Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis? — Paul Halmos Copy Share Image
Applied mathematics will always need pure mathematics just as anteaters will always need ants. — Paul Halmos Copy Share Image
When a student comes and asks, "Should I become a mathematician?" the answer should be no. If you have to ask, you shouldn't even… — Paul Halmos Copy Share Image
Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is… — Paul Halmos Copy Share Image
...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept… — Paul Halmos Copy Share Image
“In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some and here… — Paul Halmos Copy Share Image
It saddens me that educated people don't even know that my subject exists. — Paul Halmos Copy Share Image
The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites. — Paul Halmos Copy Share Image
The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom… — Paul Halmos Copy Share Image
Mathematics is not a deductive science, that's a cliché ... What you do is trial and error, experimentation, guesswork. — Paul Halmos Copy Share Image
I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by… — Paul Halmos Copy Share Image
Feller was an ebullient man, who would rather be wrong than undecided. — Paul Halmos Copy Share Image
