Richard Hamming: Trending quotes (page 4)

“There is no agreed upon definition of mathematics, but there is widespread agreement that the essence of mathematics is extension, generalization, and abstraction… [which] often bring increased confidence in the results of a specific application, as well as new viewpoints.”

Richard Hamming

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

Confidence , Mathematics

“Continuous distributions are basic to the theory of probability and statistics, and the calculus is necessary to handle them with any ease.”

Richard Hamming

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

“In the long run, the methods are the important part of the course. It is not enough to know the theory; you should be able to apply it.”

Richard Hamming

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

Parting

“Calculus systematically evades a great deal of numerical calculation.”

Richard Hamming

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

“Often it is not physical limitations… but rather it is human made laws, habits, and organizational rules, regulations, personal egos, and inertia, which dominate the evolution of the future.”

Richard Hamming

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

Law , Future , Personality

“When you are famous it is hard to work on small problems. […] The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you. […] The Institute for Advanced Study in Princeton, in my opinion, has ruined more good scientists than any institution has created, judged by what they did before they came and judged by what they did after.”

Richard Hamming

You and Your Research (1986)

Way , Error , Problem , Tree

“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)

Feeling

“We are beginning to find not only is intelligence not adequately defined so arguments can be settled scientifically, but a lot of other associated words like, computer, learning, information, ideas, decisions, expert behavior—all are a bit fuzzy…”

Richard Hamming

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

Behavior , Intelligence , Idea , Decision

“We must not forget, in all the enthusiasm for computer simulations, occasionally we must look at Nature as She is.”

Richard Hamming

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

Nature , Forgetting

“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)

Life , Idea , Suffering , Learning

“It is not easy to become an educated person.”

Richard Hamming

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

Education , Personality

“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)

Books , Mathematics , Painting

“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)

Truth , World , Question , Thinking

“Unfortunately… the ADA language was designed by experts, and it shows all the non-humane features you can expect from them. It is… a typical Computer Science hacking job—do not try and understand what you are doing, just get it running. As a result of this poor psychological design… although a government contract may specify the programming be in ADA, probably over 90% will be done in FORTRAN, debugged, tested, and then painfully, by hand, be converted to a poor ADA program, with a high probability of errors!”

Richard Hamming

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

Error , Understanding , Science

“Just as there are odors that dogs can smell and we cannot, as well as sounds that dogs can hear and we cannot, so too there are wavelengths of light we cannot see and flavors we cannot taste. Why then, given our brains wired the way they are, does the remark, "Perhaps there are thoughts we cannot think," surprise you?”

Richard Hamming

The Unreasonable Effectiveness of Mathematics (1980)

Dogs , Way , Thinking , Light

“Teachers should prepare the student for the student's future, not for the teacher's past.”

Richard Hamming

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

Teachers , Past , Future

“The applications of knowledge, especially mathematics, reveal the unity of all knowledge. In a new situation almost anything and everything you ever learned might be applicable, and the artificial divisions seem to vanish.”

Richard Hamming

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

Mathematics , Knowledge , Learning

“Faced with almost an infinity of details you cannot afford to deal constantly with the specific; you must learn to embrace more and more detail under the cover of generality.”

Richard Hamming

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

Learning

“You live in an age that is dominated by science and engineering. …Thus if you wish to be effective in the world and to achieve the things that you want, it is necessary to understand both science and engineering”

Richard Hamming

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

Age , World , Mathematics , Understanding

“We are mainly interested in the processes… not… in presenting mathematics in its most abstract form. …we will often begin with concrete forms and then exhibit the process of abstraction.”

Richard Hamming

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

Mathematics