Search

The definition of who is or what makes a "mathematician" is an important issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline--both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to highlight, examine, and challenge systemic barriers that exist in certain spaces of the community. This paper analyzes and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, we present a framework of definitions based on identity, function, and qualification and explore several different meanings of mathematician. By interrogating various definitions, we highlight their risks and opportunities, with an emphasis on implications for broadening and/or narrowing participation of underrepresented groups in the mathematics community. [ABSTRACT FROM AUTHOR]

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions--hiding one biscuit, arbitrarily sharing the extra biscuit, randomizing allocation, dividing the extra biscuit into three parts, and successively dividing it into smaller and smaller parts--involve different mathematical methods and evoke different human values. We discuss the construction of quantum biscuit splitting devices and the use of machine learning to divide biscuits. We argue that the multitude of different mathematically-correct solutions to this problem (each with its own ethical justification) might influence the values held by practicing mathematicians. The example we propose here has been used in teaching to help students understand why mathematics cannot be cleanly separated from human values. [ABSTRACT FROM AUTHOR]

The artist's vision helps decide what should be created; the mathematician's insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes? [ABSTRACT FROM AUTHOR]

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations -- one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration -- and a look at how collaborations built with that intentionality and acknowledgment can be impactful for students and institutions and be personally and professionally rewarding for the collaborators. [ABSTRACT FROM AUTHOR]

While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both the computable real numbers and his famous 'Turing machine". The final part of this paper describes the computable real numbers in enough detail to supplement the usual undergraduate real analysis class. An appendix presents programs that implement the examples in the text. [ABSTRACT FROM AUTHOR]

In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of literacy can potentially strengthen students’ understanding of ways of thinking particular to specific (academic) disciplines; ways of thinking that are otherwise often hidden when teaching focuses on more pragmatic aspects. G. H. Hardy’s A Mathematician’s Apology from 1940 serves as the recurring illustrative example in our discussions of the pedagogical potentials of an interdisciplinary rendezvous between mathematics and literature. [ABSTRACT FROM AUTHOR]

This is a review of What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles (Cambridge University Press, 2017). In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms 'mathematical' and 'concept'. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim the canonical question 'what is a mathematical concept?' from the philosophy of mathematics. This review comments on each paper in the collection. [ABSTRACT FROM AUTHOR]

I survey emigration of mathematicians from Europe, before and during WWII, to Russia. The emigration started at the end of 1920s, the time of "Great Break", and accelerated in 1930s, after the introduction in Germany of the "non-Aryan laws". Not everyone who wanted to emigrate managed to do so, and most of those who did spent a relatively short time in Russia, being murdered or deported, or fleeing the Russian regime. After 1937, the year of "Great Purge", only a handful of emigrant mathematicians remained, and even fewer managed to leave a trace in the scientific milieu of their new country of residence. The last batch of emigrants came with the beginning of WWII, when people were fleeing eastwards from the advancing German army. [ABSTRACT FROM AUTHOR]

Creativity is a broad phenomenon that scholars have interpreted in a multitude of ways. We notice that a majority of the views describe creativity as something innate. This paper aims to verge from this perspective and explore creativity in terms of the constant mutual interaction of a person and their environment. Using the theoretical framework, enactivism, and the notion of emergence, we investigate the creative processes involved in musical improvisations of south In- dian classical or Carnatic music and mathematical proof generation. Interview excerpts from professional Carnatic musicians and research mathematicians on their respective creative processes during musical improvisation and proof gen- eration are analyzed. This study gives a perspective to think about creativity, with an emphasis on emergence. This paper has been partly informed by self- reections on musical improvisations and mathematical proof generation by the first author, who is a performing Carnatic vocalist and a mathematician. [ABSTRACT FROM AUTHOR]

In this paper we report our findings of college students' images of mathematicians and we reflect on different methodologies used to assess this information. The study reported in this paper was conducted in two stages. During the first stage, we asked 179 college students to "draw a mathematician" and also asked them to list five characteristics and five careers for a mathematician. In the second stage of the study, we conducted four focus group interviews with a total of twelve college students. During the focus group interviews, we showed the students 16 photos of real people and asked them to determine which they think are mathematicians and which are not. We found that college students do hold certain stereotypic images of mathematicians and that different perspectives arose based on the different research methodologies. In this paper, we argue for the need to go beyond relying solely on the "draw a mathematician" test and we conclude with a discussion on the implications that stereotypic images of mathematicians have on the mathematical workforce. [ABSTRACT FROM AUTHOR]

Stereotypes about mathematicians that conflict with “traditionally feminine” identities are widely held by people from middle-school-age onwards, and can influence their participation in mathematics and related fields. Simply being exposed to women in mathematics is not enough to change students’ perceptions of mathematicians, and may even decrease girls’ interest in mathematics. This paper proposes a storytelling strategy to help change students’ perceptions of mathematicians. It includes several activities for intentionally incorporating women’s stories into the post-secondary classroom and a list of resources for finding existing powerful stories. The diverse stories of women mathematicians, including details of their personal lives and the barriers to success they faced, can relieve potential discord between students’ identities and those they see participating in mathematics. [ABSTRACT FROM AUTHOR]

As mathematicians, we often fail to appreciate the opportunities open to us when we teach developmental mathematics. One such opportunity is that we may deepen our understanding of mathematics that we have taken for granted. This paper contains a brief case study concerning what we have learned about operations, inverses, and exponents in the process of teaching beginning algebra. Our inquiry takes us from student questions about signed numbers, through the category of rings, to the world of Lie groups and Lie algebras. [ABSTRACT FROM AUTHOR]

Mathematics has often been referred to as an art. For some it is “the purest of the arts”, where the mathematicians’ art is “asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations”. Yet with classroom time given primarily to “covering the curriculum”, testing, and practicing problem-solving procedures, students’ opportunities to appreciate the aesthetic dimension of mathematics are often limited. To promote a responsive environment in an effort to enable students to become artists of their own mathematics experience, I consider in this paper two facets of the mathematics classroom. Content-wise I make the argument that students need to see problem-clarifying strategies in conjunction with problem-solving techniques, as the former are essential for making progress when engaging a mathematics problem where an explicit solution is not apparent. The other facet aiming to promote student agency is providing them opportunities to work with their own practical/professional concerns as students so as to become more creative and productive artists of their mathematics experience. [ABSTRACT FROM AUTHOR]

Historians of mathematics, by definition, look at mathematics of the past. But mathematicians, too, often look at mathematics of the past; mathematicians of the past themselves often looked very closely at mathematics of their own past. Is their relationship to the past the same as that of the historians? Is every view of the past an historical view? Indeed, is every historical view historical in the same way? Or is it possible that there are different kinds of relationships to the mathematics of the past? This paper will suggest that there are in fact a variety of such relationships. It will try to catalog some of these, without judgment as to whether they are necessarily correct or legitimate. It will also raise the question as to whether mathematics educators interested in the history mathematics have their own distinct relationship with the mathematics of the past or are aligned with one type or another. [ABSTRACT FROM AUTHOR]

Thursday, November 8, 2018, is the twenty-fifth anniversary of the death of the celebrated Professor A. N. Tikhonov, one of my most favorite mathematicians. The idea of writing this paper to honor his life and scientific activities came to me as I was reading many of his works; I was impressed by his knowledge, amazing research, profound scholarship, perspicuity and eloquence of expression, painstaking accuracy, and big ideas. My aim is to be clear and evocative, for in this way I feel more in touch with my subject that is very interesting. [ABSTRACT FROM AUTHOR]

A “lost chapter” from Antoine de Saint-Exupéry’s Le Petite Prince about the Little Prince visiting a mathematician, written in French in the style of the original work, is presented along with several translations. [ABSTRACT FROM AUTHOR]

This article, titled "Variations on a Meme: Thoughts and Responses to Isaac Elishakoff's 'Differential Equations of Love and Love of Differential Equations'," explores the concept of memes and their relationship to differential equations and love. The author discusses how memes, as cultural touchstones, can be used to express complex ideas in a concise way, similar to how differential equations are used in poetry. The article also includes brief comments on three poems related to the topic. Overall, the article examines the intersection of mathematics, poetry, and human relationships. [Extracted from the article]

This article chronicles the journey of an immigrant female mathematician in the United States. The chronicle encompasses early training, encouragements received, road-blocks encountered and the background while growing up which shaped the core of her being. The loving, supportive and educative background she received early in life provided the strength to withstand the hurdles thrown in the path of her career advancement. These hurdles are not unique to the author; many immigrant professionals face similar situations. The purpose of the article is to bring awareness to these challenges such professionals face and how they still persevere with discipline and focus. [ABSTRACT FROM AUTHOR]

In this paper we discuss al-Khwārzimī's life and aspects of his work and suggest a possible hermeneutic avenue into his contributions to mathematics. [ABSTRACT FROM AUTHOR]

Mathematicians sometimes judge a mathematical proof to be beautiful and in doing so seem to be making a judgement of the same kind as aesthetic judgements of works of visual art, music or literature. Mathematical proofs are also appraised for explanatoriness: some proofs merely establish their conclusions as true, while others also show why their conclusions are true. This paper will focus on the prima facie plausible assumption that, for mathematical proofs, beauty and explanatoriness tend to go together. To make headway we need to have some grip on what it is for a proof to be beautiful, and for that we need some account of judgements of beauty in general. That is the concern of the first section. The second section faces the problem that it is far from obvious how abstract entities, such as mathematical proofs, can be beautiful, strictly and literally speaking. Reasons are given for the view that they can be. The third section introduces the distinction between proofs which explain their conclusions and proofs which do not. Finally, the question whether, for mathematical proofs, the beautiful and the explanatory tend to coincide is addressed. It is argued that we have reason to doubt that explanatory proofs tend to be beautiful, and insufficient reason to believe or disbelieve that beautiful proofs tend to be explanatory. [ABSTRACT FROM AUTHOR]

In the Fall of 2013 our team of three different generations of mathematicians launched the free, online E-Brock Bugs mathematics computer game [5] which we developed from an original probabilistic board game, Brock Bugs, and its digital learning object version. We constructed E-Brock Bugs using Devlin's [9] mathematics computer game design principles for games that prompt players' development of mathematical thinking. As we created E-Brock Bugs we found it necessary to go through an evolving cyclic process of design, implementation, and analysis. In this paper we reect upon the main struggles we faced in this process and the unexpected personal growth that ensued in terms of our views and beliefs as mathematics educators. [ABSTRACT FROM AUTHOR]

We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it includes some preliminary work that facilitates the proof; therefore, the theorem can also serve as a nice exercise in induction. Additionally, we use well-known facts from calculus to clarify and enhance what is intrinsically a discrete problem. Making an unexpected but welcome explanatory appearance, the number e is pertinent. [ABSTRACT FROM AUTHOR]

In this article, we describe the invention of double-entry bookkeeping (or partita doppia as it was called in Italian) as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved. [ABSTRACT FROM AUTHOR]

We report on the top ten mathematicians with the highest number of articles, citations, and students, based on data from MathSciNet and the Mathematics Genealogy Project. [ABSTRACT FROM AUTHOR]

In this article we explore mathematical allusions in Herman Melville’s novel Moby-Dick. We argue that both the quantity and sophistication of these allusions are evidence for Melville’s high level of mathematical knowledge and ability. We discuss some of the most compelling mathematical imagery, as well as giving background on the several mathematicians and mathematics books mentioned in the novel. We also include some biographical details supporting the assertion that Melville had an unusually good mathematical education. [ABSTRACT FROM AUTHOR]

Too often mathematics is viewed by students and the general public alike as a set of formulas and techniques. However, mathematicians know that it involves so much more than banal procedures and requires deep thought and creativity. In this work we introduce an activity designed to make creative mathematical exploration accessible to young students and still interesting for those with many years of mathematical training. Popular culture often references the nautilus shell as an example of a golden spiral in nature. While many mathematicians assert this claim is false based on the formal definition, others have provided potential avenues for a relationship between the spiral created in the nautilus shell and the golden ratio. We spell out this debate and ask students to explore this question and see what patterns they can find in the nautilus shell. Might an alternative frame give the nautilus shell a golden hue or is it really just fool's gold?. [ABSTRACT FROM AUTHOR]

I investigate with examples limitations that mathematicians accept in research: aesthetic, scientific, and practical, in particular, on what bases such choices are made. Discussion is partly in terms of the ideal agents that Philip Kitcher and Brian Rotman used to analyse mathematical writing. [ABSTRACT FROM AUTHOR]

This report aims to convince readers that there are clear indications that society is increasingly taking a greater interest in science and particularly in mathematics, and thus society in general has come to recognise, through different awards, privileges, and distinctions, the work of many mathematicians. We provide examples of recognition accorded by institutions, societies, schools, communities, academies, and the public in general to these mathematicians. [ABSTRACT FROM AUTHOR]

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided. [ABSTRACT FROM AUTHOR]

Recent attempts at defining mathematical beauty fall roughly into two schools of thought. One takes its starting point in the subjective experience of the math- ematician and characterises mathematical beauty in cognitive terms. The other seeks to reduce beauty to objective notions such as truth, symmetry, or simplicity. This second approach is popular among analytic philosophers, who are commit- ted to seeing mathematics and science as prototypically rational enterprises. I criticise this stance on the grounds that this commitment makes its supporters approach beauty in mathematics not with a genuine desire to sympathetically understand it, but with the preconceived goal of explaining it away and playing it down. [ABSTRACT FROM AUTHOR]

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves. [ABSTRACT FROM AUTHOR]

Despite an extensive literature on the nature and origins of mathematical truth, few if any studies exist of the everyday practices through which the adequacy of mathematical argumentation is cultivated and assessed. The work of a novice prover afforded insight into these practices and, in particular, into the disciplined character of discovering and proving mathematical theorems. [ABSTRACT FROM AUTHOR]

This is the story of how a mathematical problem was discovered. Although it was never solved, it gave great joy to the discoverer. [ABSTRACT FROM AUTHOR]

In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments. [ABSTRACT FROM AUTHOR]