Mathematics - this may surprise or shock some - is never deductive in creation. — Paul Halmos Copy Share Image
A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant. — 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
