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Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural sciences. A mathematical paper can therefore, at least in principle, be replicated simply by reading it. While this distinction is sometimes taken as the basis to claim that the results in mathematics are therefore certain, mathematicians themselves know that the published literature contains many mistakes. Reading a proof is not easy, and checking whether an argument constitutes a proof is surprisingly difficult. This article uses peer review of submissions to mathematics journals as a site where referees are explicitly concerned with checking whether a paper is correct and therefore could be published. Drawing on 95 qualitative interviews with mathematics journal editors, as well as a collection of more than 100 referee reports and other correspondence from peer review processes, this article establishes that while mathematicians acknowledge that peer review does not guarantee correctness, they still value it. For mathematicians, peer review 'adds a bit of certainty', especially in contrast to papers only submitted to preprint servers such as arXiv. Furthermore, during peer review there can be disagreements not just regarding the importance of a result, but also whether a particular argument constitutes a proof or not (in particular, whether there are substantial gaps in the proof). Finally, the mathematical community is seen as important when it comes to accepting arguments as proofs and assigning certainty to results. Publishing an argument in a peer-reviewed journal is often only the first step in having a result accepted. Results get accepted if they stand the test of time and are used by other mathematicians. [ABSTRACT FROM AUTHOR]

This paper provides a review of the literature on rigorous definitions and constructions in quantum field theory (QFT), spanning the period of seven decades. Compared with the ideas and constructions found in the modern physics literature, we conclude that none of the existing systems of QFT axioms can cover all the physical situations. Therefore, it is still an outstanding open problem to formulate a complete definition of QFT. We argue that the question is of relevance for both physicists and mathematicians. [ABSTRACT FROM AUTHOR]

"Real Normed Algebras Revisited," the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions, and the octonions, as well as proofs of their properties, using only what was known to 19th-century mathematicians. In his research, Gadi had discovered simple and elegant proofs of the above-mentioned classical results using only basic properties of the geometry of Euclidean spaces and tools from high school geometry. His reconstructions underline an interesting connection between Euclidean geometry and these algebras, and avoid the advanced machinery used in previous derivations of these results. The goal of this article is to present Gadi's derivations in a way that is accessible to a wide audience of readers. [ABSTRACT FROM AUTHOR]

Focuses on the application of paper folding in teaching geometry. Advantages of paper folding, including the enjoyment of students; Utilization of a dynamic geometry software in the exploration of geometrical solutions; Overview of paper folding axioms developed by various mathematicians.

Prahalad Chunnilal Vaidya was an eminent general relativist, gravitation theorist, physicist, mathematician, educationist and a follower of Gandhian philosophy in post-independence India. Apart from his scientific career, Vaidya is renowned for his Vaidya metric. Though he has contributed significantly to the scientific community, very few people are aware about him or his contributions. As 23 May 2019 was the 101st birth anniversary of Vaidya, here we present his contributions and their impact through a bibliometric study. This study presents an analysis of published research works of Vaidya. During his active career, he had contributed 102 publications, including 90 journal articles, 5 conference papers, 4 book chapters, 2 review articles and 1 report. His publications have received 2004 citations, h-index of 18 and i10-index of 29 from 1979 to 2018. We analysed Vaidya's publications by type, country, journals, publishers, citations, year-wise growth, collaborated authors, top cited papers, etc. This bibliometric study is an effort to draw the attention of the younger generation of scientists to Vaidya and his contributions. [ABSTRACT FROM AUTHOR]

The purpose of the present note is to point out mathematical mistakes in some published papers on boundary value problems to prevent usage of mistaken results and methods by mathematicians. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam's very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors' purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between. [ABSTRACT FROM AUTHOR]

The question of whether there is a true isometry that approximates the ε -isometry defined on a bounded set has long interested mathematicians. The first paper on this topic was published by Fickett, whose result was subsequently greatly improved by Alestalo et al., Väisälä and Vestfrid. Recently, the authors published some papers improving the previous results. The main purpose of this paper is to improve all of the abovementioned results by utilizing the properties of the norm and inner product for Euclidean space. [ABSTRACT FROM AUTHOR]

On 5 May 1957, Leopold Löwenheim passed away in a Berlin hospital following a short but severe illness, unnoticed by the community of mathematical logicians who believed that he had perished in a Nazi concentration camp in or shortly after 1940 (the year of publication in the Journal of Symbolic Logic of his last paper before the end of World War II). The 50th anniversary of his death seems an appropriate date for the posthumous publication of a paper that was supposed to appear in Fundamenta Mathematicae in 1939, the galley proofs of which Löwenheim had already seen and corrected when German troops invaded Poland on 1 September 1939. Löwenheim managed to save the proofs through the War, despite the loss of most of his possessions during the bombing of Berlin in 1943 and 1944. By another lucky chance, a copy of the proofs survived in the present author's possession, when the originals were lost during a flat clearing in Berlin as part of the estate of Johannes Teichert (1904-1994), Löwenheim's step-son, when his widow moved into a nursing-home in May 1999. Later, I will expand these short remarks slightly but seize the present opportunity to resume (and in some places add to) the extant data on Löwenheim's life and writings. [ABSTRACT FROM AUTHOR]

The article features Russian academician and mathematician M. M. Lavrentiev and his papers that were published during the period of 1953 to 1965 which are said to have contributed to the development of the theory of inverse and ill-posed problems. His first paper focused on increasing the accuracy of the solution of a system of linear algebraic equations, while the second paper dealt with improving the accuracy of the solution to a system of linear algebraic equations.

Immediately following the commentary below, the previously published article by R. Thom is printed in its entirety: R. Thom, Ensembles et morphismes stratifyíes, Bulletin of the American Mathematical Society 75 (1969), no. 2, 240-284 (French). This is followed by the first publication of the 1970 lecture notes of J. Mather, Notes on topological stability. [ABSTRACT FROM AUTHOR]

YouTube videos by Cambridge mathematician Tadashi Tokieda: "Math Encounters - Toy Models: Extracting Mathematical Surprises from Everyday Life", "Mathematics with Paper Clips, Ribbon, Rubber Bands (Math-Byte)" and "Toy Models" Since then, several folks have directed me to a number of videos by Tokieda analyzing other interesting "simple" phenomena, including his "Toy Models" talk. A nice hands-on activity with a paper strip, paper clips, and rubber bands ends the Princeton video, and is then explored at greater length in the second I Mathbytes i video. [Extracted from the article]

The instrument collection at the Royal Swedish Academy of Sciences houses a historically significant 10-foot achromatic refractor crafted by London instrument maker John Dollond. The telescope came into use at the Academy's Observatory in Stockholm in 1761 and remained in service into the 1820s. This paper aims to add to the biography of this instrument, encompassing its six decades of active service and, after 150 years in storage, its transformation into an exhibition showpiece. The paper begins by introducing the telescope, its maker and the conflict involving Dollond and the Swedish mathematician and physicist Samuel Klingenstierna over the discovery of the achromatic lens. This dispute ultimately resulted in the telescope finding its way to the Stockholm Observatory. Subsequently, the paper delves into how Academy astronomer Pehr Wargentin perceived and utilized this state-of-the-art refractor, along with brief mentions of its use by his successors. The final section narrates how the telescope ended up in the permanent exhibition of the Stockholm Observatory Museum. [ABSTRACT FROM AUTHOR]

The article profiles Syamadas Mukhopadhyaya, an Indian mathematician. Topics discussed include his birth on June 22, 1866, educational background, award received for his essay "Intrinsic parameters in the differential geometry of curves," teaching career, organizational affiliations, introduction of the four-vertex theorem, and his research work available in the "Collected Geometrical Papers."

Mathematicians frequently attend their peers' lectures to learn new mathematical content. The goal of this paper is to investigate what mathematicians learned from the lectures. Our research took place at a 2-week workshop on inner model theory, a topic of set theory, which was largely comprised of a series of lectures. We asked the six workshop organizers and seven conference attendees what could be learned from the lectures in the workshop, and from mathematics lectures in general. A key finding was that participants felt the motivation and road maps that were provided by the lecturers could facilitate the attendees' future individual studying of the material. We conclude by discussing how our findings inform the development of theory on how individuals can learn from lectures and suggest interesting directions for future research. [ABSTRACT FROM AUTHOR]

Combining data on locations with career and educational histories of mathematicians, we study how distance and ties affect citation patterns. The ties considered include coauthorship, past colocation, and relationships mediated by advisers and the alma mater. With fixed effects capturing subject similarity and article quality, we find linkages are strongly associated with citation. Controlling for ties generally halves the negative impact of geographic barriers on citations. Ties matter more for less prominent and more recent papers and have retained their quantitative importance in recent years. The impact of distance, controlling for ties, has fallen and is statistically insignificant after 2004. [ABSTRACT FROM AUTHOR]

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The author relates his unfruitful search for the posthumous papers of late Russian mathematician Andrey Nikolaevich Kolmogorov and asks the scientific community to provide any available information regarding Kolmogorov's papers.

In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form. [ABSTRACT FROM AUTHOR]

Mathematics, both pure and applied, plays a crucial role in shaping societies and driving advancements in various fields. This research paper explores the impact of pure and applied mathematics on Nigerian society, examining their individual contributions and the synergy that emerges from their interplay. The introduction highlights the importance of mathematics in general and provides a context for understanding its significance in the Nigerian context. The subsequent sections delve into the specific impacts of pure and applied mathematics, focusing on their contributions to Nigerian society. The section on pure mathematics discusses its role in fostering critical thinking, logical reasoning, and problem-solving skills, while also showcasing the accomplishments of Nigerian mathematicians in the global mathematical community. The section on applied mathematics explores its applications in sectors such as finance, telecommunications, and engineering, and its contribution to addressing societal challenges and promoting economic development in Nigeria. The paper further investigates the synergy between pure and applied mathematics, illustrating how abstract mathematical concepts often find unexpected practical applications and how real-world challenges drive theoretical advancements. It emphasizes the collaborative efforts between researchers in both fields, the benefits of interdisciplinary perspectives, and the impact on mathematical education and pedagogy. Lastly, the paper addresses the challenges and future directions of pure and applied mathematics in Nigeria, focusing on infrastructure limitations, shortage of skilled mathematicians, integration of mathematics in industry, and the promotion of women's participation. It proposes strategies such as investment in research infrastructure, strengthening mathematics education, fostering interdisciplinary collaboration, and promoting public awareness and engagement. By addressing these challenges and charting future directions, Nigeria can harness the full potential of mathematics as a transformative force in society. [ABSTRACT FROM AUTHOR]

In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians’ research processes and discuss their usage all along the data life cycle. [ABSTRACT FROM AUTHOR]

In this paper we examine two mathematicians who published manuscripts on geometry and origami in the same year, 1893: Hermann Wiener and Sundara Row. The main question that concerns us is to situate these works in the correct historical and mathematical background. We suggest that Wiener and Row offer us, via folding a piece of paper, a new conception of geometry that is very different to the common conception at the time. [ABSTRACT FROM PUBLISHER]

In the paper by Daniel Tisdale, published in this journal, a ‘previously unpublished note’ by Jitsuro Nagura is reproduced and discussed. Actually, in 1956, this article was published in a bulletin of the Department of General Education, Rikkyo University. [ABSTRACT FROM PUBLISHER]

Analogy has received attention as a form of inductive reasoning in the empirical sciences. Its role in mathematics has, instead, received less consideration. This paper provides a novel account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an incremental and a non-incremental form of confirmation by mathematical analogy. We offer an account of the former within the popular framework of Bayesian confirmation theory. As for the non-incremental notion, we defend its role in rationally informing the prior credences of mathematicians in those circumstances in which no new mathematical evidence is introduced. The resulting framework captures many important aspects of the use of analogical inference in the domain of pure mathematics. [ABSTRACT FROM AUTHOR]

This paper describes Project NExT (New Experiences in Teaching), a professional development program for new or recent Ph.D.s in the mathematical sciences. The program consists of workshops and short courses on teaching, establishing a research program, involving undergraduates in research, grant writing, and balancing teaching and research. An introduction to the program and the testimonies of three Project NExT fellows writing about their experiences as new faculty members at research institutes are featured. (MM)