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The formula $${2\over \pi} = 1 - 5 \cdot \left({1\over 2} \right)^{3} + 9 \cdot \left({1 \cdot 3\over 2 \cdot 4} \right)^{3} - \cdots$$2π=1−5⋅(12)3+9⋅(1⋅32⋅4)3−⋯ was famously included as a discovery in Ramanujan's first letter to Hardy in 1913, and has been referred to as the Bauer–Ramanujan formula, in view of Bauer's 1859 proof of the above formula. There is a rich history associated with this formula and its many and dramatically different proofs, including a computer-based proof due to Zeilberger that may be seen as groundbreaking in the history of computer-assisted proofs. In addition to a complete survey we provide of all known proofs of the Bauer–Ramanujan formula, we introduce historical analyses based on these proofs, by arguing that the history of the Bauer–Ramanujan formula and our account of this history may be seen as being representative of much broader trends in the history of mathematics. In this regard, the earlier proofs tend to rely on one of the oldest and most basic tools in classical analysis, namely, interchanging the order of limiting operations. In contrast, the more modern proofs tend to rely on computer-related approaches toward summation problems, as in with Zeilberger-type and Gosper-type telescoping arguments. [ABSTRACT FROM AUTHOR]

Literature has emphasized the value of multidisciplinary learning strategies and the necessity of educating students to solve complex problems. It also pointed out the importance of teacher's beliefs in their practices. The purpose of this study is to understand how future teachers recognize the board game Caravelas as a didactic tool to help elementary school students develop math skills in History and Geography Portugal (HGP) classes, in a multidisciplinary way. A board game intervention was employed in the study, and both quantitative and qualitative data were gathered from sixteen future teachers enrolled in the Didactic of HGP course during their third year of the Basic Education programme. Two questionnaires were used along with a focus group discussion. The findings indicate that this group of future teachers thinks Caravelas can help students achieve their learning goals in mathematics and HGP, as well as develop their reasoning, problemsolving, and social skills. Future teachers believe Caravelas can be used as a didactic tool to integrate mathematics into HGP subjects and support multidisciplinary learning. [ABSTRACT FROM AUTHOR]

The article investigates a little‐known work titled De ponderibus et mensuris [On Weights and Measures] written by Juan de Mariana in 1599. It contains the embryo of his future monetary theories, and has other interesting aspects, not only juridical and historical but also epistemological. Significant points of convergence with the early modern mathematics and abacus tradition make it unique. Apart from its stylistic, pedagogical and technical originality, this work also appears as a watershed for the evolution of economic science, its language and methodology. [ABSTRACT FROM AUTHOR]

Mathematical problem solving remains a struggle for many students today (Celebioglu et al., 2010; Englard, 2010; Gavaz et al., 2021; N. H. Lee et al., 2014; Yeo, 2011). Though intervention studies have reported measured impact on improving students' problem-solving abilities (Gavaz et al., 2021; Gidalevich & Kramarski, 2019; N. H. Lee et al., 2014), few studies examine how learners would approach a non-routine problem without learning problem-solving strategies in school (Celebioglu et al., 2010; Saygılı, 2017; Yazgan, 2015; Yeo, 2011). The latter would complement instruction related to strategies by making known the entry point of young problem solvers. In this study, 10 Grade Two students in a neighborhood primary school in Singapore were individually engaged in solving a non-routine problem with access to manipulatives. Based on their mathematics instructional history in school, the students have not been introduced to the relevant problem-solving strategies related to the task. The study examines how the students approach and solve the problem. Findings revealed that all the ten students were able to solve the problem with eight of them using manipulatives to help them. The study recommends that prior to classroom teaching, teachers can invite students to share their problem-solving methods and demonstrate how formal notations can capture these mathematically. Appropriate manipulatives should also be made accessible during problem-solving lessons. [ABSTRACT FROM AUTHOR]

Although Hegel is generally not known as a philosopher of mathematics, he maintained a deep interest in the history of mathematics, especially in its transformations between antiquity and the modern age. Charles S. Peirce, who was the son of a distinguished mathematician and was involved in developments in mathematics in the second half of the nineteenth century, was critical of what he perceived as Hegel's lack of mathematical acumen. Nevertheless, he recognized in Hegel's Science of Logic structural features of his own mathematically informed philosophy. In this article, I look to Hegel's discussion of magnitude in The Science of Logic , and especially to his conception of the relation between continuous and discrete magnitudes, in order to articulate a solution he might have offered to difficulties encountered by Peirce in his opposition to Cantor's set-theoretical analysis of the continuum. It is argued that Hegel's interest in the ancient Platonic/Pythagorean tradition in mathematics provided him with crucial resources in this regard. [ABSTRACT FROM AUTHOR]

I argue that Gilles-Gaston Granger (1920–2016) broadly incorporates the central affirmations of Jean Cavaillès's (1903–44) philosophy of the concept into his own epistemological program. Cavaillès and Granger share three interrelated epistemological commitments: they claim (1) that mathematics has its own content and is therefore autonomous from and irreducible to logic, (2) that conceptual transformations in the history of mathematics can only be explained by an internal dialectic of concepts, and (3) that the objectivity of mathematics is an effect of the productive form of its rationality—that is, they claim that mathematical objectivity is the result of a generative process internal to mathematics. Mathematical objectivity, as I demonstrate, requires Cavaillès and Granger to modify the limits of epistemological critique as envisioned by Kant. For Cavaillès, this modification requires the elimination of the transcendental in favor of a dialectic of concepts. For Granger, the philosophy of the concept remains a genre of transcendental critique, but in a radically revised "Ptolemaic" style. I initially demonstrate how Granger extracts each of these claims from Cavaillès. I then follow Granger as he develops these claims in the service of a novel description of the content and structure of mathematical objectivity. [ABSTRACT FROM AUTHOR]

The research on the interpretation of mathematics as part of the sciences of mind, introduced as 'Geisteswissenschaften' in the German philosophy, reflects the relationship between mathematics and arts, including architecture. This study focuses on the early works of the philosopher Max Bense where he described the contours of an intellectual history of mathematics related to philosophy. He pointed out strong relationships between mathematics and all areas of human creation abilities. In particular, his investigations on the relationship between arts, including architecture, and mathematics in important historical phases reveal that the mathematics of an age is reflected aesthetically in the artistic styles or theories of art. His thesis posits that a high point in mathematics corresponds to a high point in art. Later on, Bense developed an aesthetic theory on the basis of mathematics, semiotics and information theory. [ABSTRACT FROM AUTHOR]

This study examines the outcomes of implementing a teaching unit that integrates problem-solving with the history of mathematics to improve fifth-grade students' understanding of fractions at an educational institution in Yopal, Colombia. Utilizing an educational action research methodology, the study commenced with a diagnostic assessment to identify learning gaps, followed by the design and implementation of a didactic unit. This unit comprised three activities embedded in historical contexts to facilitate the learning of fractions, with its effectiveness assessed through an exit test. Conducted with 32 fifth-grade students, the research employed diagnostic and exit tests to evaluate student performance before and after the activities. The results demonstrated that the teaching unit significantly enhanced students' abilities to understand and apply fractions, as evidenced by their improved performance in the activities within the didactic unit.

With the advent of Transformer-based generative AI, there has been a surge in research focused on large-scale generative language models, especially in natural language processing applications. Moreover, these models have demonstrated immense potential across various vertical fields, ranging from education and history to mathematics, medicine, information processing, and cybersecurity. In research on AI applications in Chinese, it has been found that the quality of text generated by generative AI has become a central focus of attention. However, research on the quality of input text still remains an overlooked priority. Consequently, based on the vectorization comparison of vertical field lexicons and text structure analysis, proposes three input indicators D1, D2, and D3 that affect the quality of generation. Based on this, we studied a text quality evaluation algorithm called VFS (Vertical Field Score) and designed an output evaluation metric named V-L (Vertical-Length). Our experiments indicate that higher-scoring input texts enable generative AI to produce more effective outputs. This enhancement aids users, particularly in leveraging generative AI for question-answering in specific vertical fields, thereby improving response effectiveness and accuracy. [ABSTRACT FROM AUTHOR]

"Numbers and the World: Essays on Math and Beyond" by David Mumford is a collection of essays that covers a wide range of topics, from mathematics to neuroscience, artificial intelligence, history, and social issues. Mumford, a highly acclaimed mathematician, offers his unique and creative perspectives on these subjects. The book is not a technical exposition of his mathematical work, but rather a collection of his thoughts and musings, originally posted on his blog. Mumford's writing style is clear and accessible, making this book an interesting read for both mathematicians and non-mathematicians alike. [Extracted from the article]

Unconstrained optimization problems have a long history in computational mathematics and have been identified as being among the crucial problems in the fields of applied sciences, engineering, and management sciences. In this paper, a new variant of the conjugate descent method for solving unconstrained optimization problems is introduced. The proposed algorithm can be seen as a modification of the popular conjugate descent (CD) algorithm of Fletcher. The algorithm of the proposed method is well-defined, and the sequence of the directions of search is shown to be sufficiently descending. The convergence result of the proposed method is discussed under the common standard conditions. The proposed algorithm together with some existing ones in the literature is implemented to solve a collection of benchmark test problems. Numerical experiments conducted show the performance of the proposed method is very encouraging. Furthermore, an additional efficiency evaluation is carried out on problems arising from signal processing and it works well. [ABSTRACT FROM AUTHOR]

The catenary is a curve that has played a significant role in the history of mathematics, finding applications in various disciplines such as mechanics, technology, architecture, the arts, and biology. In this paper, we introduce some generalizations by applying the variational method to deformable strings. We explore two specific cases: (i) in the first case, we investigate the nonlinear behavior of an elastic string with variable length, dependent on the applied boundary conditions; specifically, this analysis serves to introduce the variational method and demonstrate the process of finding analytical solutions; (ii) in the second case, we examine a deformable string with a constant length; however, we introduce mass redistribution within the string through nonlinear elastic interactions. In the first scenario, the deformation state of the string always describes elongation, as compression states prove to be unstable for fully flexible strings. In contrast, in the second scenario, the finite length constraint induces compressive states in specific configurations and regions of the string. However, it is worth noting that the solution to this problem exists only for values of the elastic constant that are not too low, a phenomenon that is studied in detail. We conduct here both analytical and graphical analyses of various geometries, comparing the elastic behavior of the two aforementioned types of strings. Understanding the elastic behavior of deformable strings, especially the second type involving mass redistribution, is crucial for enhancing comprehension in the study of biological filaments or fibers and soft matter. For instance, these investigations can contribute to understanding the mechanisms employed by cells to sense gravity or other mechanical conditions. [ABSTRACT FROM AUTHOR]

After graduating from the Mathematics Department of Darülfünun in 1911, Hasan Fehmi [Çayköy] worked as a mathematics teacher in distinguished high schools such as Kabataş High School, Mercan High School, Girls’ Teacher School and Darüşşafaka High School. Hasan Fehmi, who closely followed national and international scientific articles and had a close relationship with the teachers of the Mathematics Department, published articles in numerous journals such as Talebe Mecmuası, Riyaziyyat, and Darülfünûn Fünûn Fakültesi Mecmuası. As a teacher, it is noteworthy that he was so interested in scientific publications. Hasan Fehmi, one of the two teachers whose articles were published in the Darülfünûn Fünûn Fakültesi Mecmuası, was the fifth most published person, with six articles published between 1916 and 1917. The transliteration and mathematical evaluation of these articles, which were titled “Küre Hacminin Bi’l-Cebr İstihrâcı”, “Hendese Meselesi”, “Müsellesât [1]”, “Bir Gâye Meselesi”, “Müsellesât [2]” and “Cebir” respectively, were carried out within the scope of this study. According to the findings, these articles introduced and proved particular mathematical problems at the undergraduate level. These proofs used the basic rules of arithmetic and geometry, where no original approach was found. [ABSTRACT FROM AUTHOR]

This special issue of the Journal of Optimization Theory & Applications focuses on the work of Professors Cornelis Roos and Florian A. Potra in the field of optimization. The issue includes a biographical sketch of both professors, highlighting their achievements. The papers in the special issue cover various topics such as conic optimization, interior point methods, proximal methods, convex optimization, and stochastic optimal control. The authors of the papers have close connections to Professors Roos and Potra, either as students, visitors, or co-authors. The document is a compilation of research papers on interior-point methods (IPMs) and their applications in optimization and conic programming. The papers cover theoretical developments of IPMs, algorithms for linear complementarity problems (LCPs), weighted LCPs, and sufficient linear complementarity problems. There are also papers on new computational approaches for IPMs, applications of IPMs in different fields such as mechanics and support vector machines, and the theory and application of conic optimization. The document also includes papers on proximal methods for convex and non-convex problems, as well as papers on convexity and convex optimization. The volume concludes with acknowledgments to the authors, reviewers, and editor-in-chief. [Extracted from the article]

Mustafa Salim [Tunakan] was a significant mathematician who flourished during the final years of the Ottoman Empire. He imparted knowledge of algebra, integration and machine theory at the universities of this period. In addition to his textbooks in these fields, he published one article in Osmanlı Mühendis ve Mimar Cemiyeti Mecmuası, one article in Mühendis Mektebi Mecmuası, two articles in Genç Mühendis and seven articles in Darülfünun Fünun Fakültesi Mecmuası. The aim of this study is to make a mathematical analysis of all of Mustafa Salim's articles published in the field of mathematics in the journals named Osmanlı Mühendis ve Mimar Cemiyeti Mecmuası, Mühendis Mektebi Mecmuası and Genç Mühendis. For this purpose, Mustafa Salim's four articles published in these journals were initially translated into Latin letters, after which mathematical analyses were conducted on the topics covered in the articles. In these articles; Mustafa Salim defined and solved problems at undergraduate levels in the subjects of integral, differential calculus, linear algebra, functions and geometric location. Mustafa Salim, who adopted a very simple and concise narrative style, did not make any mathematical mistakes in his articles, except for a few minor errors. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Considering the content of history of mathematics textbooks, it's evident that their emphasis is primarily on the illustrative aspects of recurring numerical sequences, with a particular focus on the Fibonacci sequence. Unfortunately, this limited approach results in the neglect of other sequences akin to the Fibonacci numbers, thus rendering the subject challenging for teaching purposes. This study aims to address this gap by offering a concise exploration of the combinatorial aspects of the Padovan numbers, specifically through the concept of a board as initially examined by mathematicians. In line with the research methodology of didactic engineering and the teaching theory of the theory of didactic situations, two problem situations have been developed, centered on the Padovan combinatorial model, thereby contributing to the enrichment of mathematical education within initial teacher training programs. Within this framework, various strategies are introduced that rely on visualization and counting, with the objective of illustrating specific mathematical identities suitable for potential classroom applications. [ABSTRACT FROM AUTHOR]

This article discusses the historical approach to the philosophy of mathematics, with a focus on the influence of philosopher Imre Lakatos. The author, Donald Gillies, argues that Lakatos played a significant role in introducing historical approaches to the philosophy of mathematics, although he was not the first to do so. Gillies examines various works that cite Lakatos and explores the impact of the historical approach on the field. He concludes that historical approaches to the philosophy of mathematics have produced valuable insights and should be considered a progressive research program. [Extracted from the article]

The article "Mathematics and Literature" deals with the relationships between mathematics and literature. It emphasizes that the study of mathematically relevant literature can contribute to the social history of mathematics. Literary studies use mathematical terms and methods, and mathematics can also help in the creation of new literature. The importance of fiction for the social history of mathematics is discussed, and various examples of mathematicians who were also involved in writing are mentioned. The text emphasizes the importance of promoting interest and understanding in mathematics and shows that mathematicians are not always dry and detached from the world. It also addresses literature about mathematics and mathematicians and discusses the connection between mathematics and literature. [Extracted from the article]

This article discusses a collaboration between mathematician and poet Sarah Glaz and collage artist Mark Sanders, who created a poem and collage inspired by Claudius Ptolemy's influential treatise in astronomy, Almagest. The poem, titled "Ptolemy's Almagest: Book I," is a found poem formed by Glaz from the introduction and table of contents of Almagest: Book I. The collage, also titled "Ptolemy's Almagest: Book I," reflects and extends the imagery and ideas in the poem. The article provides background information on Ptolemy, the city of Alexandria, and the decline of the Golden Age of Greek Mathematics. It also discusses Almagest and its geocentric model of the universe. The collage incorporates imagery related to Ptolemy's work in astronomy and geography, as well as references to other astronomers such as Copernicus and Tycho Brahe. [Extracted from the article]

The article discusses Oxford's History of Mathematics Forum, which was established in 2001 and has held nearly 200 meetings. The forum provides a platform for mathematicians and historians to share their work and ideas, covering a wide range of topics from ancient mathematics to current research. The group was formed in honor of mathematician John Fauvel and aims to promote the social element of academic work. The forum has adapted to the COVID-19 pandemic by transitioning to online seminars, but has recently returned to in-person meetings to maintain its informal and social character. [Extracted from the article]

Vito Volterra, an influential Italian mathematician, played a significant role in the rise of Italian mathematics after the country's unification in 1861. However, his career took a downturn under the Fascist regime. Volterra refused to pledge allegiance to the regime and was subsequently removed from his position as a university professor. Despite his contributions to mathematics, Volterra was largely forgotten in Italy until the availability of his letters in the 1970s shed new light on his research and public influence. Volterra's life serves as a lens to examine the trajectory of Italian science during this period. [Extracted from the article]

The article discusses a book titled "Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books," edited by Philip Beeley, Yelda Nasifoglu, and Benjamin Wardhaugh. The book contains eleven essays that examine the intellectual and physical practices of mathematical writing, publishing, and reception. The essays cover a range of topics, including the use of diagrams, the history of mathematical libraries, the annotation of mathematical texts, and the challenges of publishing scholarly editions of classical mathematical authors. The book provides valuable insights into the history of mathematics and its relationship with material texts. [Extracted from the article]

Universal presentations and interpretations of the history of mathematics have now been challenged, identifying the need of resurrecting hitherto marginalized contributions. In such studies, cognitive factors influencing the related development trajectories play a crucial role. Different societies would have had different mathematical cognitions contributing to the development of distinct forms of mathematics. This study attempts to surface the related cognitive contents of using large numbers. The principal source used for the study—the Buddhist Commentaries—determines the period and region covered. As such, it explores the conditions prevailed in 5th century CE (approximately) in Sri Lanka. 2000 Mathematics Subject Classification (MSC 2000) code: 01A07 [ABSTRACT FROM AUTHOR]

This article describes significant contributions of OSU professors Arnold Ross, F. Joe Crosswhite, and others, who played key roles in providing access to appropriate mathematics for all students. Behind-the-scenes stories and personal anecdotes from the Ukraine to the OSU campus reveal how they laid the groundwork for improving the way mathematics is currently taught and the preparation of those who teach it, especially with regard to equity and technology. The article provides an insightful look into OSU’s lasting impact on mathematics education. [ABSTRACT FROM AUTHOR]

The article is a review of two books by John Stillwell: "Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether" and "The Story of Proof: Logic and the History of Mathematics." The reviewer acknowledges that Stillwell's works may not be directly relevant to modeling and applied mathematics, but praises his writing skills. The review discusses the content and structure of "Algebraic Number Theory for Beginners," noting that it may not be suitable for beginners due to unclear prerequisites and a lack of depth in certain topics. The reviewer also briefly mentions the overlap between algebraic number theory and elementary number theory. The review concludes with a brief mention of "The Story of Proof," describing it as a senior-level book on logic and the history of mathematics. [Extracted from the article]

This article tells the story of the first international topological conference in Moscow (1935), an outstanding event that, for the first time, brought together the most notable American, European, and Soviet mathematicians, including those who would later play decisive roles in the mathematization of economics: John von Neumann, Leonid Kantorovich, and Albert W. Tucker. The fact that Kantorovich was in contact with von Neumann and his closest colleagues, Solomon Lefschetz and Garrett Birkhoff, is hardly appreciated in the histories of mathematics and mathematical economics. Their brief academic exchange was interrupted by the increasing international isolation of Soviet mathematics and by the wars that ensued. The article provides a historical account of the conference and traces the intellectual and personal affinities of Soviet and non-Soviet mathematicians, as well as their conceptual innovations. It argues that the conference, as a singular event linking several research communities, mattered for the development of various formal frameworks and their dissemination, contributing to the intellectual landscape in which postwar mathematical economics could emerge. The article calls for a deeper analysis of conceptual affinities and motivations in applying mathematics to economics and for a more nuanced narrative linking these motivations to social and political contexts of economic modeling. [ABSTRACT FROM AUTHOR]

This article explores the problem of finding the fastest descent path under uniform gravity, known as the brachistochrone curve. The traditional method involves using variational calculus, but the authors propose a simpler approach using straight lines. By dividing the path into segments and calculating the time for a particle to cover each segment, a curve resembling the brachistochrone can be found. This alternative method helps students understand kinematical and dynamical concepts and introduces them to mathematical optimization. The article also discusses the properties of the cycloid curve and provides equations for calculating the descent time. The authors compare their method to the analytical solution and suggest that prior knowledge of the solution can improve accuracy. [Extracted from the article]

Luca Pacioli (ca. 1447–1517) is widely considered a central figure in the Italian Renaissance, particularly in the history of practical mathematics. The perspectival representations of geometrical bodies that Leonardo da Vinci drew for Pacioli's Compendium de divina proportione are, in turn, often singled out to illustrate the relationships between the visual arts and mathematics in the late fifteenth century. Yet despite increasing scholarly attention, the philosophical framework of Pacioli's works deserves to be further explored. This paper discusses how Pacioli ably developed his arguments on regular geometrical bodies by relying on a predominantly Aristotelian philosophical framework. In this way, Pacioli established correlations among the quantitative, material, and formal properties of regular geometrical bodies, concluding with the visualisation of their (geometrically defined) form at the level of the intellect. [ABSTRACT FROM AUTHOR]

In the academic world, there are also gender inequalities, which are especially visible in certain masculinized STEM areas, such as physics and mathematics. An essential factor in correcting these inequalities is the involvement of men, who should act as "allies" in the university setting. Likewise, as the literature shows us, we must offer models with gender-incongruent roles to break down stereotypes and promote non-traditional behaviors. However, to date, these actions have been especially directed toward women, who generally do not hold power and therefore have less possibility of promoting change. For the first time, this work compiles, in a single document, important male physicists and mathematicians who acted as allies of women throughout history. These examples can be presented to provide male references in the teaching of physics and mathematics at university (and high school). With this initiative, we intend to contribute to incorporating the gender perspective in university teaching, since, in practice, university professors are unaware of references of alternative masculinities in the academic world. We hope that this article will be the seed to recover hidden male allies in these and other scientific fields. This can help break down stereotypes, and contrary to previous actions, this work is especially directed toward men. [ABSTRACT FROM AUTHOR]

Recognizing the omnipresence of mathematics across various contexts, this paper addresses the untapped potential of museums as rich venues for informal mathematics learning beyond traditional educational settings like classrooms. This paper presents the InformalMath program, designed for the professional development of primary and middle school teachers using integrating mathematics education within art and history museums through designing mathematics visit workshops. Specifically, the focus is placed on Phase 1 of the program, in which teachers participated in two informal mathematics education workshops at two museums in Turin, Italy, and were asked to reflect on their participation through a written essay. The analysis of the essays reveals significant engagement, appreciation of mathematics as a cultural artifact, and the emergence of creativity and inclusion among participating teachers. These findings highlight the benefits of such interdisciplinary approaches in enhancing mathematical understanding and pedagogical strategies. Conclusions emphasize the program's success in not only enriching teachers' instructional repertoire but also in promoting a more holistic, engaging, and contextualized approach to mathematics education, suggesting a promising avenue for future educational practices and research in informal learning environments. [ABSTRACT FROM AUTHOR]

Copyright of Revista Góndola, Enseñanza y Aprendizaje de las Ciencias is the property of Gondola, Ensenanza y Aprendizaje de las Ciencias and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Generative AI systems designed to produce text do so by drawing on inferences made from training data, which may mean they reproduce factual errors or biases contained in that data. This process is illustrated by querying ChatGPT with questions from a history of mathematics quiz designed to highlight the common occurrence of mathematical results being misattributed. ChatGPT's performance on a set of decades-old common misconceptions is mixed, illustrating the potential for these systems to reproduce and reinforce historical inaccuracies and misconceptions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss the emergence of recursive thinking through the famous problem posed by Fibonacci regarding the growth of the rabbit population. This paper qualitatively analyzes and discusses the semiotic aspects raised by the students working with this historical source in the form of a story. From this perspective, the value of the historical problems as socio-cultural references (voices) and of the narrations as mediating factors to enhance students' learning of new mathematical concepts, such as recursion, is explored in depth. The focus lies on the pivotal role played by the students' construction of personal senses during in-group mathematical activities, in dialectics with the normative and mathematical meanings. It is highlighted that fostering environments conducive to dialogue among peers, as well as linking various shapes and contexts of knowledge, is necessary. Here, storytelling and history are regarded as fruitful resources aiding students in the gradual construction of a personal sense of mathematical concepts, including recursion. [ABSTRACT FROM AUTHOR]