Zitate von Richard Hamming

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Richard Hamming

Geburtstag: 11. Februar 1915
Todesdatum: 7. Januar 1998

Richard Wesley Hamming war ein amerikanischer Mathematiker, dessen Arbeit großen Einfluss auf die Informatik und Telekommunikation hatte. Wikipedia

Zitate Richard Hamming

„The purpose of computing is insight, not numbers.“

—  Richard Hamming

Numerical Methods for Scientists and Engineers (1962) Preface

„Education is what, when, and why to do things. Training is how to do it. Either one without the other is not of much use.“

—  Richard Hamming

The Art of Doing Science and Engineering: Learning to Learn (1991)
Kontext: I am concerned with educating and not training you.... Education is what, when, and why to do things. Training is how to do it. Either one without the other is not of much use. You might think education should precede training, but the kind of educating I am trying to do must be based on your past experiences and technical knowledge.<!-- Preface

„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.“

—  Richard Hamming

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

„Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited. …The two topics“

—  Richard Hamming

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

„There is no unique, correct answer in most cases. It is a matter of taste“

—  Richard Hamming

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

„Great scientists tolerate ambiguity very well.“

—  Richard Hamming

You and Your Research (1986)
Kontext: 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.

„It is the same as an art course.“

—  Richard Hamming

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

„There is simply too much known to continue the older approach of giving detailed results.“

—  Richard Hamming

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

„No vision, not much of a future.“

—  Richard Hamming

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

„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“

—  Richard Hamming

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

„Science is supposed to be cumulative, not almost endless duplication of the same kind of things.“

—  Richard Hamming

One Man's View of Computer Science (1969)
Kontext: 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.

„Until we understand languages of communication involving humans as they are then it is unlikely many of our software problems will vanish.“

—  Richard Hamming

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

„The newer aspects of many fields start with the admission of uncertainty.“

—  Richard Hamming

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

„Euclid's postulates came from the Pythagorean theorem, not the other way around.“

—  Richard Hamming

The Unreasonable Effectiveness of Mathematics (1980)
Kontext: 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.

„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“

—  Richard Hamming

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

„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.“

—  Richard Hamming

You and Your Research (1986)
Kontext: 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.

„The assumptions and definitions of mathematics and science come from our intuition“

—  Richard Hamming

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

„When a theory is sufficiently general to cover many fields of application, it acquires some "truth" from each of them.“

—  Richard Hamming

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

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