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Articles on History of mathematics
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A brief illustrated guide to ‘scissors congruence’ − an ancient geometric idea that’s still fueling cutting-edge mathematical research
Maxine Calle , University of Pennsylvania and Mona Merling , University of Pennsylvania
X marks the unknown in algebra – but X’s origins are a math mystery
Peter Schumer , Middlebury
Women’s History Month: 5 groundbreaking researchers who mapped the ocean floor, tested atomic theories, vanquished malaria and more
Maggie Villiger , The Conversation
Return of imperial system on cards for Brexit Britain – measurements have always been political
Aashish Velkar , University of Manchester
Emmy Noether faced sexism and Nazism – over 100 years later her contributions to ring theory still influence modern math
Tamar Lichter Blanks , Rutgers University
Is mathematics real? A viral TikTok video raises a legitimate question with exciting answers
Daniel Mansfield , UNSW Sydney
Using computers to crack open centuries-old mathematical puzzles
Christopher Rasmussen , Wesleyan University
The weird world of one-sided objects
David Gunderman , University of Colorado Boulder and Richard Gunderman , Indiana University
Written in stone: the world’s first trigonometry revealed in an ancient Babylonian tablet
Daniel Mansfield , UNSW Sydney and Norman Wildberger , UNSW Sydney
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- ARTS REVIEW
- 14 March 2024
A Black mathematical history
- Noelle Sawyer ORCID: http://orcid.org/0000-0001-7164-2420 0
Noelle Sawyer is an assistant professor of mathematics at Southwestern University in Georgetown, Texas.
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Virginia Newell is a champion for equality and education. Credit: Zala Films
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Journeys of Black Mathematicians: Forging Resilience Zala Films Directed by George Csicsery
What does a mathematician look like? Standing in front of a room of Black children aged six to twelve, research mathematician Zerotti Woods — who posed the question — is not far off their description. Woods, who is based at Johns Hopkins University in Baltimore, Maryland, is wearing nice trousers, a jacket and even round glasses. Yet he’s told he doesn’t look like a mathematician. Their unspoken assumption seems to be that mathematicians are white.
In the documentary Journeys of Black Mathematicians: Forging Resilience , film maker George Csicsery interviews more than 50 scholars, who speak about the value of mathematics, share parts of their journeys and look to the future. The film, which was co-produced with the Mathematical Sciences Research Institute, premiered in January and has been released online . By juxtaposing career paths with the historical timeline of the civil-rights movement in the United States, the film seeks to show what Black mathematicians have been through and provide hope for what can be. That hope is more than a wish. It is backed up by descriptions of supportive programmes, nurturing educators, positive changes in the community and success stories.
Historical attitudes toward Black mathematicians thread through the film. Scholars such as William Claytor faced blatant discrimination throughout their careers. The US Supreme Court’s 1954 integration decision, in which segregated schools were deemed unconstitutional, gave Black students access to white educational spaces. But such access did not necessarily come with better education or treatment. One interviewee notes that the good teachers at Black schools did not follow the children to the desegregated schools. In higher education, Black spaces did not cease to exist. Historically Black colleges and universities (HBCUs) were almost all founded before desegregation, because most pre-existing institutions, particularly in the southern states, either prohibited Black students from attending, or limited their presence through quotas.
Role models
Teaching and learning at HBCUs is a point of pride throughout the documentary. These are places where Black maths students are nurtured rather than ‘othered’. Many interviewees describe how the representation and support they found at these colleges propelled them into the field.
Academic workplaces are still failing Black women; they must do better
Among those acknowledged as impactful educators are Claude Dansby, who was at Morehouse College in Atlanta, Georgia, from 1922 to 1967, and Etta Falconer, who was mainly at Spelman College, also in Atlanta, between 1965 and 1985. Through interviews with former students and colleagues, Csicsery draws parallels between them and two mathematicians currently at Morehouse: Duane Cooper and Ulrica Wilson. All are beloved by students and are considered the main reason that some pursued and succeeded in maths. All four had a crucial influence on the paths of dozens of Black mathematicians — which speaks not just to their teaching methods, but more importantly to how they supported their students, and believed in and cared about them. Woods specifically mentions that Cooper taking responsibility for him was the only reason that he was allowed to finish his degree at Morehouse after having been expelled for a year. That care made all the difference.
Many who were interviewed in the film note just how few Black people they met on their maths journey. I’ve also found this. According to the 2018 US Mathematical and Statistical Sciences Annual Survey, 2.9% of US maths PhDs were awarded to Black mathematicians that year (see go.nature.com/3tphae6 ). Given that around 14% of the US population is Black, this number is incredibly low.
If you’re looking for an explanation, the documentary describes some of the roots of the systemic racism that still permeates maths. The US National Association for Mathematicians (NAM), created in 1969, aims to promote excellence in the mathematical sciences and “the mathematical development of underrepresented minorities”. Civil-rights pioneer and former educator at Winston-Salem State University in North Carolina, Virginia Newell, who appears in the film, makes its origins clear: “The reason why we started the NAM was because the whites did not want us at their meetings.” And how could Black mathematicians be welcome when meetings were being held at segregated institutions?
William Claytor was discouraged by the racism prevalent in the field. Credit: Courtesy of the Dolph Briscoe Centre for American History
Black people are often still being treated disrespectfully at maths meetings, confirmed a 2021 report by an American Mathematical Society task force (see go.nature.com/43dhf67 ). By organizing a range of events — such as lecture series, sessions at large maths conferences and MATHFest, an annual meeting and networking event for undergraduate students — and by ensuring Black scholars are invited to them, NAM provides, crucially, a community.
Aspirations for the future
The stories of Black mathematicians shared in the film are inspiring. It is wonderful to learn about successes in academia and industry — but there is still a long way to go. Csicsery makes that clear by titling the final chapter of the film ‘Unfinished business’. The percentage of US maths PhDs earned by Black people has remained mostly unchanged since 1978. “We’ve not moved the needle in producing PhDs,” notes Freeman Hrabowski III, former president of the University of Maryland in Catonsville, who grew up in segregated Alabama.
Stirring biopic of the first woman to win top maths prize
The question that needs to be asked now is which spaces are worth entering. The film suggests that Black people should be everywhere, so that there are those with similar mindsets and values in every room. But I disagree; there are some rooms that we should not aspire to enter. Not just because they provide a hostile environment — that can eventually be changed. But because some spaces have too high a moral cost. Is it worthwhile to create weapons or work for security agencies, for example, in a push for representation? For me, the answer to that is absolutely not.
Csicsery’s film did not interrogate that idea, but we should. We should sit with the discomfort of the fact that pushing back against the inequities of the past and present should not include contributing to the oppression of others. When watching this worthwhile film, you will be equipped with enough history to ponder another question: where do we go from here?
Nature 627 , 486-487 (2024)
doi: https://doi.org/10.1038/d41586-024-00798-y
Competing Interests
The author declares no competing interests.
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Frontiers in Educational Research , 2023, 6(14); doi: 10.25236/FER.2023.061403 .
Value Research of Integrating History of Mathematics into Primary School Mathematics Teaching
Wei Haiyan 1,2 , Mohd Faizal Nizam Lee bin Abdullah 1
1 Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak Darul Ridzuan, Malaysia
2 College of Teacher Education, Taishan University, Tai’an, China
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Jules Henri Poincaré, the great French mathematician, said that if we wanted to see the future of mathematics, the proper way was to study the history and present state of the science. Integrating the History of Mathematics into primary school mathematics classroom teaching can stimulate students' interest in learning, inspire their thinking and enhance their mathematical literacy, while cultivating good qualities, promoting mathematical culture and enhancing cultural confidence. In the paper, the value of integrating the History of Mathematics into students' learning will be specifically explained through the explanation of mathematics knowledge points in primary schools.
History of Mathematics; Mathematics Teaching in Primary Schools; Value Research
Cite This Paper
Wei Haiyan, Mohd Faizal Nizam Lee bin Abdullah. Value Research of Integrating History of Mathematics into Primary School Mathematics Teaching. Frontiers in Educational Research (2023) Vol. 6, Issue 14: 12-18. https://doi.org/10.25236/FER.2023.061403.
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[7] E. Leyva, C. Walkington, H. Perera, and M. Bernacki, "Making Mathematics Relevant: an Examination of Student Interest in Mathematics, Interest in STEM Careers, and Perceived Relevance," International Journal of Research in Undergraduate Mathematics Education, 2022.
[8] F. Cajori, "The pedagogic value of the history of physics," The School Review, vol. 7, no. 5, pp. 278-285, 1899.
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[12] H. L. Xiao, "A Research on the Application of Mathematical History into Primary Mathematics Class," Master, Central China Normal University, 2018.
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[14] M. Alpaslan, M. Iksal, and I. Haser, "Pre-service Mathematics Teachers' Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education," Science & Education, vol. 23, no. 1, pp. 159-183, 2014.
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Title: a wasserstein perspective of vanilla gans.
Abstract: The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for good dimension reduction properties. Statistical results for Vanilla GANs, the original optimization problem, are still rather limited and require assumptions such as smooth activation functions and equal dimensions of the latent space and the ambient space. To bridge this gap, we draw a connection from Vanilla GANs to the Wasserstein distance. By doing so, existing results for Wasserstein GANs can be extended to Vanilla GANs. In particular, we obtain an oracle inequality for Vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be satisfied by network architectures commonly used in practice, such as feedforward ReLU networks. By providing a quantitative result for the approximation of a Lipschitz function by a feedforward ReLU network with bounded Hölder norm, we conclude a rate of convergence for Vanilla GANs as well as Wasserstein GANs as estimators of the unknown probability distribution.
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Encyclopedia of Mathematics Education pp 349–354 Cite as
History of Research in Mathematics Education
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An account of activities and events concerned with the development of disciplined inquiry in mathematics education as a flourishing academic enterprise.
Although mathematics has been taught and learned for millennia, not until the past century or so have the nature and quality of teaching and learning mathematics been studied in any a serious manner. Clay tablets from ancient Babylonia (c 1900 BC to c 1600 BC), for example, show that students in the scribal school were expected to solve problems involving quadratic polynomials (Høyrup 1994 , pp. 4–9), but no available evidence indicates how much drill and practice either they received or their instructors thought they needed. As of 1115 BC, applicants to the Chinese civil service had to pass an examination in arithmetic (Kilpatrick 1993 , p. 22), but as far as anyone knows, no one ever investigated how well their examination performance predicted their job performance. In Plato’s Meno , he relates how, in the fifth...
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History of Mathematics. Created 09 Mar 2023 | Updated 26 Apr 2023 | 21 articles A curated collection of papers on Math History from MAA journals. Additional papers from Convergence and Math Values available here. Select to download all citations or PDFs. ... Register to receive personalised research and resources by email. Sign me up.
Over the last 40 years, exploring the possible interrelations between the history of mathematics and mathematics education has gradually emerged as an interdisciplinary domain of educational research and practice, and entered a maturity stage during the last two decades. This development calls for an account of the general issues concerning the rationale and main themes underlying research and ...
The History of Mathematics: A Source-Based Approach (Volumes 1 & 2) by June Barrow-Green, Jeremy Gray, In many mathematics depart-ments, a history of mathematics course can be difficult to im-plement. Most departments do not have an expert historian of mathematics and often rely on well-intentioned, but possibly untrained, faculty to offer this
RESEARCH PAPER . Fundamental Concepts of History of Mathematics ... Keywords: Mathematics, History, Calculating, Measuring . Article Publication . Published Online: 15-Ju l-2021
Abstract. This paper aims to provide an overview of the research on the relations between History of Mathematics and Mathematics Education (what we call the "HPM domain" 1) with emphasis on some ...
This article sums up recent developments in the history of mathematics. The range of mathematics considered has considerably broadened, expanding well beyond the traditional field of original research. As new topics have been brought under consideration, methodologies borrowed from neighboring academic fields have been fruitfully put into use. In the first section, we describe how well-known ...
This paper aims to provide an overview of the research on the relations between History of Mathematics and Mathematics Education (what we call the "HPM domain" 1) with emphasis on some of the more ...
This paper concerns the history of mathematics and mathematics education. I should say from the start that I will not display results from empirical research showing how the history of mathematics is good for this or that. ... However, much of that research treats the history of mathematics as a tool, to use the phrase Jankvist has popularized ...
There were different ways of doing mathematics in the ancient Greek and Roman world. This essay will explore historiographical approaches to this diversity, from the claim that there were different traditions, to explorations of the social status of mathematicians, to attempts to go beyond written traditions in order to reconstruct practices. I will draw on Jean Lave's studies on situation ...
sources and research papers, others use manuals of history of mathematics, popularization books, readers, etc.; - having introduced history in the classroom the teacher tends to consider the experience positive. This opinion, which is common to the majority of the cases, usually comes from subjective impressions and not from regular
Mathematics, like any other human activity, has its fashions, and the nearer one is to a given period, the more likely these fashions are to look like the wave from the past to the future. For this reason, the writer needs to have relevant references to assess the essence of the history of ancient mathematics. 1.
Download. by Andy R German. 10. Plato , Aristotle , History of Mathematics , Critical Thinking. Novalis. Mathematical Fragments (1798-1800) A selection of some of Novalis's most important reflections on mathematics from the years 1798-1800. Introduced and translated into English by David W. Wood.
Barbin et al. (2020) in the chapter History of Mathematics in Education in the Encyclopedia of Mathematics Education. In the section Current Concerns and Emergent Questions in the Field, the authors mention the need for (1) common ground between the history of mathematics and mathematics education, (2) effective theoretical and conceptual frame-
student presentations and research papers are more common in mathematics history courses than in other math courses. These presentations and papers vary in length (from course to course or within a single course), but typically focus on individual mathematicians or on individual results or topics in mathematics history.
Abstract and Figures. In this work, we present a periodization of the history of mathematics, which is focused on the nature of mathematical problems solved in each period; this division takes ...
More than a century after publishing major papers in theoretical mathematics, German-born Emmy Noether continues to challenge and inspire mathematicians with her story and mathematical legacy ...
Abstract. This paper is an attempt to reflect on class sessions during the fall 2010 in a course 'Theory and Research in Mathematical Learning and Development'. This reflection as a learning journey portrays discussions based on foundational perspectives (FP), historical highlights (HH), and guiding questions (GQ) related to mathematics ...
• History of perfect numbers from Euclid to the day before yesterday • The influence of social needs on the uses of mathematics • History of the binomial theorem • The quadratic equation • An insight into Islamic mathematics • Goldbach and his famous conjecture • The history of logarithms and logarithm tables
without requiring too specialized knowledge in the history of mathematics). These papers also suggest fresh avenues for research, some bearing on potential methodological connections between mathematics, education, and history (e.g., the ... supports research in mathematics education; or as a resource for didactic inter-vention in all aspects ...
The film, which was co-produced with the Mathematical Sciences Research Institute, premiered in January and has been released online. By juxtaposing career paths with the historical timeline of ...
Abstract. This paper surveys central justifications and approaches adopted by educators interested in incorporating history of mathematics into mathematics teaching and learning. This interest itself has historical roots and different historical manifestations; these roots are examined as well in the paper. The paper also asks what it means for ...
The essay describes the developments in mathematics over human history. It is a short account of important steps taken by humanity in the development of mathematics, its methods and applications.
Developing Research in Mathematics Education Twenty Years of Communication, Cooperation and Collaboration in Europe, 2018. [10] Y. D. Arthur, S. K. Appiah, K. Amo-Asante, and B. Asare, "Modeling student's interest in mathematics: Role of history of mathematics, peer-assisted learning, and student's perception," EURASIA Journal of ...
The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for good dimension reduction properties. Statistical results for Vanilla GANs, the original optimization problem, are still rather limited and require ...
The history of the field had been discussed at various international conferences beginning in 2004, and a series of biennial conferences devoted to the topic began in Iceland in 2009. As the field of mathematics education has grown, research in the field has grown even faster.
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