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.
The feeling of awed wonder that science can give us is one of the highest experiences of which the human psyche is capable. It is a deep aesthetic passion to rank with the finest that music and poetry can deliver. It is truly one of the things that make life worth living and it does so, if anything, more effectively if it convinces us that the time we have for living is quite finite.
Unlike science, creationism cannot predict anything, and it cannot provide satisfactory answers about the past.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
Men became scientific because they expected Law in Nature, and they expected Law in Nature because they believed in a Law Giver.
The investigation of nature is an infinite pasture-ground where all may graze, and where the more bite, the longer the grass grows, the sweeter is its flavor, and the more it nourishes.
Refining is inevitable in science when you have made measurements of a phenomenon for a long period of time.
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