60 quotes
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?
Mathematics on a Distant Planet (1998)
Any unwillingness to learn mathematics today can greatly restrict your possibilities tomorrow.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
As a practicing computer veteran, this reviewer has the habit of looking at the hypothesis of a theorem and asking
Science and mathematics... have added little to our understanding of such things as Truth, Beauty, and Justice. There may be definite limits to the applicability of the scientific method.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
The past is... much more uncertain—or even falsely reported—than is usually recognized.
The Art of Doing Science and Engineering: Learning to Learn (1991)
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?
The Art of Probability for Scientists and Engineers (1991)
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!
The Art of Doing Science and Engineering: Learning to Learn (1991)
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.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
The Postulates of Mathematics Were Not on the Stone Tablets that Moses Brought Down from Mt. Sinai.
The Unreasonable Effectiveness of Mathematics (1980)
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.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
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.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
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.
The Art of Doing Science and Engineering: Learning to Learn (1991)
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.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
I know that the great Hilbert said, "We will not be driven out of the paradise Cantor has created for us," and I reply, "I see no reason for walking in!" Indeed, in time, as more and more people get used to computers, I am inclined to believe that we here on this Earth will decide that the computable numbers are enough.
Mathematics on a Distant Planet (1998)
The people at the bottom do not have the larger, global view, but at the top they do not have the local view of all the details, many of which can often be very important, so either extreme gets poor results.
The Art of Doing Science and Engineering: Learning to Learn (1991)
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.
The Art of Doing Science and Engineering: Learning to Learn (1991)
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.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
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.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
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.
Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
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 Art of Doing Science and Engineering: Learning to Learn (1991)