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.
It will be another million years, at least, before we understand the primes.
What I want to do is demonstrate that biology can learn how to make a vast array of molecules that people thought were outside the realm of biology.
In the Middle East, where populations are growing fast, the world is seeing the first collision between population growth and water supply at the regional level. For the first time in history, grain production is dropping in a geographic region with nothing in sight to arrest the decline. Each day now brings 10,000 more people to feed and less irrigation water with which to feed them.
I sometimes try to imagine what would have happened if we’d known the bonobo first and the chimpanzee only later—or not at all. The discussion about human evolution might not revolve as much around violence, warfare and male dominance, but rather around sexuality, empathy, caring and cooperation. What a different intellectual landscape we would occupy!
We are in a fool's climate, accidentally kept cool by smoke, and before this century is over billions of us will die and the few breeding pairs of people that survive will be in the Arctic where the climate remains tolerable.
There is a duality in recognising what an incredible disease it is - in terms of its origin, that it emerges out of a normal cell. It's a reminder of what a wonderful thing a normal cell is. In a very cold, scientific sense, I think a cancer cell is a kind of biological marvel.
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