Oscar II's prize competition and the error in Poincar�'s memoir on the three body problem

Barrow-Green, June

doi:10.1007/bf00374436

Cited by 20 publications

(9 citation statements)

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“…Cominciarono allora quelle interminabili passeggiate per le vie di Roma, durante le quali la geometria algebrica fu il tema preferito dei nostri discorsi. [11,3] As this anecdote shows, Enriques had both a very accentuated personal inclination to deal with problems in an intuitive or even approximate way and a decided dislike of methodical and pedantic study. It also shows the role intuitive geometrical thought played in his development; it shaped his scientific practice as well as his epistemological system.…”

Section: The Philosophy and The Methodology Of Science Of Federigo Enmentioning

confidence: 99%

“…a quella fué la é poca en que, segú n decía graciosamente un compañ ero y maestro mío, bastaba sembrar una alubia para ver nacer un geó metra. [25,3] As Corrado Segre had observed many years earlier in an important article that had opened a new phase in Italian geometry [89], 26 a clever form of geometry had been 25 Of fundamental importance to Luigi Cremona's thought and activity are his letters, conserved in the Department of Mathematics of the University of Rome ''La Sapienza,'' which are in the process of being published [13; 14; 15]. See also [66; 68].…”

Section: The Philosophy and The Methodology Of Science Of Federigo Enmentioning

confidence: 99%

“…Et pour les phé nomè nes fortuits eux-mê mes, il est clair que les renseignements que nous fournit le calcul des probabilité s ne cesseront pas d'ê tre vrais le jour où ces phé nomè nes seront mieux connus. [83,3] Following this discussion of chance, Poincaré proceeded to an interesting analysis of the phenomenon of ''sensitivity toward initial conditions,'' which is at the root of what we today call ''chaotic systems.'' Specifically, he identified the situations in which prediction is impossible with those in which the phenomenon must be considered fortuitous: Une cause trè s petite, qui nous é chappe, dé termine un effet considé rable que nous ne pouvons pas ne pas voir, et alors nous disons que cet effet est dû au hasard.…”

Section: Poincaré and Qualitative Analysisunclassified

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The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

Israel

Menghini

1998

Historia Mathematica

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Section: The Philosophy and The Methodology Of Science Of Federigo Enmentioning

confidence: 99%

Section: The Philosophy and The Methodology Of Science Of Federigo Enmentioning

confidence: 99%

Section: Poincaré and Qualitative Analysisunclassified

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The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

Israel

Menghini

1998

Historia Mathematica

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“…Poincaré's articles on the three body problem are discussed in depth in the book of Barrow-Green Poincaré and the Three Body Problem (Barrow-Green 1997). In Barrow-Green (1994), she had already analyzed the erroneous paper that Poincaré presented to the competition that celebrated the 60th birthday of King Oscar of Sweden and Norway in 1889 (Poincaré 1889). The efforts made to correct the error gave rise to another paper published in 1890 (Poincaré 1890).…”

Section: Introductionmentioning

confidence: 99%

Stability of trajectories from Poincaré to Birkhoff: approaching a qualitative definition

Roque

2011

Arch. Hist. Exact Sci.

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The article investigates the different conceptions of stability found in qualitative studies on the solutions of differential equations. We start from the definitions proposed by Poincaré and criticized by Birkhoff for not being fully qualitative, and show that the clarification of the criterion for stating that a property is qualitative comes precisely with Birkhoff. In addition, we note that the stability conceptions of Lyapunov and Levi-Civita are also important in this transition from the appearance of the first qualitative tools in the study of differential equations to the definition of stability in use in dynamical systems theory. The history of stability can help to explain the meaning of the word "qualitative" in this context.

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“…7 The literature on Poincaré's contribution to dynamical systems theory is immense; surveys can be found in Chabert and Dahan Dalmedico [1992] and Bottazzini [2000]. Among the studies devoted to the qualitative theory of differential equation, let us mention Hadamard [1912a], Gilain [1991], Gray [1992], Mawhin [1996], and Parker [1998]; concerning celestial mechanics, see Hadamard [1912b], Anderson [1994] and Barrow-Green [1994;.…”

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Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures

Aubin

Dalmedico

2002

Historia Mathematica

132

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Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined-"chaos." Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincaré who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-durée history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincaré to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as much as a sociodisciplinary convergence. C 2002 Elsevier Science (USA) Entre la fin des années 1960 et le début des années 1980, la reconnaissance du fait que des lois dynamiques simples peuvent donner naissanceà des comportements très compliqués aété souvent ressentie comme une vraie révolution concernant plusieurs disciplines en train de former une nouvelle science, la "science du chaos." Rapidement, les mathématiciens ont réagi en soulignant l'ancienneté de la théorie des systèmes dynamiques fondéeà la fin du XIXème siècle par Henri Poincaré qui avait déjà obtenu ce résultat précis. Dans cet article, nous mettons enévidence les tensions historiographiques issues de diverses confrontations: l'histoire de longue durée versus la notion de révolution, les mathématiques pures versus l'utilisation des techniques mathématiques dans d'autres domaines.1 A first version of this paper was delivered at the workshop "Epistémologie des Systèmes dynamiques," Paris, November 25-26, 1999. We thank the organizers and our colleagues from the sciences (and especially Yves Pomeau) for their useful comments. In the course of our research, interviews have been conducted and letters exchanged with various people; we thank in particular Vladimir Arnol'd, Alain Chenciner, Pedrag Cvitanovic, Monique Dubois, Marie Farge, Mitchell Feigenbaum, Micheal Hermann, Igor Gumowski, Edward Lorenz, Jacques Laskar, Paul Manneville, Paul C. Martin, Christian Mira, Mauricio Peixoto, David Ruelle, René Thom, and JeanChristophe Yoccoz. For their comments on parts of this paper, we thank Umberto Bottazzini, Philip J.

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Oscar II's prize competition and the error in Poincar�'s memoir on the three body problem

Cited by 20 publications

References 10 publications

The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

Stability of trajectories from Poincaré to Birkhoff: approaching a qualitative definition

Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures

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