A Univ. of Illinois professor wrote this 1913 essay in Popular Science Monthly:
IT has not seemed to me appropriate, nor would there be time, nor should I be able, to enter into an exhaustive study of the life-work of a master-mind like Jules Henri Poincaré. Indeed, to analyze his contributions to astronomy needs a Darwin; to report on his investigations in mathematical physics needs a Planck; to expound his philosophy of science needs a Royce; to exhibit his mathematical creations in all their fullness needs Poincaré. Let it suffice that he was the pride of France, not only of the aristocracy of scholars, but of the nation. He was inspired by the genius of France, with its keen discernment, its eternal search for exact truth, its haunting love of beauty. The mathematical world has lost its incomparable leader, and its admiration for the magnitude of his achievements will be tempered only by the vain desire to know what visions he had not yet given expression to. Investigators of brilliant power for years to come will fill out the outlines of what he had time only to sketch. His vision penetrated the universe from the electron to the galaxy, from instants of time to the sweep of space, from the fundamentals of thought to its most delicate propositions. ...See also Wikisource.
Poincaré's conception of science can be summed up in these terms: Science consists of the invariants of human thought. ...
We are witnesses too of an evolution in science and mathematics from the continuous to the discontinuous. In mathematics it has produced the function defined over a range rather than a line — a chaos, as it were, of elements — and the calculable numbers of Borel. In physics it has produced the electron, the magneton, and the theory of quanta, 5 about which Poincaré said shortly before his death:A physical system is capable of only a finite number of distinct states; it abruptly jumps from one state to another without passing through the inter- mediate states.
The Literary Digest, April 15, 1912 p.751, had an article titled, Does Everything Go By Jerks?
Do all the processes of the universe, which appear to go on smoothly and continuously, gliding from one state to another, really take place with a series of infinitesimal jerks? Does a ball, when thrown into the air, move with a series of tiny leaps so close together than they blend to the eye? This is precisely what takes place in a moving picture. Is nature, in this respect, one vast cinematograph? This would appear to be the result of a striking and almost revolutionary theory propounded first in Germany, but elucidated and extended in the Revue Scientifique (Paris, February 24) by Henri Poincaré, an eminent French physicist. According to this theory, energy consists of discontinuous portions just as matter does. There are "atoms" of energy as well as of matter, and possibly also "atoms" of time, causing all duration to be jerky instead of smooth, as it appears to be.Poincare's last essay in 1912 was on The New Conceptions of Matter. He tells how he was finally persuaded by atomism. Presiously he had been a proponent of continuity, and referred to the "atomic hypothesis" as it were just a convention.