Citas de Paul Halmos

• La única manera de aprender matemáticas es haciendo matemáticas.

  Paul Halmos

  Learning, Math, Way

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• La mejor manera de aprender es hacer; la peor manera de enseñar es hablar.

  Paul Halmos

  Way, Mathematics, Worst

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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?

  Paul Halmos

  Fighting, Example, Doe

  "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.

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• El corazón de las matemáticas está formado por ejemplos y problemas concretos. Las grandes teorías generales suelen ser reflexiones a posteriori basadas en pequeñas pero profundas ideas; las propias ideas proceden de casos especiales concretos.

  Paul Halmos

  Heart, Profound, Special

  Paul Richard Halmos (1983). “Selecta: expository writing”, Springer Verlag

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• Una buena pila de ejemplos, lo más grande posible, es indispensable para comprender a fondo cualquier concepto,y cuando quiero aprender algo nuevo, mi primera tarea es construir una.

  Paul Halmos

  Education, Jobs, Math

  28 Copiar cita

• 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

  Educación, Conocimiento, Matemáticas

  P.R. Halmos, Paul Richard Halmos (1982). “A Hilbert Space Problem Book”, p.7, Springer Science & Business Media

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• 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

  Teacher, Teaching, Knowledge

  Paul Richard Halmos (1983). “Selecta: expository writing”, Springer Verlag

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• The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.

  Paul Halmos

  Reading, Doe, Beginners

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• A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.

  Paul Halmos

  Teacher, Teaching, Challenges

  31 Copiar cita

• [Las matemáticas son seguridad. Certeza. Verdad. Belleza. Perspicacia. Estructura. Arquitectura. Veo las matemáticas, la parte del conocimiento humano que yo llamo matemáticas, como una sola cosa, una cosa grande y gloriosa. Ya se trate de topología diferencial, de análisis funcional o de álgebra homológica, todo es una sola cosa. ... Están íntimamente interconectadas, son todas facetas de la misma cosa. Esa interconexión, esa arquitectura, es verdad segura y es belleza. Eso son para mí las matemáticas.

  Paul Halmos

  Knowledge, Science, Analysis

  "Celebrating 50 Years of Mathematics".

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• Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

  Paul Halmos

  Math, Science, Errors

  "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.

  28 Copiar cita

• Applied mathematics will always need pure mathematics just as anteaters will always need ants.

  Paul Halmos

  Ants, Needs, Mathematics

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• The heart of mathematics is its problems.

  Paul Halmos

  Heart, Problem, Mathematics

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• ...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

  Science, Essence, Special

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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.

  Paul Halmos

  Mark, Profession, Drudgery

  "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.

  6 Copiar cita

• You are allowed to lie a little, but you must never mislead.

  Paul Halmos

  Lying, Littles, Mislead

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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.

  Paul Halmos

  Math, Luck, Taste

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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.

  Paul Halmos

  Math, Answers, Students

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• Feller was an ebullient man, who would rather be wrong than undecided.

  Paul Halmos

  Men, Undecided

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• It saddens me that educated people don't even know that my subject exists.

  Paul Halmos

  People, Mathematics, Educated

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• 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 thinking about mathematics. God is keeping secrets from us, and it's fun to try to learn some of the secrets.

  Paul Halmos

  God, Religious, Fun

  Paul Richard Halmos, John Ewing, F.W. Gehring (1991). “PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics”, p.21, Springer Science & Business Media

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• 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 Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."

  Paul Halmos

  Math, Class, Numbers

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• The library is the mathematician's laboratory.

  Paul Halmos

  Library, Mathematician, Laboratory

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• The most spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.

  Paul Halmos

  Memories, Science, Thinking

  "PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics".

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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.

  Paul Halmos

  Truth, Learning, Math

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