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.
Interpretation
The quote emphasizes the importance of rigorous mathematical principles in practical applications.
Richard Hamming's quote highlights the significance of foundational mathematical concepts, such as the difference between Lebesgue and Riemann integrals, and poses a rhetorical question about their relevance to real-world phenomena, like the ability of an airplane to fly. Hamming suggests that if the underlying mathematics were flawed or misunderstood, it would be unreasonable to trust the outcomes they produce in practical applications like aviation.
In practice
During a lecture on the importance of mathematical foundations in engineering.
When you are famous it is hard to work on small problems. This is what did [Claude Elwood] Shannon in. After information theory, what do you do for an encore? 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.
Science is composed of laws which were originally based on a small, carefully selected set of observations, often not very accurately measured originally; but the laws have later been found to apply over much wider ranges of observations and much more accurately than the original data justified.
If you don't work on important problems, it's not likely that you'll do important work.
Beware of finding what you're looking for._x000D_ _x000D_ A favorite aphorism he often used.
One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to.
Put glibly:_x000D_ _x000D_ In science if you know what you are doing you should not be doing it._x000D_ _x000D_ In engineering if you do not know what you are doing you should not be doing it._x000D_ _x000D_ Of course, you seldom, if ever, see either pure state.
By curious accident of history and geography, the world's major energy resources are located pretty much in Shiite regions. They're a minority in the Middle East, but they happen to be where the oil is, right around the northern part of the Gulf.
When we see the shadow on our images, are we seeing the time 11 minutes ago on Mars? Or are we seeing the time on Mars as observed from Earth now? It's like time travel problems in science fiction. When is now; when was then?
The kitchen's a laboratory, and everything that happens there has to do with science. It's biology, chemistry, physics. Yes, there's history. Yes, there's artistry. Yes, to all of that. But what happened there, what actually happens to the food is all science.
A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.
Science predicts that many different kinds of universe will be spontaneously created out of nothing. It is a matter of chance which we are in.
When a physician is called to a patient, he should decide on the diagnosis, then the prognosis, and then the treatment. ... Physicians must know the evolution of the disease, its duration and gravity in order to predict its course and outcome. Here statistics intervene to guide physicians, by teaching them the proportion of mortal cases, and if observation has also shown that the successful and unsuccessful cases can be recognized by certain signs, then the prognosis is more certain.
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