The story of a team of female African-American mathematicians who served a vital role in NASA during the early years of the U.S. space program.
Reassembling Mathematical Practices: a Philosophical-Anthropological Approach
In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.
Untangling Knots: Embodied Diagramming Practices in Knot Theory
The low visibility and specialised languages of mathematical work pose challenges for the ethnographic study of communication in mathematics, but observation-based study can offer a real-world grounding to questions about the nature of its methods. This paper uses theoretical ideas from linguistic pragmatics to examine how mutual understandings of diagrams are achieved in the course of conference presentations. Presenters use shared knowledge to train others to interpret diagrams in the ways favoured by the community of experts, directing an audience’s attention so as to develop a shared understanding of a diagram’s features and possible manipulations. In this way, expectations about the intentions of others and appeals to knowledge about the manipulation of objects play a part in the development and communication of concepts in mathematical discourse.
Historical Context of the Gender Gap in Mathematics
This chapter is based on the talk that I gave in August 2018 at the ICM in Rio de Janeiro at the panel on The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective. It provides some examples of the challenges and prejudices faced by women mathematicians during last two hundred and fifty years. I make no claim for completeness but hope that the examples will help to shed light on some of the problems many women mathematicians still face today.
Marjorie Rice (16 February 1923–2 July 2017)
Marjorie Jeuck Rice, a most unlikely mathematician, died on 2 July 2017 at the age of 94. She was born on 16 February 1923 in St. Petersburg, Florida, and raised on a tiny farm near Roseburg in southern Oregon. There she attended a one-room country school, and there her scientific interests were awakened and nourished by two excellent teachers who recognized her talent. She later wrote, ‘Arithmetic was easy and I liked to discover the reasons behind the methods we used.… I was interested in the colors, patterns, and designs of nature and dreamed of becoming an artist’?
Mathematicians Writing for Mathematicians
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.
Philosophy of mathematical practice: a primer for mathematics educators
In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice. In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the distinction between formal and informal proofs, visualization and artefacts, mathematical explanation and understanding, value judgments, and mathematical design. We conclude with some remarks on the potential connections between the philosophy of mathematical practice and mathematics education.
Objectionable Commemorations, Historical Value, and Repudiatory Honouring
Many have argued that certain statues or monuments are objectionable, and thus ought to be removed. Even if their arguments are compelling, a major obstacle is the apparent historical value of those commemorations. Preservation in some form seems to be the best way to respect the value of commemorations as connections to the past or opportunities to learn important historical lessons. Against this, I argue that we have exaggerated the historical value of objectionable commemorations. Sometimes commemorations connect to biased or distorted versions of history, if not mere myths. We can also learn historical lessons through what I call repudiatory honouring: the honouring of certain victims or resistors that can only make sense if the oppressor(s) or target(s) of resistance are deemed unjust, where no part of the original objectionable commemorations is preserved. This type of commemorative practice can even help to overcome some of the obstacles objectionable commemorations pose against properly connecting to the past.
Against Simple Removal: A Defence of Defacement as a Response to Racist Monuments
In recent years, protesters around the world have been calling for the removal of commemorations honouring those who are, by contemporary standards, generally regarded as seriously morally compromised by their racism. According to one line of thought, leaving racist memorials in place is profoundly disrespectful, and doing so tacitly condones, and perhaps even celebrates, the racism of those honoured and memorialized. The best response is to remove the monuments altogether. In this article, I first argue against a prominent offense-based account of the wrong of simply leaving memorials in place, unaltered, before offering my own account of this wrong. In at least some cases, these memorials wrong insofar as they express and exemplify a morally objectionable attitude of race-based contempt. I go on to argue that the best way of answering this disrespect is through a process of expressively “dehonouring” the subject. Removal of these commemorations is ultimately misguided, in many cases, because removal, by itself, cannot adequately dishonour, and simple removal does not fully answer the ways in which these memorials wrong. I defend a more nuanced approach to answering the wrong posed by these monuments, and I argue that public expressions of contempt through defacement have an ineliminable role to play in an apt dishonouring process.
The Duty to Remove Statues of Wrongdoers
This paper argues that public statues of persons typically express a positive evaluative attitude towards the subject. It also argues that states have duties to repudiate their own historical wrongdoing, and to condemn other people’s serious wrongdoing. Both duties are incompatible with retaining public statues of people who perpetrated serious rights violations. Hence, a person’s being a serious rights violator is a sufficient condition for a state’s having a duty to remove a public statue of that person. I argue that this applies no less in the case of the ‘morally ambiguous’ wrongdoer, who both accomplishes significant goods and perpetrates serious rights violations. The duty to remove a statue is a defeasible duty: like most duties, it can be defeated by lesser-evil considerations. If removing a statue would, for example, spark a violent riot that would risk unjust harm to lots of people, the duty to remove could be outweighed by the duty not to foreseeably cause unjust harm. This would provide a lesser-evil justification for keeping the statue. But it matters that the duty to remove is outweighed, rather than negated, by these consequences. Unlike when a duty is negated, one still owes something in cases of outweighing. And it especially matters that it is outweighed by the predicted consequences of wrongful behaviour by others.