Richard Hamming Quotes

86 Sourced Quotes

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.

Richard Hamming
Much of present science rests on engineering tools, and as time goes on, engineering seems to involve more and more of the science part.... the two fields are growing together!... and now there is not enough time to allow us the leisure which comes from separating the two fields.

Richard Hamming
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!

Richard Hamming
It may be said "In research, if you know what you are doing, then you shouldn't be doing it." In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.

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

Richard Hamming
We intend to teach the doing of mathematics. The applications of these methods produce the results of mathematics (which usually is only what is taught)... There is also a deliberate policy to force you to think abstractly... it is only through abstraction that any reasonable amount of useful mathematics can be covered. There is simply too much known to continue the older approach of giving detailed results.

Richard Hamming
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!

Richard Hamming
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.

Richard Hamming
When you yourself are responsible for some new application in mathematics... then your reputation... and possibly even human lives, may depend on the results you predict. It is then the need for mathematical rigor will become painfully obvious to you.... Mathematical rigor is the clarification of the reasoning used in mathematics.... a closer examination of the numerous "hidden assumptions" is made.... Over the years there has been a gradually rising standard of rigor; proofs that satisfied the best mathematicians of one generation have been found inadequate by the next generation. 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
If you expect to continue learning all your life, you will be teaching yourself much of the time. You must learn to learn, especially the difficult topic of mathematics.

Richard Hamming
The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

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

Richard Hamming
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
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
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? In a sense the first is Science... The second is Engineering.. The third is ethics, morals, or... value judgements.... you will probably have an idea of how to alter things to make the more desirable future occur... having a vision is what tends to separate the leaders from the followers.

Richard Hamming
Calculus is the mathematics of change.... Change is characteristic of the world.

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

Richard Hamming
This is the type of AI I am interested in—what can the human and machine do together, and not in the competition which can arise.... There are doubts as to what fraction of the population can compete with computers, even with nice interactive prompting menus.

Richard Hamming
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
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 (and those require mathematics).

Richard Hamming
Without real experience in using the computer to get useful results the computer science major is apt to know all about the marvelous tool except how to use it. Such a person is a mere technician, skilled in manipulating the tool but with little sense of how and when to use it for its basic purposes.

Richard Hamming
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
Apparently an "art"—which almost by definition cannot be put into words—is probably best communicated by approaching it from many sides and doing so repeatedly, hoping thereby students will finally master enough of the art, or if you wish, style, to significantly increase their future contributions to society.

Richard Hamming
The more complex the designed system the more field maintenance must be central to the final design. Only when field maintenance is part of the original design can it be safely controlled... This applies to both mechanical things and to human organizations.

Richard Hamming