Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.
Lord KelvinRead
Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress.
Interpretation
Simplifying proofs shows knowledge growth and readiness for future advancements.
Lord Kelvin's quote emphasizes that as we deepen our understanding of a subject, simplifying the methods of proof not only reflects our advanced knowledge but also indicates that we are prepared to make further progress in that area. This highlights the interplay between clarity in thought and the ability to push the boundaries of knowledge.
In practice
In a lecture about scientific methods, one could use this quote to illustrate the importance of clarity in research.
Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.
We only know God in His works, but we are forced by science to admit and to believe with absolute confidence in a Directive Power-in an influence other than physical, or dynamical, or electrical forces.
In science there is only physics; all the rest is stamp collecting.
There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.
Let nobody be afraid of true freedom of thought. Let us be free in thought and criticism; but, with freedom, we are bound to come to the conclusion that science is not antagonistic to religion, but a help to it.
I need scarcely say that the beginning and maintenance of life on earth is absolutely and infinitely beyond the range of all sound speculation in dynamical science. The only contribution of dynamics to theoretical biology is absolute negation of automatic commencement or automatic maintenance of life.
There's a misconception that survival of the fittest means survival of the most aggressive. The adjective 'Darwinian' used to refer to ruthless competition; you used to read that in business journals. But that's not what Darwinian means to a biologist; it's whatever leads to reproductive success.
Tiny differences in input could quickly become overwhelming differences in output.... In weather, for example, this translates into what is only half-jokingly known as the Butter- fly Effect—the notion that a butterfly stirring the air today in Peking can transform storm systems next month in New York.
Economics has never been a science - and it is even less now than a few years ago.
Well, biology today as I see it has an amiable look - quite different from the 19th-century view that the whole arrangement of nature is hostile, 'red in tooth and claw.' That came about because people misread Darwin's 'survival of the fittest.'
You can’t say A is made of B or vice versa. All mass is interaction.
There is no science in this world like physics. Nothing comes close to the precision with which physics enables you to understand the world around you. It's the laws of physics that allow us to say exactly what time the sun is going to rise. What time the eclipse is going to begin. What time the eclipse is going to end.
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