viii, 332 hlm, 28 c

This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective dimensions of mathematics. These approaches aim to make mathematics humanize. It proposes novel directions in mathematics, stressing that the ideas presented here are provisional. Furthermore, it argues that mathematics can take multiple humanized forms. Even traditional mathematics can be interpreted as a form of humanized mathematics. To support this perspective, several mathematical observations are provided. Additionally, a general approach to addressing the Riemann Hypothesis, focusing on proof by contradiction and mathematical logic, particularly model theory, is outlined. The paper also briefly reflects on my prior research through this idea on humanization and concludes with general remarks and future directions.

316 p. ; 25 cm

This Master's Thesis analyzes thoroughly the topic of the Mathematics Education in Russia and Mathematical Circles. It deals with the historical context of the Mathematics Education in Russia in the XVIIIth, XIXth and XXth centuries; the programs of the Mathematics Education which were developed between 1930 and 1985 in the Soviet Union, including the Mathematical Circles for its particularly importance and influence on the rest of the Programs and on the way of understanding the Mathematics Education; the objectives and the organization of practical cases nowadays, legacy of the Russian Mathematical Circles; and the way of establishing the didactic process of the Mathematical Circles. Finally it is attached an appendix with a practical proposal in order to develop a session following the Mathematic Circle manner within the current framework of the Spanish Middle and High School education.

iv, 331 p. ; 25 cm

The received Hilbert-style axiomatic foundations of mathematics has been designed by Hilbert and his followers as a tool for meta-theoretical research. Foundations of mathematics of this type fail to satisfactory perform more basic and more practically-oriented functions of theoretical foundations such as verification of mathematical constructions and proofs. Using alternative foundations of mathematics such as the Univalent Foundations is compatible with using the received set-theoretic foundations for meta-mathematical purposes provided the two foundations are mutually interpretable. Changes in foundations of mathematics do not, generally, disqualify mathematical theories based on older foundations but allow for reconstruction of these theories on new foundations. Mathematics is one but its foundations are many.

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by CMI; the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved

xvi, 612 p. ; 28 cm

We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.

xvi, 639 hlm. :il. ;25 cm

We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community. We engage in this project with a focus on including research that highlights, documents, or quantifies (in)equities that exist in the mathematical sciences, specifically, and STEM (science, technology, engineering, and mathematics) more broadly. We seek to enhance social justice in the mathematics and data science communities by providing numerous examples of the ways in which the mathematical sciences fails to meet standards of equity, equal opportunity and inclusion. We introduce the term ``mathematics of Mathematics" for this project, explicitly building upon the growing, interdisciplinary field known as ``Science of Science" to interrogate, investigate, and identify the nature of the mathematical sciences itself. We aim to promote, provide, and posit sources of productive collaborations and we invite interested researchers to contribute to this developing body of work.

Peer review is the driving force of journal development, and reviewers are gatekeepers who ensure that Mathematics maintains its standards for the high quality of its published papers [...]

xv, 645 hlm. :il. ;21 cm

One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

Rigorous peer-review is the corner-stone of high-quality academic publishing [...]

x;ill.;149hal.;28c

The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic $p$ is more general (fundamental) than standard mathematics. The belief of most mathematicians and physicists that standard mathematics is the most fundamental arose for historical reasons. However, simple mathematical arguments show that standard mathematics (involving the concept of infinities) is a degenerate case of finite mathematics in the formal limit $p\to\infty$: standard mathematics arises from finite mathematics in the degenerate case when operations modulo a number are discarded. Quantum theory based on a finite ring of characteristic $p$ is more general than standard quantum theory because the latter is a degenerate case of the former in the formal limit $p\to\infty$.

This study aims to examine the perspectives of various stakeholders, such as students and educators, on the use of artificial intelligence in teaching mathematics, specifically after the launch of ChatGPT. The study adopts a qualitative case study approach consisting of two stages: content analysis of interviews and investigation of user experience. The first stage of the study shows that ChatGPT is recognized for its improved math capabilities and ability to increase educational success by providing users with basic knowledge of mathematics and various topics. ChatGPT can offer comprehensive instruction and assistance in the study of geometry, and the public discourse on social media is generally positive, with enthusiasm for the use of ChatGPT in teaching mathematics and educational settings. However, there are also voices that approach using ChatGPT in educational settings with caution. In the second stage of the study, the investigation of user experiences through three educational scenarios revealed various issues. ChatGPT lacks a deep understanding of geometry and cannot effectively correct misconceptions. The accuracy and effectiveness of ChatGPT solutions may depend on the complexity of the equation, input data, and the instructions given to ChatGPT. ChatGPT is expected to become more efficient in resolving increasingly complex mathematical problems. The results of this investigation propose a number of avenues for research that ought to be explored in order to guarantee the secure and conscientious integration of chatbots, especially ChatGPT, into mathematics education and learning.

The editorial team greatly appreciates the reviewers who have dedicated their considerable time and expertise to the journal’s rigorous editorial process over the past 12 months, regardless of whether the papers are finally published or not [...]

xiii, 110 hlm. : il. ; 24 cm

This chapter takes a historical view of the development of mathematics education, from its initial status as a business mostly managed by mathematicians to the birth of mathematics education as a scientific field of research. Starting from the acknowledgement that research in mathematics education demands more than the traditional focus on discussing curricular options at distinct grade levels, we identified several specialized clusters, debating specific issues related to mathematics education at an international level. We grouped the clusters into three main areas: relationships with psychology, the study of social, cultural and political dimensions, and the relevance of a theory for mathematics education.

Indeks *** *** Bibliografi hlm. 799-804xiii, 804 hlm. :il.;25 cm

Robust preparation of future secondary mathematics teachers requires attention to the acquisition of mathematical knowledge for teaching. Many future teachers learn mathematics content primarily through mathematics major courses that are taught by mathematicians who do not specialize in teacher preparation. How can mathematics education researchers assist mathematicians in making explicit connections between the content of undergraduate mathematics courses and the content of secondary mathematics? We present an articulation of five types of connections that can be used in secondary mathematics teacher preparation and give examples of question prompts that mathematicians can use as applications of teaching secondary mathematics in undergraduate mathematics courses.

Peer review is an essential part in the publication process, ensuring that Mathematics maintains high quality standards for its published papers.[...]

x,776 hal,;ill,;23 c

An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This nontechnical article discusses the motivating ideas behind the constructive approach to mathematics and the implications of constructive mathematics for the history of mathematics.