The desire to understand the world and the desire to reform it are the two great engines of progress.
Marriage and Morals.
Loci: Convergence
Mathematical Quotations
Our library of quotations is organized alphabetically by surname of the author.
Halmos, Paul R.
[T]he student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."
Halmos, Paul R.
Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Hamilton, Sir William Rowan (1805-1865)
On earth there is nothing great but man; in man there is nothing great but mind.
Hamilton, Sir William Rowan (1805-1865)
I regard it as an inelegance, or imperfection, in quaternions, or rather in the state to which it has been hitherto unfolded, whenever it becomes or seems to become necessary to have recourse to x, y, z, etc.
Hamilton, [Sir] William Rowan (1805-1865)
Who would not rather have the fame of Archimedes than that of his conqueror Marcellus?
Hamming, Richard W.
Mathematics is an interesting intellectual sport but it should not be allowed to stand in the way of obtaining sensible information about physical processes.
Hamming, Richard W.
Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.
Hardy, Thomas
[H]e seemed to approach the grave as an hyperbolic curve approaches a line, less directly as he got nearer, till it was doubtful if he would ever reach it at all.
Hardy, Godfrey H. (1877 - 1947)
The fact is that there are few more "popular" subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.
Hardy, Godfrey H. (1877 - 1947)
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.