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Paul Halmos Quotes

A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better Picture Quote #1
A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant Picture Quote #1
Mathematics is not a deductive science, that’s a cliché... What you do is trial and error, experimentation, guesswork Picture Quote #1
You are allowed to lie a little, but you must never mislead Picture Quote #1
Feller was an ebullient man, who would rather be wrong than undecided Picture Quote #1
The computer is important, but not to mathematics Picture Quote #1
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The only way to learn mathematics is to do mathematics Picture Quote #1
Applied mathematics will always need pure mathematics just as anteaters will always need ants Picture Quote #1
The author discusses valueless measures in pointless spaces Picture Quote #1
It saddens me that educated people don’t even know that my subject exists Picture Quote #1
The heart of mathematics is its problems Picture Quote #1
Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? Where does the proof use the hypothesis? Picture Quote #1
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The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites Picture Quote #1
The best way to learn is to do; the worst way to teach is to talk Picture Quote #1
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 Picture Quote #1
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 Picture Quote #1
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts Picture Quote #1
... 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 Picture Quote #1
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To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess Picture Quote #1
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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.  (Paul Halmos Quotes) A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant  (Paul Halmos Quotes) Mathematics is not a deductive science, that’s a cliché... What you do is trial and error, experimentation, guesswork  (Paul Halmos Quotes) You are allowed to lie a little, but you must never mislead  (Paul Halmos Quotes) Feller was an ebullient man, who would rather be wrong than undecided  (Paul Halmos Quotes) The computer is important, but not to mathematics  (Paul Halmos Quotes) The only way to learn mathematics is to do mathematics  (Paul Halmos Quotes) Applied mathematics will always need pure mathematics just as anteaters will always need ants  (Paul Halmos Quotes) The author discusses valueless measures in pointless spaces  (Paul Halmos Quotes) It saddens me that educated people don’t even know that my subject exists  (Paul Halmos Quotes) The heart of mathematics is its problems  (Paul Halmos Quotes) Don’t just read it; fight it! Ask your own questions, 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 Quotes) The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites  (Paul Halmos Quotes) The best way to learn is to do; the worst way to teach is to talk  (Paul Halmos Quotes) 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 Quotes) 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  (Paul Halmos Quotes) It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts  (Paul Halmos Quotes) ... 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 Quotes) To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess  (Paul Halmos Quotes)