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.
Interpretation
Great scientists often transform obstacles into advantages by reframing their perspectives on problems.
The quote by Richard Hamming highlights the innovative mindset of great scientists who, when faced with challenges, don't just seek to solve problems directly. Instead, they analyze the reasons behind their difficulties, leading to a deeper understanding and often revealing essential insights that can turn a perceived failure into a significant success.
In practice
During a scientific conference, one might share this quote to illustrate how researchers can harness challenges for breakthroughs.
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.
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.
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.
Forty years as an astronomer have not quelled my enthusiasm for lying outside after dark, staring up at the stars. It isn't only the beauty of the night sky that thrills me. It's the sense I have that some of those points of light are the home stars of beings not so different from us, daily cares and all, who look across space with wonder, just as we do.
There may be many Big Bangs that happened at various and far-flung locations, each creating its own swelling, spatial expanse, each creating a universe - our universe being the result of only one of those Big Bangs.
Low socioeconomic status carries with it an enormously increased risk of a broad range of diseases, and this gradient cannot be fully explained by factors such as health-care access.
That is the way of the scientist. He will spend thirty years in building up a mountain range of facts with the intent to prove a certain theory; then he is so happy with his achievement that as a rule he overlooks the main chief fact of all-that all his accumulation proves an entirely different thing.
In the history of physics, there have been three great revolutions in thought that first seemed absurd yet proved to be true. The first proposed that the earth, instead of being stationary, was moving around at a great and variable speed in a universe that is much bigger than it appears to our immediate perception. That proposal, I believe, was first made by Aristarchos two millenia ago ... Remarkably enough, the name Aristarchos in Greek means best beginning.
We know very little about the universe. I personally don't believe it's uniform and the same everywhere. That's like saying the earth is flat.
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