This paper attempts an improved classification of the Latin textsof the Elements printed between 1482 and 1703. It uses primarily a comparisonof the 114 terms defined within the text, supplemented by a comparison of thenumber of definitions included in each book and spot-check comparison ofportions of the text and diagrams. The result is a classification into fourteenfamilies. The process of classification permits some reflections on the degree towhich the Latin Euclidean vocabulary stabilized during this period, and on thepractices of the editors of these versions of the text, which prove to have been ina high proportion of cases eclectic, with definitions, enunciations, proofs anddiagrams frequently based on different sources or modified idiosyncratically,even in cases where a specific model was named in the paratext.
We discuss the emergence of Hilbert's 6th problem and Hilbert'spresentation of Bohlmann's axioms. An improved version of the axioms,which appeared in 1908, has been largely ignored by history. It overlaps withKolmogorov's "Grundbegriffe".
This article explores the daily life and career of Andreas B & ouml;hm(1720-1790), a Wolffian polymath who was professor of philosophy and math-ematics at the University of Gie ss en. B & ouml;hm represents the "ordinary" professorat work, and his career exemplifies the practice of mathematics in 18th-centuryGerman universities. He published several textbooks, trained local surveyors,edited a scholarly journal and even entertained scholarly correspondence witha German countess. Using a large set of archival sources, we follow the negoti-ation of his academic chair and document in detail his teaching activities-aswell as his lasting influence on surveying and practical geometry. By examiningB & ouml;hm's multifaceted career, the article challenges the notion of 18th-centuryuniversities as stagnant, instead portraying them as dynamic centers of mathe-matical education and expertise, deeply embedded in the needs of local societies
- In 1892, the French mathematician Louis G & eacute;rard defended a thesis on non-Euclidean geometry at the Facult & eacute; des Sciences in Paris. After the work of De Tilly and Flye Sainte-Marie published in the early 1870s, this was the most important work published on this subject in French. G & eacute;rard presented a new method for founding non-Euclidean trigonometry. He also solved numerous construction problems and presented a theory of polygon area in Euclidean and non-Euclidean geometry. G & eacute;rard's thesis is an original work, unparalleled in France at the time. It bears witness to the rising standards of rigor observed in the last decade of the 19th century, in conjunction with a growing interest in axiomatics. It enriched the corpus of non-Euclidean geometry with new results. It also illustrates the scientific activity of a high school teacher at the end of the 19th century.
The emerging discipline of mathematical analysis exhibited various threads during the nineteenth century, with different values and priorities as to basic definitions and approaches being used in different national and local contexts. In this paper we examine the "concrete" analysis of Charles Her-mite, looking at its roots in his own research and the developing pedagogical versions of it that appeared in his courses and the work of certain of his students.
- Edmond Laguerre and Charles Hermite are both French mathematicians of the 19th century. They shared a common professional background in various institutions and the way they did mathematics. They were both interested in the subject of polynomial equations and we shall see in this article what role Hermite played in Laguerre's works. We describe how the results published by Laguerre emphasized the importance of Hermite. A last part deals with common points and similarities between the approaches of Laguerre and Hermite. More globally, we show that they had comparable conceptions of var-ious issues: about the question of generality in mathematics and about interac-tions between calculus and algebra.
This paper considers the beginnings of a theory of invariants in the early 1850s in the broader contexts of individual pathways toward the establishment of reputation and of the professionalization of mathematics in the nineteenth century. In particular, it treats the different, but intersecting, mathematical paths by which two Englishmen, Arthur Cayley and James Joseph Sylvester, and one Frenchman, Charles Hermite, came to focus on an analysis per se of the transformation of homogeneous forms by linear substitutions. It then looks at the intense mathematical exchanges in the first half of the 1850s that resulted in their early invariant-theoretic results. Although by the close of the 1850s, Cayley, Hermite, and Sylvester had largely gone their own separate mathematical ways, the three remained united in their sense of having created what they called the "New Algebra."
- Mihailo Petrovic, the founder of the first school of mathematics in Serbia, was one of the first foreigners to be chosen as an "internal student" ("& eacute;l & egrave;ve interne") at the prestigious & Eacute;cole normale sup & eacute;rieure in France. After graduation, he decided to stay in Paris and complete his doctoral thesis on differential equations entitled "Sur les z & eacute;ros et les infinis des int & eacute;grales des & eacute;quations diff & eacute;rentielles alg & eacute;briques," defended on June 21, 1894 at the University of Paris before the examination committee composed of Charles Hermite, & Eacute;mile Picard and Paul Painlev & eacute;. He thus became one of the first six doctors of mathematical sciences in Serbia. This paper looks into Petrovic's education at the & Eacute;cole Normale Sup & eacute;rieure in Paris and the influence of his professors on his academic work. Also, this paper focuses on how Petrovic brought the spirit of modern European mathematics to Serbia and set the direction of the development of mathematics in Serbia based on the model of French mathematics.
This paper presents a commented edition of the letters from August Gutzmer to Francisco Gomes Teixeira, a Portuguese mathematician, present in the Coimbra Archive of correspondence sent to Gomes Teixeira. These detail the relationship between the two mathematicians, shedding a new light on the correspondence network established by Gomes Teixeira throughout his life.
The theme of the unity of mathematics developed during the nineteenth century as specialized articles proliferated and it has often been associated for this period with the definition of new types of mathematical objects in a structuralist setting. This article focusses on the almost opposite point of view of Charles Hermite. Although his work was praised by his contemporaries for beautifully contributing to and displaying the unity of mathematics, he himself strongly opposed the idea of free conceptual creation in mathematics and favored explicit, extensive computations with algebraic forms and classical functions. Hermite's way of testifying to the unity of mathematics must thus be reconstructed by a close reading of his papers, here based on a focus on a few keywords. The result appears proteiform; Hermite operates sometimes by constructing bridges within mathematics through formulas, sometimes by recycling and adapting well-known algebraic expressions, and even occasionally by providing alternative proofs of a theorem. The coherence of these practices with Hermite's general viewpoint on mathematics leads us to advocate for a richer history of the problem of the unity of mathematics.
This paper tackles the issue of Charles Hermite's style of writing. The approach, supported by the techniques of statistical textual data analysis, is quantitative and comparative, the chosen point of comparison being Camille Jordan. Two main facets of the notion of style are scrutinized. On the one hand, the investigation focuses on lexical richness, with a particular stress on lexical diversity and the use of hapaxes, that is, words appearing only once in each corpus. On the other hand, specificities of words and of grammatical categories are examined. It is shown that Hermite's prose is characterized by a higher lexical diversity than Jordan, and reflects a lively mathematical narration where the first person and other words which describe the mathematical processes are of great importance.
