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The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights the insights themselves come from concrete special cases.

Paul Halmos

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Paul Halmos
Age: 90 †
Born: 1916
Born: March 3
Died: 2006
Died: October 2
Mathematician
Philosopher
Statistician
Buda Pest
Paul R. Halmos
Paul Richard Halmos
Small
Based
Insights
Bigs
General
Examples
Problem
Usually
Theories
Come
Theory
Concrete
Heart
Problems
Consists
Cases
Insight
Example
Profound
Special
Mathematics

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You are allowed to lie a little, but you must never mislead.
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The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.
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A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one.
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The best way to learn is to do the worst way to teach is to talk.
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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 to admit to the priesthood.
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A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better.
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The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.
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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 ask.
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Feller was an ebullient man, who would rather be wrong than undecided.
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Mathematics - this may surprise or shock some - is never deductive in creation.
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It saddens me that educated people don't even know that my subject exists.
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If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as we now have, and I don't see anything wrong with that.
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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?
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The only way to learn mathematics is to do mathematics.
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The author discusses valueless measures in pointless spaces.
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The library is the mathematician's laboratory.
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Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.
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I read once that the true mark of a pro - at anything - is that he understands, loves, and is good at even the drudgery of his profession.
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Applied mathematics will always need pure mathematics just as anteaters will always need ants.
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