Richard Hamming: Use

Richard Hamming was American mathematician and information theorist. Explore interesting quotes on use.
Richard Hamming: 180 quotes1 like

“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)
Context: 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

“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)
Context: 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.

“They are learned by the constant use of the language and cannot be taught in any other fashion.”

Richard Hamming

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

“Much of present science rests on engineering tools, and as time goes on, engineering seems to involve more and more of the science part. …the two fields are growing together! …and now there is not enough time to allow us the leisure which comes from separating the two fields.”

Richard Hamming

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

“Understanding the methods of calculus is vital to the creative use of mathematics… Without this mastery the average scientist or engineer, or any other user of mathematics, will be perpetually stunted in development, and will at best be able to follow only what the textbooks say; with mastery, new things can be done, even in old, well-established fields.”

Richard Hamming

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

“The calculus is probably the most useful single branch of mathematics. …I have found the ability to do simple calculus, easily and reliably, was the most valuable part of mathematics I ever learned.”

Richard Hamming

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

“We constantly use the word "simplify", but its meaning depends on what you are going to do next, and there is no uniform definition.”

Richard Hamming

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

“Without real experience in using the computer to get useful results the computer science major is apt to know all about the marvelous tool except how to use it. Such a person is a mere technician, skilled in manipulating the tool but with little sense of how and when to use it for its basic purposes.”

Richard Hamming

One Man's View of Computer Science (1969)

“The feeling of having free will is deep in us and we are reluctant to give it up for ourselves—but we are often willing to deny it to others!”

Richard Hamming

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

“Besides the theory there are a lot of small technical details that must be learned so well that you can recall them almost instantaneously, such as the trigonometric identities… put one part of the identity on one side of a 3 x 5 card and the other part on the other side. Using these flash cards you can, in the odd moments of your daily life, learn the mechanical parts of the course. …for this kind of low-level material many short learning sessions are much more efficient than a few long, intense ones; but this is not necessarily true for larger ideas. …most students will not use such trivial devices as flash cards; it seems to be beneath their dignity. They suffer accordingly.”

Richard Hamming

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

“Most mathematics books are filled with finished theorems and polished proofs, and to a surprising extent they ignore the methods used to create mathematics. It is as if you merely walked through a picture gallery and never told how to mix paints, how to compose pictures, or all the other "tricks of the trade."”

Richard Hamming

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

“Although textbooks (and professors) like to make definite statements indicating that they know what they are talking about, there is in fact a great deal of uncertainty and ambiguity in the world. …we will not evade this question but rather explore (overexplore?) it. …great progress is often made when what was long believed to be true is now seen to be perhaps not the whole truth. Thus the text often uses words… to cause you to think about the uncertainess and even the arbitrariness of much of our current conventions and definitions, to ponder about your acceptance of them.”

Richard Hamming

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

“Since I was trying to teach "style" of thinking in science and engineering, and "style" is an art, I should therefore copy the methods of teaching used for the other arts—once the fundamentals have been learned. How to become a great painter cannot be taught in words… Art teachers usually let the advanced student paint, and then make suggestions… more or less as the points arise in the student's head—which is where learning is supposed to occur!”

Richard Hamming

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

“Formal proofs, where there is deliberately no meaning, can convince only formalists, and of the results they themselves seem to deny any meaning. Is that to be the mathematics we are to use to understand the world we live in?”

Richard Hamming

Source: Mathematics on a Distant Planet (1998), p. 645