Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

Richard Hamming

Categorized in : Believe Math Airplane

The purpose of computing is insight, not numbers.

Richard Hamming

learning math numbers

Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. 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

greatness science believe

A parable: A man was examining the construction of a cathedral. He asked a stone mason what he was doing chipping the stones, and the mason replied, "I am making stones." He asked a stone carver what he was doing. "I am carving a gargoyle." And so it went, each person said in detail what they were doing. Finally he came to an old woman who was sweeping the ground. She said. "I am helping build a cathedral." ...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.

Richard Hamming

men science thinking

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

Richard Hamming

hard-work important problem

Given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.

Richard Hamming

two people thinking

If you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you dont quite know what problems are worth working on.

Richard Hamming

office doors years

True greatness is when your name is like ampere, watt, and fourier-when it's spelled with a lower case letter.

Richard Hamming

greatness names science

Once in a while a person does only one thing in his whole life, and we'll talk about that later, but a lot of times there is repetition. I claim that luck will not cover everything. And I will cite Pasteur who said, "Luck favors the prepared mind." And I think that says it the way I believe it.

Richard Hamming

favors luck mind

Often the great scientists, by turning the problem around a bit, changed a defect to an asset. For example, many scientists when they found they couldn't do a problem finally began to study why not. They then turned it around the other way and said, "But of course, this is what it is" and got an important result.

Richard Hamming

important change science

Newton said, "If I have seen further than others, it is because I've stood on the shoulders of giants." These days we stand on each other's feet!

Richard Hamming

giants feet science

What you learn from others you can use to follow.

Richard Hamming

learning use science

There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think.

Richard Hamming

science people thinking

The most dangerous thought you can have as a creative person is to think you know what you’re doing.

Richard Hamming

creative inspirational thinking

Put glibly:

Richard Hamming

engineering doing-you science

Typing is no substitute for thinking.

Richard Hamming

typing substitutes thinking

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

careers teacher thinking

Mathematics is not merely an idle art form, it is an essential part of our society.

Richard Hamming

our-society essentials art

Science is concerned with what is possible while engineering is concerned with choosing, from among the many possible ways, one that meets a number of often poorly stated economic and practical objectives.

Richard Hamming

engineering numbers science

Computer scientists stand on each other's feet.

Richard Hamming

scientist computer feet

Mathematics is an interesting intellectual sport but it should not be allowed to stand in the way of obtaining sensible information about physical processes.

Richard Hamming

intellectual sports interesting