Richard Hamming Quotes

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.

If you don’t work on important problems, it’s not likely that you'll do important work.

I have often wondered what would have happened if I had had a modern, high-speed computer. Would I ever have acquired the feeling for the missile, upon which so much depended in the final design?

The purpose of computation is insight, not numbers.

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.

"As a result I early asked the question, "Why should I do all the analysis in terms of Fourier integrals? Why are they the natural tools for the problem?" I soon found out, as many of you already know, that the eigenfunctions of translation are the complex exponentials. If you want time invariance, and certainly physicists and engineers do (so that an experiment done today or tomorrow will give the same results), then you are led to these functions. Similarly, if you believe in linearity then they are again the eigenfunctions. In quantum mechanics the quantum states are absolutely additive; they are not just a convenient linear approximation. Thus the trigonometric functions are the eigenfunctions one needs in both digital filter theory and quantum mechanics, to name but two places.

Now when you use these eigenfunctions you are naturally led to representing various functions, first as a countable number and then as a non-countable number of them-namely, the Fourier series and the Fourier integral. Well, it is a theorem in the theory of Fourier integrals that the variability of the function multiplied by the variability of its transform exceeds a fixed constant, in one notation l/2pi. This says to me that in any linear, time invariant system you must find an uncertainty principle."

The beauty of mathematics often makes the subject matter much more attractive and easier to master.

In forming your plan for your future you need to distinguish three different questions: What is possible? What is likely to happen? What is desirable to have happen?

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

Is it not fair to say, “The program learned from experience”? Your immediate objection is that there was a program telling the machine how to learn. But when you take a course in Euclidean geometry, is not the teacher putting a similar learning program into you? Poorly, to be sure, but is that not, in a real sense, what a course in geometry is all about? 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. Think it over carefully. If you deny the machine learns from experience because you claim the program was told (by the human programmer) how to improve its performance, then is not the situation much the same with you, except you are born with a somewhat larger initial program compared to the machine when it leaves the manufacturer’s hands? Are you sure you are not merely “programmed” in life by what chance events happen to you?

Somewhere in the mid-to-late 1950s in an address to the President and V.Ps of Bell Laboratories I said, "At present we are doing 1 out of 10 experiments on the computers and 9 in the labs, but before I leave it will be 9 out of 10 on the machines". They did not believe me... by now we do somewhere between 90% to 99% on the machines... And this trend will go on!

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

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.

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.

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!