Richard Hamming

1915–1998 · American mathematician and information theorist

Topics: learning, mathematics, software engineering, creativity

• 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.

  — 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

• If the prior distribution, at which I am frankly guessing, has little or no effect on the result, then why bother; and if it has a large effect, then since I do not know what I am doing how would I dare act on the conclusions drawn?

  — Richard Hamming

• 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.

  — Richard Hamming

• 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

• A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or extend something you have just done.

  — Richard Hamming

• 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

• 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

• 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

• 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

• Perhaps thinking should be measured not by what you do but by how you do it.

  — Richard Hamming

• 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

• 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

• The standard process of organizing knowledge into departments, and subderpartments, and further breaking it up into separate courses, tends to conceal the homogeneity of knowledge, and at the same time to omit much which falls between the courses.

  — Richard Hamming

• 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

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

  — Richard Hamming

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

  — Richard Hamming

• Unforeseen technological inventions can completely upset the most careful predictions.

  — Richard Hamming

• 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

• Any unwillingness to learn mathematics today can greatly restrict your possibilities tomorrow.

  — Richard Hamming