; there is no permanent place in the world for ugly mathematics.

    G. H. Hardy

  9. My mind rebels at stagnation. Give me problems, give me work, give me the most obstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere.

    Sherlock Holmes, The sign of the four

  10. Don't just read it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? Where does the proof use hypothesis?

    P. R. Halmos

  11. The secret in science is to ask the right questions, and it is the choice of problem more than anything else that marks the man of genius in the scientific world.

    Sir Henry Tizard

  12. If there is one central idea which is common to all aspects of modern algebra it is the notion of homomorphism.

    I. N. Herstein

  13. The value of a principle is the number of things it will explain.

    R. W. Emerson

  14. It is a great nuisance that knowledge can only be acquired by hard work.

    W. Somerset Maugham

  15. A mathematician is a machine for turning coffee into theorems.

    Paul Erdos

  16. When things go wrong as they sometimes will,
    When the road you are trudging seems all up hill,
    ...When care is pressing you down a bit,
    Rest, if you must -- but don't you quit.
    ... Often the goal is nearer than
    It seems to a faint and faltering man,
    Often the struggler has given up
    When he might have captured the victor's cap.


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