Mathematics is not a deductive science, that's a cliché ... What you do is trial and error, experimentation, guesswork. — Paul Halmos Copy Share Image
It saddens me that educated people don't even know that my subject exists. — Paul Halmos Copy Share Image
Mathematics - this may surprise or shock some - is never deductive in creation. — Paul Halmos Copy Share Image
Applied mathematics will always need pure mathematics just as anteaters will always need ants. — Paul Halmos Copy Share Image
The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to… — 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… — 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… — Paul Halmos Copy Share Image
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… — Paul Halmos Copy Share Image
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 Image
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more… — 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… — Paul Halmos Copy Share Image
A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better. — 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… — Paul Halmos Copy Share Image
Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he… — 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… — Paul Halmos Copy Share Image
If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as… — Paul Halmos Copy Share Image
... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us… — Paul Halmos Copy Share Image
To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize… — Paul Halmos Copy Share Image
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to… — Paul Halmos Copy Share Image
The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound… — 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
