“The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.”
Light Waves and Their Uses. By Albert A. Michelson. Published by The University of Chicago Press, 1903, pp 23-25.
Context: Before entering into these details, however, it may be well to reply to the very natural question: What would be the use of such extreme refinement in the science of measurement? Very briefly and in general terms the answer would be that in this direction the greater part of all future discovery must lie. The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i. e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions.As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second—an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet by observations of the small irregularities noticed by Leverier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many instances might be cited, but these will suffice to justify the statement that "our future discoveries must be looked for in the sixth place of decimals." It follows that every means which facilitates accuracy in measurement is a possible factor in a future discovery, and this will, I trust, be a sufficient excuse for bringing to your notice the various methods and results which form the subject matter of these lectures.
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Albert A. Michelson 5
American physicist 1852–1931Related quotes

1894, dedication of Ryerson Physical Laboratory, quoted in Annual Register 1896, p. 159 https://books.google.com/books?id=HysXAAAAYAAJ&pg=PA159.
Variants of this quote have been misattributed to Lord Kelvin since the 1980s, though there is no evidence that he said anything of the sort. The identity of the unnamed "eminent physicist" is unknown.

Quote in: 'Plastic Art and Pure Plastic Art', Piet Mondrian (1937); in 'Documents of modern Art' ed. Robert Motherwell for Wittenborn, Schulz, New York 1945
1930's

reported by Lance Dixon http://www.preposterousuniverse.com/blog/2013/10/03/guest-post-lance-dixon-on-calculating-amplitudes/

Misattributed to Kelvin since the 1980s, either without citation or stating that it was made in an address to the British Association for the Advancement of Science in 1900. There is no evidence that Kelvin said this, and the quote is instead a paraphrase of Albert A. Michelson, who in 1894 stated: "… it seems probable that most of the grand underlying principles have been firmly established … An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals." The attribution to Kelvin giving an address in 1900 is presumably a confusion with his “Two clouds” speech, delivered to the Royal Society in 1900 (see above), and which on the contrary pointed out areas that would subsequently see revolutions.
Misattributed
Source: Superstring: A theory of everything? (1988) by Paul Davies and Julian Brown
Source: Rebuilding the Matrix : Science and Faith in the 21st Century (2003) by Denis Alexander
Source: Einstein (2007) by Walter Isaacson, page 575
Source: The End of Science (1996), by , p. 19 https://books.google.com/books?id=S1Lmqh79dOoC&pg=PA19

“So far as we know, all the fundamental laws of physics, like Newton’s equations, are reversible.”
volume I; lecture 46, "Ratchet and Pawl"; section 46-5, "Order and entropy"; p. 46-8
The Feynman Lectures on Physics (1964)

Source: "Outlines of the Science of Energetics," (1855), p. 121; Second paragraph
"The Magic of Science" in Imperial Oil Review (Spring, 1994) http://sites.utoronto.ca/jpolanyi/public_affairs/public_affairs4f.html.
Context: It is not the laws of physics that make science possible but the unprovable proposition that there exists a grand design underlying the physical world. And not just any old "grand design" but one that is accessible to the limited senses and modest reasoning powers of the species to which we belong. Scientists subscribe with such conviction to this article of faith that they are willing to commit a lifetime to the pursuit of scientific discovery. It is hardly surprising that an activity so magical is also undefinable. Science is what scientists do. And what they do is look around themselves for messages written in the sky, the earth, the oceans and all living things – messages that tell of the unity of creation. These messages have been there – unseen, though at times written in letters miles high – since the dawn of history. But we have just passed through an epoch in which, quite suddenly, scientists seem to have learnt speed reading. Discoveries have been coming at an unprecedented pace. In the wake of such a period it is common to consider that we may be approaching the point where all that is readable in nature will have been read. We should be skeptical of such claims. Success in reading some messages brings with it a temporary blindness to others. We forget that between the words written in black in nature's book there are likely to be messages of equal importance written in white. It is a truism that success in science comes to the individuals who ask the right questions.