Frases de Paul Halmos

“Feller era un hombre brillante. Prefería errar a permanecer indeciso.”

“No lo leas a secas. ¡Lucha! Hazte tus propias preguntas, busca tus propios ejemplos, descubre tus propias pruebas.”

“La biblioteca es el laboratorio del matemático.”

Extraído de "I want to be a Mathematician"

“La informática es importante, pero no para las matemáticas.”

“Una buena cantidad de ejemplos, tan grande como sea posible, es indispensable para la aprehensión profunda del concepto. Cuando quiero aprender algo nuevo, lo primero que hago es construir un ejemplo.”

“La matemática aplicada necesita de la matemática pura tanto como los hormigueros necesitan de las hormigas.”

“What does it take to be [a mathematician]?”

Paul Halmos: Frases en inglés

“Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared.”

Fuente: I Want to be a Mathematician: An Automathography (1985)
Contexto: What does it take to be [a mathematician]? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up.

“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? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?”

I Want to be a Mathematician: An Automathography (1985)
Contexto: 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. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does. Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared.

“The author discusses valueless measures in pointless spaces.”

I Want to be a Mathematician: An Automathography (1985)

“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.”

Proposal for a humorous first sentence to a review of a mathematical paper, rejected by editors.
I Want to be a Mathematician: An Automathography (1985)

“André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That's one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity.”

I Want to be a Mathematician: An Automathography (1985)

“I was too near it then to see how shallow it all was...”

I Want to be a Mathematician: An Automathography (1985)