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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]

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]

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]

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]

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 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]

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]

We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. In this MSS, Fibonacci systematically describes finding the integer part of the square root of an integer in numerous examples with three to seven decimal digits. The results of these examples are summarized in a table in the paper. Liber Abaci also describes in detail finding an approximation to the fractional part of the square root. However, in other examples in Liber Abaci and De Practica Geometrie, only the approximate values of the fractional part of the square roots are stated. This paper further explores these approximate values using techniques like reverse engineering. Contrary to many claims that Fibonacci also used other methods or approximations, we show that all examples can be explained using one digit-by-digit method to compute the integer part of the square root and one approximation scheme for the fractional part. Further, it is shown that the approximation scheme is tied to the method to compute the integer part of the square root. [ABSTRACT FROM AUTHOR]

The article "Issue 32(1)" in the Communications of the German Mathematical Society (DMV) covers various topics such as the DMV Student Conference 2024 in Ilmenau, the significance of mathematics in museums, job opportunities for mathematics graduates, and the name of the DMV. The president of the DMV emphasizes the need to attract more and younger members and to make greater efforts towards women and diversity. It also reports on the discussion about renaming the DMV, for which suggestions from members are being collected. The 2023 PISA study shows that the average mathematical and reading competencies of adolescents in many OECD countries have declined compared to the previous study in 2018. Scientific competence has also decreased. In Germany, the performance losses in all three areas are above average. The reasons for the deterioration are mainly attributed to the effects of the COVID-19 pandemic, as well as language difficulties, interest, and motivation. The exhibition "From Newton to Einstein - a journey through space and time" was developed at the Max Planck Institute for Gravitational Physics in Potsdam and is now on display in Tübingen. The award winner Carla Cederbaum has also developed other projects, such as a book on mathematical magic tricks and the publication series "Oberwolfach-Snapshots of Modern Mathematics". Mathematicians Carolin Mehlmann and Thomas Richter from the University of Magdeburg participated in an expedition of the Polarstern to the Arctic Ocean to calibrate a new hybrid sea ice model. The hybrid sea ice model combines particle and continuum methods to better resolve the different sea ice regimes on different local scales. The text deals with the deformation theorem in differential geometry. It is shown that a manifold with boundary possesses a metric with certain properties if the double of the manifold carries such a metric. The question of whether the converse of this statement holds is also raised. The text deals with hypothesis testing and the problem of multiple error probability. Various methods for solving this problem are presented, including the Bonferroni correction and the development of better methods taking into account the dependency structure of the tests. It also addresses pseudoline arrangements, which have connections to combinatorics, geometry, and computer science. The text deals with various mathematical topics, including sorting networks, pseudoline arrangements, Rubik's cube, the PISA study, calculating machines, student studies, Felix Klein, and international cooperation in mathematics. Various concepts and applications are explained, such as the creation of sorting networks from pseudoline arrangements, the use of Markov chains to generate random pseudoline arrangements, and the development of calculation aids and calculating machines. The importance of student studies and international cooperation in mathematics is also emphasized. The text provides an insight into various mathematical topics and their applications. The article reports on Renate Tobies, a visiting scientist at Friedrich Schiller University Jena. She studied chemistry and mathematics and obtained her habilitation in the history of mathematics and natural sciences. Tobies has taught in various German cities and in Austria and was the managing editor of NTM History and Ethics of Natural Sciences, Technology, and Medicine. The article deals with a position paper by the professional societies DMV. [Extracted from the article]

theory is examined, highlighting his approach to teaching the subject and the impact it had on the field of mathematics. The author discusses Klein's emphasis on the historical development of the theory and his use of concrete examples to illustrate abstract concepts. The study provides insight into the pedagogical methods employed by Klein and their influence on the teaching of mathematics. [Extracted from the article]

This document is a collection of postage stamps from around the world that feature mathematicians, mathematical concepts, and related topics. The stamps are presented in chronological order and provide a visual representation of the history of mathematics. Each stamp is accompanied by a brief description of the mathematician or concept depicted. The collection showcases the global recognition of mathematics and its impact on society, with stamps from various countries and time periods. The document also includes stamps that depict computer art, op art, mathematical olympiads, geometry teaching, and other mathematical themes. Additional reading materials and online resources are suggested for further exploration. [Extracted from the article]

The field of history of science has evolved and diversified over the past few decades, encompassing not only the natural sciences, medicine, and mathematics, but also the social sciences, humanities, and the study of the relationship between science and technology. The discipline has embraced inter- and transnational perspectives, as well as postcolonial and decolonial aspects. The history of science has become an interdisciplinary field, exploring the relationship between science and other forms of knowledge. This special issue aims to highlight the diversity and vibrancy of current research topics and approaches in the histories of science, including the history of the humanities, social sciences, mathematics, communication practices, digital history, and the role of technology. The contributions also demonstrate the connections between histories of science and other fields of historical research, such as gender history, colonial history, media history, and environmental history. [Extracted from the article]

This article is an interview with mathematician Martin Raussen, who discusses his involvement with the Nordic Congress of Mathematicians and his experiences interviewing Abel Prize recipients. Raussen reflects on his early interest in mathematics and his education, highlighting the challenges and excitement of studying the subject. He delves into his research on the interplay between directed homotopy in algebraic topology and concurrency in theoretical computer science, explaining the concept of concurrency and its relevance in distributed computing. Raussen also discusses his involvement in public outreach and conducting interviews with Abel Prize laureates. The article emphasizes the importance of promoting mathematics and the challenges in communicating its beauty and significance to the general public. It also mentions the increasing influence of mathematics in technology and society, as well as the role of computers and artificial intelligence in advancing mathematical research. The interview concludes with a discussion on the different approaches to mathematics and the importance of both theory building and problem solving. Raussen also shares his interests outside of mathematics, including reading popular science books, listening to music, and spending time with family. [Extracted from the article]

After the Hindu-Arabic decimal positional system was introduced in Europe, throughout many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organization of content, usually starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Europe--the Latin translations of al-Khwarizmi's treatise on decimal arithmetic, and Leonardo's Liber Abaci, containing examples of reading a 16-digit and a 15-digit number respectively. Throughout the centuries, the order of magnitude of these introductory numbers increased, in general up to some 30 digits, but in some cases to over 60 digits. In this paper we examine the development and extent of this characteristic of introductory arithmetic textbooks from the period 13th-19th century, and the conditions which lead to this, now extinct, practice. [ABSTRACT FROM AUTHOR]

The text discusses two books on the philosophy of mathematics education. The first book, "Connecting Humans to Equations," explores the human dimensions of mathematics and covers topics such as the ontological and epistemological aspects of mathematics. The second book, "Critical Mathematics Education," presents the Critical Mathematics Education (CME) paradigm, which aims to empower students to think critically about mathematics and its societal implications. Both books offer valuable insights into the philosophy of mathematics education and are recommended for philosophers and mathematics teachers. [Extracted from the article]

This article explores the relationship between mathematics and ethics, particularly in the context of promoting nonviolence and peace. It discusses the historical association of mathematics with violence but emphasizes its potential to contribute to a more equitable and peaceful civilization. The text calls for a deeper understanding of the connection between mathematics and human behavior and highlights the responsibility of mathematicians in promoting peace. It also discusses the role of emotions, intuition, and sensorial perceptions in knowledge generation and emphasizes the importance of ethics, nonviolence, and cooperation in achieving a better quality of life for all. The text proposes a curriculum that includes discussions on the primordial triangle, the evolution of the human species, and the basic ideas of mathematics, with the aim of demystifying mathematical language and promoting a global understanding of peace and ethics. [Extracted from the article]

This document is a list of references and citations related to the history of mathematics education. It includes various articles, books, and studies that cover topics such as the development of geometry teaching, the role of proof in mathematics education, and the reforms in mathematics education in different countries. The references provide a comprehensive overview of the research and scholarship in the field of mathematics education history, making it a valuable resource for library patrons conducting research on these topics. [Extracted from the article]

The given text is a list of various publications by Dr. A. Drago, covering topics such as the organizational structures of geometry, the history of Western science, the relationships between chemistry and mathematics, and the birth of alternative mechanics. The publications also touch on non-violence, conflict resolution, and the impact of bodies as a metaphor for conflict resolution. The text includes references to other authors and works, such as Einstein, Freud, Gandhi, and Leibniz. [Extracted from the article]

The article explores the concept of a nonkilling society and its implications for mathematics. It emphasizes that society can exist without killing and highlights the role of education in promoting peace. The author calls for further research on the relationship between mathematics and other disciplines and raises questions about the responsibility of mathematicians and educators in fulfilling their commitments to humanity. The text also discusses the connection between mathematics and various aspects of society, including technology and the military, and argues for a broader view of the world and the role of mathematics in promoting peace and dignity. It concludes by emphasizing the importance of ethics and nonviolence in human behavior and the production of knowledge. [Extracted from the article]

It is difficult for mathematics teachers to find and utilize relevant historical content for their students. In this study, we aimed to examine how prospective mathematics teachers (PMTs) evaluate the history of mathematics (HM) in curriculum resources and how they integrate the HM into lesson plans. We collected data through PMTs' evaluation reports on the analysis of textbooks, lesson plans, and lesson plan reflections. PMTs evaluated textbooks critically, acknowledging the limits and recognizing the possibilities. They mostly provided negative evaluations and criticized the quality of HM in the textbooks. The findings revealed that PMTs' evaluations of the analysis of HMs in textbooks served as a bridge to assist their utilization of HMs in lesson plans. When PMTs incorporated HM into their lesson plans in an effort to engage students in the learning of mathematics, the HM integration reached higher levels of cognitive demand. However, they performed less well when incorporating pedagogical instructions and student thinking. The theoretical and practical implications of the study are discussed. [ABSTRACT FROM AUTHOR]

The notion of d'epaysement 'epist'emologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel's incompleteness theorem, with the aim of provoking in the participants the experience of d'epaysement 'epist'emologique. Results show that several of the teachers participating in the activity felt d'epaysement 'epist'emologique, and this feeling triggered empathy towards their own students. The article ends with a discussion of the real possibilities of integrating the history of mathematics in secondary mathematics courses and in the training of teachers. [ABSTRACT FROM AUTHOR]