The object of mathematics is the honor of the human spirit.
– Carl Jacobi
I keep the subject constantly before me and wait till the first dawnings open little by little into the full light.
– Sir Isaac Newton
Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long as the relations don't change. Matter is not important, only form interests them.
– Henri Poincaré
Mathematics is not a deductive science � that's a clich�. 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, guess-work.
– Paul Richard Halmos
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
– Henri Poincaré
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