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.
Any scientist who can't explain to an eight-year-old what he is doing is a charlatan.
If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down. But I can find no such case.
All great scientists have, in a certain sense, been great artists; the man with no imagination may collect facts, but he cannot make great discoveries.
The intelligent beings in these regions should therefore not be surprised if they observe that their locality in the universe satisfies the conditions that are necessary for their existence. It is a bit like a rich person living in a wealthy neighborhood not seeing any poverty.
If we think of our chromosomes - they carry our genetic material - as being like shoelaces, I work on the plastic tips at the end that protect them.
It could be that at some earlier time, somewhere in the universe, a civilization evolved by probably some kind of Darwinian means to a very, very high level of technology- and designed a form of life that they seeded onto perhaps this planet. And I suppose it's possible that you might find evidence for that if you look at the details of biochemistry, molecular biology, you might find a signature of some sort of designer.
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