...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case. — Paul Halmos Copy Share Image
Applied mathematics will always need pure mathematics just as anteaters will always need ants. — Paul Halmos Copy Share
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
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
...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
“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
The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites. — Paul Halmos Copy Share
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
Mathematics is not a deductive science, that's a cliché ... What you do is trial and error, experimentation, guesswork. — Paul Halmos Copy Share
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
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method, ... — Paul Halmos Copy Share
... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty… — Paul Halmos Copy Share
What's the best part of being a mathematician? I'm not a religious man, but it's almost like being in touch with God when you're… — Paul Halmos Copy Share
