Henri Poincaré  Wikipedia
Henri Poincaré. "Classical Mechanics". Chapter 6 inScience and Hypothesis . London: Walter Scott Publishing (1905):89110.
Science and Hypothesis by Henri Poincaré
Here then is the methodological analogy and link between the principleof induction, conventions in the sense of apparent hypotheses andverifiable hypotheses. All are guided by experience without being(entirely) experimental, and all involve presupposed categories ornatural hypotheses. Verifiable hypotheses employ conventional elementsin the generalization process and may presuppose the (empirical)principle of induction. Geometrical conventions are apparenthypotheses guided by the experience of muscular sensations and involvethe category of groups. Both these sorts of hypotheses, verifiable andapparent, employed in physics and geometry, are inPoincaré’s hierarchy of sciences framed on the one handby a priori principles and natural hypotheses that are toolsboth for mathematicians and experimenters, and on the other hand, byindifferent hypotheses and physical principles. The indifferenthypotheses are conventional (in the ordinary sense) stipulations ofontological entities—mechanical models that increase ourtheoretical insight, while the physical principles are eitherverifiable hypotheses elevated by decree beyond the crucible ofexperiment or wellfounded with respect to the network of actualscience.
Finally, apparent hypotheses are definitions or conventions ratherthan actual claims about the world. They therefore may not beconsidered to be hypotheses at all, although they are, however, oftenmistaken for hypotheses. Poincaré argues that (metric) geometryis the hypothesis most prone to such confusion. Although he presentsarithmetic in Science and Hypothesis without mentioninghypotheses explicitly, we can see a role for them in his analysis hereas well, which we will present in the order that he follows.
Science and Hypothesis, by Henri Poincaré : chapter3
Poincaré is especially noted for effectively discovering chaos theory,and for posing ;that conjecture was one of the most famousunsolved problems in mathematics for an entire century,and can be explained without equations to a layman.
We come across a different kind of hypothesis and fully perceive itsproductivity. Undoubtedly, the theories seem at first sight fragileand the history of science shows us how fleeting they are. However,they do not entirely die out and something remains of each of them. Itis this something that we must try to sort out, for there and onlythere is true reality (Poincaré 1902: 26; 2017:3–30).
Henri Poincaré (Author of Science and Hypothesis)
To define a concept implicitly is to determine it by means of itsrelations to other concepts. But to apply such a concept to reality isto choose, out of the infinite wealth of relations in the world, acertain group or complex and to embrace as a unit by designating itwith a name. By suitable choice it is always possible under certaincircumstances to obtain an unambiguous designation of the real bymeans of the concept. Conceptual definitions and coordinations thatcome into being in this fashion we call conventions (using this termin the narrower sense, because in the broader sense, of course, alldefinitions are agreements). It was Henri Poincaré whointroduced the term convention in this narrower sense into naturalphilosophy; and one of the most important tasks of that discipline isto investigate the nature and meaning of the various conventions foundin natural science (Schlick 1925, 91–92).
Poincaré makes hypotheses central to his analysis of science,distinguishing four kinds, which are actually given in two lists ofthree each (Poincaré 1902: 24 and 166–167; 2017: 1 and109110). Combining the two lists, these are:
Science and Hypothesis by Henri Poincar

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Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science

Science and Hypothesis : Jules Henri Poincare : …
"Science and Hypothesis" is a study written in 1902, by the French mathematician, Henri Poincaré
Science and Hypothesis eBook: Henri Poincare: …
In 1889 Poincaré won a prize from the King of Sweden for aquestion posed by Weierstrass on the stability of the solar system,that is, the threebody (or (n)body) problem in classicalmechanics. Despite a mathematical error that he discovered at the lastmoment (after questions raised by the Swedish mathematician LarsEdvard Phragmén) and frantically corrected, the work wasimportant for its use of topology and as a founding document in chaostheory, for Poincaré showed that in general, the stability ofsuch systems cannot be demonstrated. It is also in this context thathe proved his famous recurrence theorem.
Science and Hypothesis av Henri Poincare (Ebok)  Bokus…
Note that Friedman mentions the theory of mathematical magnitude aswell. There is a step between arithmetic and geometry, namely thetheory of mathematical magnitude, which is precisely the topic ofChapter 2 of Science and Hypothesis. The theory ofmathematical magnitude presupposes the possibility of indefiniterepetition, and therefore something like mathematical induction, whichPoincaré presents as central to arithmetic in Chapter 1 ofScience and Hypothesis.
Science and Hypothesis by Henri Poincare, David J. …
Jules Henri Poincaré was born on April 29, 1854 in Nancy in theLorraine region of France. His father was professor of Hygiene in theSchool of Medicine at the University of Nancy. His cousin Raymond wasto become the President of the Republic of France during the period1913–1920 and his younger sister Aline married the philosopherEmile Boutroux. Henri was a precocious student who rose immediately tothe top of his class, excelling in both science and letters. At age13, his teacher told his mother that “Henri will become amathematician … I would say a great mathematician”(Bellivier 1956: 78). During the FrancoPrussian war in 1870 theGermans occupied Nancy and the Poincaré family was obliged tobillet the secretary of the civil commissar of Nancy, with whom Henriwould have a round of conversation each night after dinner in order toimprove his German.
Science and Hypothesis by Henri Poincaré
Henri Poincaré was a mathematician, theoretical physicist and aphilosopher of science famous for discoveries in several fields andreferred to as the last polymath, one who could make significantcontributions in multiple areas of mathematics and the physicalsciences. This survey will focus on Poincaré’sphilosophy. Concerning Poincaré’s scientific legacy, seeBrowder (1983) and Charpentier, Ghys, Lesne (2010).