This study bridges a critical gap by formalizing the mathematical algorithms of the Ethiopian Orthodox Tewahedo Church's (EOTC) calendar, the Bahre Hasab. Despite its significance, these computations remain largely inaccessible, preserved in Ge'ez manuscripts and orally by ecclesiastical scholars (Alemiyan). Employing a qualitative approach with expert interviews in Tigray, this research systematically extracts and documents the core procedures. It elucidates the theological chronology of Amete Alem and deconstructs the hierarchical cyclical system of Abiy Qemer (532-year cycle) and Nius Qemer (19-year cycle) that manages solar-lunar discrepancies. The study formalizes algorithms for calculating key variables like Abeqte and Metqie and demonstrates their application through an algebraic system of Tewsak values to determine movable feasts. This work translates ancient knowledge into a standardized, reproducible format, preserving intangible cultural heritage and providing a vital resource for scholars and the global community.
This study investigates the pedagogical potential of incorporating historical content into Key Stage 3 mathematics education in England. Drawing on a structured framework emphasizing classical sources, historical development, biographies and anecdotes, and curriculum relevance, the intervention aimed to humanize mathematics and foster positive student attitudes. The research was conducted in a multicultural secondary school in England and involved both quantitative and qualitative methods, with pre- and post-intervention surveys and classroom observations forming the data corpus. The findings suggest that while anxiety-related and confidence-related responses showed limited change, students in the experimental group improved significantly in overall attitude scores, enjoyment of mathematics, engagement with historical content, and some measures of multicultural awareness. These results point to the value of history-infused mathematics education in improving affective outcomes and fostering deeper connections to the subject.
Thoralf Skolem (1887-1963) is rightly regarded as one of the most significant figures in modern logic, and is widely seen as the founding father of model theory. His groundbreaking results (most notably the jointly eponymous L & ouml;wenheim-Skolem Theorems) have shaped mathematical logic as we know it and have initiated ongoing philosophical debate for over 100 years. In this paper, we provide the first English translation of Sur la Port & eacute; du Th & eacute;or & egrave;me L & ouml;wenheim-Skolem. To accompany this translation, we also provide a foreword to help situate the paper in its proper historical and philosophical context.
To determine participation of the Italian and German delegations in the International Congress of Mathematicians (1940) and that of the German and American delegations in the IX Volta Conference (1939), the mathematicians of these three countries were to engage in a series of stress-tests of scientific diplomacy. The paper offers the reconstruction of what went on behind-the-scenes of these two non-events, focusing in particular on the plot of academic opportunism and rivalry between individuals and research institutions that characterized Italian mathematics in those years.
This article examines the contested status and evolving proofs of the Binomial Theorem in Britain during the period 1750-1830. Although universally acknowledged as true and widely used in calculus, algebra, and the theory of infinite series, the theorem's general proof remained a source of prolonged mathematical and philosophical debate. The authors investigate why over forty British publications from this era sought to re-prove or reinterpret the theorem, linking this phenomenon to broader shifts in mathematical rigour and the eventual decline of the Newtonian fluxional calculus. The paper analyzes challenges surrounding the multiplicity of binomial forms and exponents, the lack of accepted general principles governing infinite series, and deep unease over Newton's own inductive, non-proof-based approach. Despite its central role in British mathematical education and its celebrated association with Newton, the Binomial Theorem's exact scope and justification remained elusive for decades. The authors argue that the persistence of divergent proofs and unresolved doubts reflects a transitional era in British mathematics-one marked by growing awareness of foundational uncertainty and the influence of more rigorous continental methods. This study thus offers insight into how mathematical authority, legacy, and proof were contested concepts in Enlightenment and post-Enlightenment Britain.
Van Aubel's theorem states that if squares are constructed on the sides of a quadrilateral then the line segments joining the centres of the squares on opposite sides are equal and perpendicular. The main goal of this paper is to provide a translation of (Van Aubel, H, ['Note concernant les centres de carr & eacute;s construits sur les & ccirc;ot & eacute;s d'un polygon quelconque', Nouvelle Correspondance Math & eacute;matique, 4 (1878), 40-44].) paper in which this and other results are proven. The paper is interesting in its use of the method of equipollences developed by Giusto Bellavitis in 1835. From a modern perspective, the method combines vectors and complex numbers. Bellavitis knew about complex numbers but developed his system to avoid them as a given and instead provide a method that was fundamentally geometrical. What it means to be geometrical is certainly an educational issue arising naturally from reading Van Aubel's original paper. In that way, it can be very useful to teachers interested in using original sources in mathematics classrooms.
This article examines the posthumous reception of Sofya Kovalevskaya to explore how female genius was negotiated around 1900 at the intersection of neurology, sexology, biography, and scientific culture. Rather than reconstructing the historical Kovalevskaya, it analyses the discursively produced figure that emerged after her death. It begins with the dispute between Paul Julius M & ouml;bius and Gustaf Retzius over the localisation of mathematical talent, in which Kovalevskaya's preserved brain became evidence in competing claims about cerebral function and scientific authority. The article then contrasts degeneration theory, concepts of sexual intermediacy, and Otto Weininger's masculinised conception of genius. Read alongside biographies by Anna Charlotte Leffler and Laura Marholm, these debates reveal the unstable ways female scientific genius could be acknowledged within a discourse that continued to code originality and authorship as masculine.
This article examines historical methods for constructing the regular heptagon in the works of Abu al-Wafa al-Buzjani (940-998 CE) and Albrecht D & uuml;rer (1471-1528). The regular heptagon cannot be constructed with the classical Euclidean instruments of compass and straightedge; mathematicians and artisans developed practical approximation methods suited to geometric design. Drawing on Abu al-Wafa's Book on those geometric constructions which are necessary for a craftsman and Albrecht D & uuml;rer's Four books of measurement with compass and ruler (1525), this article reconstructs approximatin procedures within their respective historical contexts. The study shows that both scholars employed analogical reasoning, adapting geometric relations established in constructing the regular pentagon. The article introduces the notion of meta-analogy as a comparative instrument to examine structural similarities in theiranalogical strategies. A systematic comparison reveals how proportional reasoning and geometric transformation functioned as practical tools bridging theoretical geometry and artisanal practice, in Islamic and Renaissance applied geometry.
Recognising that gender and mathematics remains a topical issue, this paper considers the 'gendered spaces' of nineteenth-century mathematician Mary Somerville (1780-1872) through representations of her in poetry. Whilst Somerville features in histories of science about women and has attracted discussion due to the poetic nature of her scientific writing, there is little analysis of poetry written about her by contemporaries. Considering two such poems, one from poet William Sotheby (1757-1833) and one from mathematician William Whewell (1794-1866), this paper explores what they reveal about her and the culture of mathematics of the time. It proceeds to argue that in twenty-first century culture whilst qualitative space-time conditions have changed Somerville's contribution requires further repositioning.
In this study, we examine the early stages of the introduction of the theory of functions of a complex variable, also known as complex analysis, to Spain. We identify thirteen textbooks written by Spanish authors that present concepts that are currently framed within this mathematical theory, and trace the conceptual development that underpinned the subsequent publication of the first Spanish-language textbook exclusively devoted to complex analysis in 1907 by Luis Octavio de Toledo. Having identified all topics related to complex analysis within these documents, we conducted an in-depth analysis of how the concept of continuity is presented. To this end, we adapted three forms of mathematical knowledge production reported in the literature describing how complex analysis developed throughout history. Our research revealed different approaches to addressing the concept of continuity of a complex function and continuity of a complex variable through the use of algebraic expressions and figures.
Proponents of the history and pedagogy of mathematics (HPM) argue that the integration of the history of mathematics can help inculcate positive attitudes towards the study of mathematics. However, to the best of our knowledge, little has been done on the opportunity for the integration of the narrative accounts of the history of circle theorems. In this paper, senior high school students were exposed to a lesson that integrates a brief narrative of the history of Euclidean geometry with particular focus on Book III of the Elements. It was shown that students held positive beliefs and higher confidence about learning circle theorems after being exposed to the story of the history of the Elements. The findings imply that teachers could incorporate the history of mathematics concepts into lessons to promote students' attitudes towards learning. Further research is needed to investigate the effect that history-integrated instruction may have on students' performance in circle theorems and extend the study to other geometric topics.
In November 1842, Charles Babbage was devastated when informed by the British Prime Minister, Sir Robert Peel, that the Government would no longer finance the development of his Difference Engine. So when he learned that Ada, Countess of Lovelace, had translated Luigi Menabrea's account of his Analytic Engine to English, he seized upon this opportunity to publicize his grievances with the British Government. He collaborated with Ada to add significant notes to her translation, and to this, prefixed his account of his Difference and Analytic Engines and the Government's withdrawal of finance. But when the Scientific Memoirs editor refused to include the account of his conflict with the Government, Babbage promptly arranged for it to be published in the Philosophical Magazine and for offprints of this to be inserted into offprints of Ada's publication. This article examines the circumstances surrounding the compilation and circulation of these conjoint offprints.
This paper studies early attempts to extend the concept of continuity to functions of several variables during the first decades of the nineteenth century, focussing in particular on Augustin-Louis Cauchy's Cours d'analyse and Bernard Bolzano's Functionenlehre. The analysis combines a historical and philosophical reflection as well as technical issues regarding the formulation of this notion addressing how these authors grappled with foundational challenges at a time when even the notion of continuity for functions of a single variable was still undergoing consolidation. We trace the evolution of Cauchy's thinking on continuity and examine the theorems he formulated in this context, along with the difficulties they raise when interpreted through the lens of functions of several variables. Bolzano's contribution is then analysed in detail, with particular emphasis on his decomposition of change and his notion of simultaneous continuity, concepts that reflect a systematic effort to articulate the complexities involved in the continuity of functions of several variables. Despite their differences, both Cauchy and Bolzano ultimately approached the problem by reducing it to the behaviour of one variable at a time, a strategy that proved inadequate for addressing the full conceptual demands of the calculus of several variables. The paper thus highlights how these efforts illustrate the need for a deeper conceptual transformation, one that would only be fully realized in the second half of the nineteenth century.
Russia was devastated by the aftermath of the First World War and the Bolshevik Revolution that started in 1917. As a result, many people, particularly members of the intelligentsia, were forced to flee their country, prompting waves of migration. They were reasonably safe in some European countries and the USA, and the newly established Kingdom of Serbs, Croats, and Slovenes was one such destination. Here I discuss the case of two Russian mathematicians, Anton Bilimovich (1879-1970) and Nikolay Saltykov (1872-1961), who were established figures within the Russian scientific community, but upon arrival in Belgrade their status shifted immediately to that of refugees. Nevertheless, they promptly continued their scientific careers as integrated members of Yugoslav society, ultimately reaching the ranks of academicians of the Serbian Academy of Sciences and Arts, the highest academic distinction in Serbia to this day. Their lives in Yugoslavia were characterized by new beginnings and continuing with mathematical practices. I also argue that their arrival in Belgrade was mutually beneficial for them and for the state, since their contributions to the development of Yugoslav mathematics were substantial at a time when the country was struggling to establish its national identity.
