Frases de Richard Hamming

Fuente: The American Mathematical Monthly, 87 (2), febrero de 1980, pág. 81-90

Fuente: «Al dar su discurso de recepción del premio Nobel de Física en 1956, Brattain, casi con lágrimas en los ojos, dijo: "Conozco ese efecto del Premio Nobel y yo no voy a dejar que me afecte, yo voy a seguir siendo el viejo Walter Brattain". Bueno, me dije a mi mismo, "Eso está bien". Pero en un par de semanas vi que le estaba afectando. Ahora sólo podía trabajar en grandes problemas. Cuando eres famoso es difícil trabajar en los problemas pequeños».

Existen tres unidades de medida en honor de estos tres científicos.
Fuente: Richard Hamming You and Your Research, Bell Communications Research Colloquium Seminar, 7 de marzo de 1986.

The Art of Doing Science and Engineering: Learning to Learn (1991), p. 5

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: When you yourself are responsible for some new application in mathematics... then your reputation... and possibly even human lives, may depend on the results you predict. It is then the need for mathematical rigor will become painfully obvious to you.... Mathematical rigor is the clarification of the reasoning used in mathematics.... a closer examination of the numerous "hidden assumptions" is made.... Over the years there has been a gradually rising standard of rigor; proofs that satisfied the best mathematicians of one generation have been found inadequate by the next generation. Rigor is not a yes-no property of a proof... it is a vague standard of careful treatment that is currently acceptable to a particular group.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: Increasingly... the application of mathematics to the real world involves discrete mathematics... the nature of the discrete is often most clearly revealed through the continuous models of both calculus and probability. Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited.... The two topics, discrete and continuous mathematics, are both ill served by being rigidly separated.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: There is no unique, correct answer in most cases. It is a matter of taste, depending on the circumstances... and the particular age you live in.... Gradually, you will develop your own taste, and along the way you may occasionally recognize that your taste may be the best one! It is the same as an art course.

You and Your Research (1986)
Contexto: Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: There is no unique, correct answer in most cases. It is a matter of taste, depending on the circumstances... and the particular age you live in.... Gradually, you will develop your own taste, and along the way you may occasionally recognize that your taste may be the best one! It is the same as an art course.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: We intend to teach the doing of mathematics. The applications of these methods produce the results of mathematics (which usually is only what is taught)... There is also a deliberate policy to force you to think abstractly... it is only through abstraction that any reasonable amount of useful mathematics can be covered. There is simply too much known to continue the older approach of giving detailed results.

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contexto: In a lifetime of many, many independent choices, small and large, a career with a vision will get you a distance proportional to n, while no vision will get you only the distance √n.... the accuracy of the vision matters less than you suppose, getting anywhere is better than drifting, there are potentially many paths to greatness for you... No vision, not much of a future.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: It is easy to measure your mastery of the results via a conventional examination; it is less easy to measure your mastery of doing mathematics, of creating new (to you) results, and of your ability to surmount the almost infinite details to see the general situation.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

One Man's View of Computer Science (1969)
Contexto: Indeed, one of my major complaints about the computer field is that whereas Newton could say, "If I have seen a little farther than others, it is because I have stood on the shoulders of giants," I am forced to say, "Today we stand on each other's feet." Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way. Science is supposed to be cumulative, not almost endless duplication of the same kind of things.

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contexto: The fundamentals of language are not understood to this day.... Until we understand languages of communication involving humans as they are then it is unlikely many of our software problems will vanish.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of "noise" is officially admitted. The newer aspects of many fields start with the admission of uncertainty.

The Unreasonable Effectiveness of Mathematics (1980)
Contexto: The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: In the face of almost infinite useful knowledge, we have adopted the strategy of "information regeneration rather than information retrieval."... most importantly, you should be able to generate the result you need even if no one has ever done it before you—you will not be dependent on the past to have done everything you will ever need in mathematics.

You and Your Research (1986)
Contexto: I noticed the following facts about people who work with the door open or the door closed. I notice that if you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But 10 years later somehow you don't quite know what problems are worth working on; all the hard work you do is sort of tangential in importance. He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: When a theory is sufficiently general to cover many fields of application, it acquires some "truth" from each of them. Thus... a positive value for generalization in mathematics.

You and Your Research (1986)
Contexto: Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contexto: When you take a course in Euclidean geometry is not the teacher putting a... learning program into you?... You enter the course and cannot do problems; the teacher puts into you a program and at the end of the course you can solve such problems.... Are you sure you are not merely "programmed" in life by what by chance events happens to you?

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contexto: The more complex the designed system the more field maintenance must be central to the final design. Only when field maintenance is part of the original design can it be safely controlled... This applies to both mechanical things and to human organizations.

The Unreasonable Effectiveness of Mathematics (1980)
Contexto: The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

The Art of Doing Science and Engineering: Learning to Learn (1991)
Contexto: The people at the bottom do not have the larger, global view, but at the top they do not have the local view of all the details, many of which can often be very important, so either extreme gets poor results.

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: This text is organized in the "spiral" for learning. A topic... is returned to again and again, each time higher up in the spiral. The first time around you may not be completely sure of what is going on, but on the repeated returns to the topic it should gradually become clear. This is necessary when the ideas are not simple but require a depth of understanding...

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Contexto: Mathematics, being very different from the natural languages, has its corresponding patterns of thought. Learning these patterns is much more important than any particular result... They are learned by the constant use of the language and cannot be taught in any other fashion.

Preface
The Art of Doing Science and Engineering: Learning to Learn (1991)

storage
The Art of Doing Science and Engineering: Learning to Learn (1991)

The Art of Doing Science and Engineering: Learning to Learn (1991)