Richard Hamming Quotes

86 Sourced Quotes

Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture. For example, in education, a teacher might say in the next class he was going to "explain Young's modulus and how to measure it," rather than, "I am going to educate the students and prepare them for their future careers".

Richard Hamming
Some people believe that a theorem is proved when a logically correct proof is given; but some people believe a theorem is proved only when the student sees why it is inevitably true. The author tends to belong to this second school of thought.

Richard Hamming
Calculus systematically evades a great deal of numerical calculation.

Richard Hamming
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...

Richard Hamming
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.

Richard Hamming
The past is... much more uncertain—or even falsely reported—than is usually recognized.

Richard Hamming
Statistics should be taught early so that the concepts are absorbed by the student's flexible, adaptable mind before it is too late.

Richard Hamming
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.

Richard Hamming
We do not always know what we are talking about.... Troubles... can be made to arise whenever what is being said includes itself—a self-referral situation.

Richard Hamming
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.

Richard Hamming
Put glibly:
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
Of course, you seldom, if ever, see either pure state.

Richard Hamming
It is probable that the future will be more limited by the slow evolution of the human animal and the corresponding human laws, social institutions, and organizations than it will be by the rapid evolution of technology.

Richard Hamming
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.

Richard Hamming
Probability and statistics are now so obviously necessary tools for understanding many diverse things that we must not ignore them even for the average student.

Richard Hamming
The Postulates of Mathematics Were Not on the Stone Tablets that Moses Brought Down from Mt. Sinai.

Richard Hamming
Teachers should prepare the student for the student's future, not for the teacher's past.

Richard Hamming
Probability is the mathematics of uncertainty.... many modern theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential.

Richard Hamming
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
All of engineering involves some creativity to cover the parts not known, and almost all of science includes some practical engineering to translate the abstractions into practice.

Richard Hamming
You ought to try to make significant contributions to humanity rather than just get along through life comfortably... the life of trying to achieve excellence in some area is in itself a worthy goal... A life without a struggle on your part to make yourself excellent is hardly a life worth living.... a life without such a goal... is merely existing...

Richard Hamming
There are so many ways of being wrong and so few ways of being right that it is much more economical to study successes.

Richard Hamming
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
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.

Richard Hamming
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.

Richard Hamming
Unforeseen technological inventions can completely upset the most careful predictions.

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

Richard Hamming
Theorems... record more complex patterns of thinking that once shown to be valid need not be repeated every time they are needed.

Richard Hamming
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
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?

Richard Hamming
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