Archive for History of Exact Sciences最新文献

The half-century from 1910 to 1960, fractured by two world wars, was marked by profound changes in the French society and its scientific institutions. The mathematician Joseph Pérès, who played a major role in these changes, stands out as one of the most remarkable personalities of the time. A student of Émile Borel at the École normale supérieure and of Vito Volterra in Rome, then professor in 1921, Pérès became the first director, in 1930, of the institute for fluid mechanics of Marseille, a foundation of the Ministry of Air. Two years later, he joined the institute for mechanics of Paris where, with Lucien Malavard, he developed electrical analogies for solving hydrodynamic problems, work rapidly acknowledged by academics and the aeronautical industry. Elected in 1942 to the French Académie des Sciences, he helped found in 1946 the International Union of Theoretical and Applied Mechanics (IUTAM) and became its first president. A highly respected figure in aeronautical circles, he helped create the Office national des études et recherches aéronautiques (ONERA). Appointed deputy director of the CNRS, he promoted scientific computing, founding and directing the Institut Blaise Pascal, matrix for French laboratories in applied mathematics and computer science. Dean of the Paris faculty of sciences from 1954 and faced with a considerable increase in the number of students, he created two new campuses in Paris and Orsay. A radiant personality and member of numerous learned societies, he also contributed to general reflection on the relationship between science and society, notably at the International Academy of the History of Science. He died in 1962, leaving behind him a remarkable body of work and the memory of a “smiling wisdom”. His work would have a major influence on the subsequent development of French research and teaching in the 1960s and beyond.

Évariste Galois is celebrated for his groundbreaking contributions to algebra and group theory, but his last published paper, containing two essays, has been largely ignored by historians. We will show that the first essay contains an incorrect proof of the statement that continuous functions are differentiable, due to several very naive mistakes. We will see that the second essay contains an elegant and novel derivation of the formula for the curvature of space curves. While the formula itself was already known to Euler and Cauchy, Galois’s method, which uses a family of planes, is strikingly original and conceptually insightful. This paper reevaluates both the historical and mathematical significance of Galois’s last publication, comparing it with his other minor manuscripts and challenging Neumann’s dismissal of its value in his edition of Galois’s works (Neumann 2011). By highlighting Galois’s overlooked contribution to differential geometry, this paper provides a fuller picture of his mathematical genius, thereby helping to avoid the Whiggish tendencies found in many studies of his work.

This study examines a remarkable passage in the Treatise on astronomy 天文志 (Tianwen zhi) of the New book of Tang 新唐書 (Xin tangshu), which offers a detailed textual description of a star chart traditionally attributed to the eminent Tang dynasty (618–907 CE) astronomer Yi Xing 一行 (683–727 CE). The chart adopts the gaitian 蓋天 (canopy heaven) model and is structured around three concentric circles delineating the twenty-eight lunar lodges 二十八宿 (ershiba xiu) and several prominent constellations. Its most striking feature is the depiction of the ecliptic as nearly elliptical rather than circular, a rare representation that distinguishes it among scientific star charts of ancient China. This paper provides a close analysis of the drawing techniques and geometric configuration of the ecliptic, arguing that accurate reconstruction requires an accurate understanding of the “ecliptic discrepancy” 黃道差數 (huangdao chashu), interpreted here as the difference in polar distance between a point on the ecliptic and its counterpart on the celestial equator at the same polar angle. Under this interpretation, the ecliptic naturally assumes a near-elliptical form. Beyond its geometric analysis, this study also investigates the cosmological assumptions embedded in the chart, suggesting that Yi Xing synthesized elements of both the gaitian and huntian 渾天 (sphere heaven) models into a complementary framework. This pragmatic and inclusive approach, characteristic of Tang dynasty astronomical thought, gradually evolved into a widely accepted view among later generations of calendar makers.

This article examines some constructions of conic sections found in a manuscript (UCLA, MS 170/624, fol. 85r) and attributed to Guidobaldo dal Monte. Following centuries of limited access to Greek sources in the Latin West, the sixteenth century saw a revival of interest in conics, spurred by translations of Apollonius and the work of figures such as as Commandino and Maurolico. Like other mathematicians of the period, Guidobaldo developed, or recovered from ancient sources, methods to draw conic sections. In doing so, he addressed both the theoretical needs of mathematics and the practical requirements of gnomonics, astronomy, and mechanics. The folio includes three geometrical constructions of the conic sections and a marginal note: “Del Galileo”, suggesting a possible link with Galileo Galilei. The article analyzes these constructions, highlighting both the theoretical rigor and practical intent of Guidobaldo’s approach. Particular focus is given to the construction of the hyperbola, which plays a key role in the solution of the Apollonian three circles problem, a topic Guidobaldo discussed in correspondence with Galileo. This problem is another example of the scientific relationship between Galileo and Guidobaldo, along with the study of the centers of gravity of solid figures, already described by the same authors in a paper published in 2022: “Galileo Galilei and the centers of gravity of solids: a reconstruction based on a newly discovered version of the conical frustum contained in manuscript UCLA 170/624”.

This paper analyzes Kepler’s ephemerides for 1604 and 1605, along with related documentation, in light of his evolving models for Mars. Drawing on known manuscripts, we present and examine Kepler’s calculations for both ephemerides—calculations that, although preserved in previously identified sources, have not yet been studied by scholars. By reconstructing these computations and analyzing the tables used as sources, we demonstrate that both ephemerides were based on a metopoid model, similar to the one described in chapter 46 of the Astronomia Nova. We also show that one of the tables used for the 1605 ephemeris contains a second table built under the model proposed in chapter 48. This case study captures a key moment in Kepler’s search for a physically grounded planetary theory, just before the final formulation of the Astronomia Nova.

This article observes and describes distinct stylistic registers that appear in the two main sections of Archimedes’ Quadrature of the Parabola. The correspondence between prose register and mathematical method indicates that in the mechanical propositions of the first section of Quadrature of the Parabola, as well as in several of his other treatises, Archimedes was purposefully deploying a unique style as a kind of rhetorical branding for his most innovative work. This Archimedean register may have been designed to be persuasive to a naturally resistant audience, or to draw mathematical theory into the world of daily experience without compromising its precision. Later authors who took inspiration from Archimedes also imitated his stylistic choices, and the Archimedean register became a signifier of mathematics that pushed the limits of conventional practice.

In this article, I examine how research on the foundations of quantum mechanics contributed to the development of quantum optics during the 1970s and 1980s. To this end, I draw on the scientific trajectories of two renowned physicists, John Clauser and Alain Aspect, both of whom were awarded the 2022 Nobel Prize in Physics for their experimental tests of Bell’s inequalities. These experiments, which rely on optical techniques, not only shed light on the debate between Bohr and Einstein on the interpretation of quantum mechanics, but also prompted Clauser and Aspect to conceive and carry out new experiments that directly addressed the quantum properties of light. I will explain the technical features of this shift, particularly Aspect’s source of entangled photons, which shows an instrumental continuity between his tests of Bell’s inequalities and his subsequent single-photon interference experiments.

In 2007, a trove of bamboo and wooden slips clandestinely smuggled out of China was sold to the Yuelu Academy of Hunan University by a Hong Kong cultural relics dealer. The following year, another small number of slips that later proved to belong to the same group were also donated to the Academy. These slips are believed to date from no later than 212 bce. Among the documents conveyed to the Yuelu Academy is a mathematical text, the 數 Shu (Mathematics), a character that appears on the verso of slip 01(0956) and generally regarded as the title of this work. The problems in the Shu can be divided into eleven distinctive types, namely: areas, fractions, military encampments, norms, grain conversions, proportional distributions, shao-guang ([method for] slightly [increasing] widths), volumes, excess and deficiency, right triangles (gou-gu), and taxation. The original collators of the Shu published photographs of a majority of the Shu slips along with transcriptions and notes concerning their contents in 2011; the rest appeared in 2022. In the course of the research presented here, each character on the Shu slips has been individually examined, special scribal marks have been identified, and their functions are explained. Also, each Chinese sentence has been carefully punctuated, resulting in a more readable version of the Chinese text. In what follows, the Shu is translated into English for the first time, with corresponding notes to help readers better understand the context of the Shu as well as many of the paleographic, philological, and various technical details necessary for a correct understanding of the translation. This work serves as a window into the evolution and development of Chinese mathematics during the pre-Qin and Qin periods, and thereby reflects the state of ancient Chinese mathematics at that time.

I show on the basis of unpublished sources how Hilbert’s conviction of the solvability of all mathematical problems originated from an engagement with Kant’s philosophy of mathematics. Furthermore, I consider other sense of the “solvability” or “decidability” of mathematical problems which Hilbert thought about later: decidability in finitely many steps, which is an issue Hilbert inherited from Kronecker, “finitistic decidability” which Hilbert develops by reflecting on Kronecker’s methodological strictures, and finally the decision-problem as raised by Behmann in the 1920s. I argue that these different preoccupations have different historical and biographical roots, and should also be kept conceptually distinct.

This article analyzes the fragments connected with Hipparchus' Star Catalogue (i.e., the fragment in the Codex Climaci Rescriptus, those in the so-called Aratus Latinus, and P.Aberd. 12) and compares them to the evidence provided by the Exegesis to the Phaenomena of Aratus and Eudoxus, the only work by Hipparchus that has reached us by direct tradition, to assess their value and what they can tell us about Hipparchus’ engagement with stars and star catalogues.