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.
Natural gas emits only half the carbon dioxide of coal when burned, but if methane leaks when oil companies extract it from the ground in a sloppy manner - methane is far more potent a greenhouse gas than carbon dioxide - it can wipe out all the advantages of natural gas over coal.
It is the desire for explanations that are at once systematic and controllable by factual evidence that generates science; and it is the organization and classification of knowledge on the basis of explanatory principles that is the distinctive goal of the sciences.
At lunch Francis [Crick] winged into the Eagle to tell everyone within hearing distance that we had found the secret of life.
I tell my students, with a feeling of pride that I hope they will share, that the carbon, nitrogen, and oxygen that make up ninety-nine per cent of our living substance were cooked in the deep interiors of earlier generations of dying stars. Gathered up from the ends of the universe, over billions of years, eventually they came to form, in part, the substance of our sun, its planets, and ourselves. Three billion years ago, life arose upon the earth. It is the only life in the solar system.
We have never observed infinity in nature. Whenever you have infinities in a theory, that's where the theory fails as a description of nature. And if space was born in the Big Bang, yet is infinite now, we are forced to believe that it's instantaneously, infinitely big. It seems absurd.
...99 percent confident that the world really was getting warmer and that there was a high degree of probability that it was due to human-made greenhouse gases.
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