Mathematical Images and Gender Identities: A report on the gendering of representations of mathematics and mathematicians in popular culture and their influences on learners

This report details research into the following questions: How are representations of mathematics and mathematicians in popular culture gendered? How are the effects of these representations of mathematics and mathematicians in popular culture on learners gendered? To address these questions, we draw on detailed analysis of the following data, collected as part of an earlier Economic and Social Research Council funded project: About 50 popular cultural texts including films, websites, books, radio and television programmes. Over 500 questionnaires from 14-15 year-old GCSE students and 100 questionnaires from undergraduates in mathematics and media studies. 15 focus groups with 15-16 year-old GCSE school students and 12 focus groups with undergraduates in mathematics and social sciences and humanities. 26 individual interviews with 15-16 year-old GCSE school students and 23 individual interviews with final year undergraduates in mathematics and with undergraduates and postgraduates in social sciences and humanities. The main findings in relation to the gendering of representations of mathematicians and mathematics in popular culture are that: Mathematical representations are both invisible and ubiquitous in popular culture. And whether something is seen as mathematical depends upon context and upon the reader’s understanding of and relationship with mathematics as well as on their other cultural resources. Popular culture texts strongly support the association of mathematics with masculinity, and also with Whiteness, middle-classness and heterosexuality. This gendering happens through: the dominant representations of mathematicians being men, the disappearing of women’s mathematical contributions and the ways that women doing mathematics are subordinated in a range of ways including their youth and their positioning as appendages to ‘greater’ male mathematicians. Representations of male mathematicians combine features that ally them with heroic and powerful men and also features that present them as other, including: mental health problems, obsessiveness, fragility, and social incompetence. Their ‘genius’ is seen to mark them out from others and all other aspects of the self are subjugated to this. There is an emerging group of cultural texts featuring women mathematicians, several of which are part of a growing trend of young, attractive ‘smart girls’. While encouraging, there are questions to be raised about the low proportion of adult women mathematicians, the dramatised tensions between feminine heterosexuality and mathematics and the hyper-attractiveness of these characters. Both the representations of women and of men mathematicians, in different ways, present their mathematical abilities as ‘natural’ and as something people are born with rather than something that is acquired. Associated with the last point, representations of mathematics generally present this in ways that support ideas of its inaccessibility to the majority of the population. Popular representations of processes of doing mathematics show it as being about sudden and individual moments of inspiration that are accessible only to ‘geniuses’. This creative process is aligned with masculinity. There are some trends in popular mathematics that offer alternatives to the clichés, notably mathematics incorporating aspects of beauty, creativity, empathy and accessibility. In particular, much popular mathematics is contestable rather than set in stone. The main findings in relation to the gendered influence on learners of representations of mathematicians and mathematics in popular culture are that: There are very strong default images of mathematicians that are easily called up; these default images of mathematicians are of old, White, middle-class, heterosexual men and are associated with markings onto and into the body, including states of clothing, posture, mental health and social awkwardness or geekiness. These images reflect those circulating in popular culture. They are shared by men and women. Most participants were unable to identify attractive but unknown women as mathematicians while being aware that this was problematic. There were mixed feelings about the use of such images to sell mathematics, particularly when they were overtly sexual. Mathematics is constructed through a series of gendered oppositions such as numbers vs. words, technical vs. emotional and everyday vs. esoteric. These make mathematics something that is less attractive to women than to men. Discourses of mathematicians are also characterised by oppositions, for example between ‘normal’ mathematicians and ‘real’ mathematicians, people with ‘natural’ ability and those who just cannot get it or who need to work hard to do so. These discourses link to distinctions between everyday and esoteric mathematics. Again, these images reflect those circulating in popular culture and were shared by men and women but have gendered effects. Women are less likely to self-identify as having mathematical ability than men and this makes it more difficult for them to choose to continue with the subject. Both men and women’s sense of their mathematical ability derived largely from external factors, prominent among these were assessment results and positions within teaching groups that are setted by ‘ability’. The ways that people read images of mathematicians and mathematics depend on the understandings or resources people bring to them. For example, participants who identified with feminism more often read mathematical ability into feminine bodies and participants who identified with mathematics more often read examples of creativity as mathematical. Popular mathematicians and mathematics can provide a resource for developing positive relationships with mathematics. In particular, popular mathematicians can provide points of identification and popular mathematics can provide a space to explore ‘alternative’ understandings of mathematics that cut across some of the oppositions

'Magic coins' and 'magic squares': the discovery of astrological sigils in the Oldenburg Letters

Enclosed in a 1673 letter to Henry Oldenburg were two drawings of a series of astrological sigils, coins and amulets from the collection of Strasbourg mathematician Julius Reichelt (1637–1719). As portrayals of particular medieval and early modern sigils are relatively rare, this paper will analyse the role of these medals in medieval and early modern medicine, the logic behind their perceived efficacy, and their significance in early modern astrological and cabalistic practice. I shall also demonstrate their change in status in the late seventeenth century from potent magical healing amulets tied to the mysteries of the heavens to objects kept in a cabinet for curiosos. The evolving perception of the purpose of sigils mirrored changing early modern beliefs in the occult influences of the heavens upon the body and the natural world, as well as the growing interests among virtuosi in collecting, numismatics and antiquities

The Cryptographic Imagination

Originally published in 1996. In The Cryptographic Imagination, Shawn Rosenheim uses the writings of Edgar Allan Poe to pose a set of questions pertaining to literary genre, cultural modernity, and technology. Rosenheim argues that Poe's cryptographic writing—his essays on cryptography and the short stories that grew out of them—requires that we rethink the relation of poststructural criticism to Poe's texts and, more generally, reconsider the relation of literature to communication. Cryptography serves not only as a template for the language, character, and themes of much of Poe's late fiction (including his creation, the detective story) but also as a "secret history" of literary modernity itself. "Both postwar fiction and literary criticism," the author writes, "are deeply indebted to the rise of cryptography in World War II." Still more surprising, in Rosenheim's view, Poe is not merely a source for such literary instances of cryptography as the codes in Conan Doyle's "The Dancing-Men" or in Jules Verne, but, through his effect on real cryptographers, Poe's writing influenced the outcome of World War II and the development of the Cold War. However unlikely such ideas sound, The Cryptographic Imagination offers compelling evidence that Poe's cryptographic writing clarifies one important avenue by which the twentieth century called itself into being. "The strength of Rosenheim's work extends to a revisionistic understanding of the entirety of literary history (as a repression of cryptography) and then, in a breathtaking shift of register, interlinks Poe's exercises in cryptography with the hyperreality of the CIA, the Cold War, and the Internet. What enables this extensive range of applications is the stipulated tension Rosenheim discerns in the relationship between the forms of the literary imagination and the condition of its mode of production. Cryptography, in this account, names the technology of literary production—the diacritical relationship between decoding and encoding—that the literary imagination dissimulates as hieroglyphics—the hermeneutic relationship between a sign and its content."—Donald E. Pease, Dartmouth Colleg

Letter counting: a stem cell for Cryptology, Quantitative Linguistics, and Statistics

Counting letters in written texts is a very ancient practice. It has accompanied the development of Cryptology, Quantitative Linguistics, and Statistics. In Cryptology, counting frequencies of the different characters in an encrypted message is the basis of the so called frequency analysis method. In Quantitative Linguistics, the proportion of vowels to consonants in different languages was studied long before authorship attribution. In Statistics, the alternation vowel-consonants was the only example that Markov ever gave of his theory of chained events. A short history of letter counting is presented. The three domains, Cryptology, Quantitative Linguistics, and Statistics, are then examined, focusing on the interactions with the other two fields through letter counting. As a conclusion, the eclectism of past centuries scholars, their background in humanities, and their familiarity with cryptograms, are identified as contributing factors to the mutual enrichment process which is described here

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Poe\u27s Poisoned Pen: A Study in Fiction as Vendetta

Edgar Allan Poe, widely regarded as an extremely influential American writer and prolific literary critic, exacted high standards in both his writing and in the writing of those he reviewed. Though his criticism was harsh, it was a necessary part of the growing process for American literature to become a separate and distinct body of literature. However, Poe\u27s literary criticism is not his only work that bore the stinging marks of his pen; his fiction was also a venue for Poe to express his dissatisfaction with the literary field in America. Using a combination of close reading for textual analysis and Walter Fisher\u27s narrative paradigm, this thesis explores the question of who, exactly, Poe was chastising in his literature. Some have said Poe was a racist, or a misogynist, or just bitter. This thesis examines Poe\u27s literature, focusing on his short stories, in light of his literary milieu. In his detective stories, Poe seems to be questioning and attacking the established literary authority--the Transcendentalists and the Literati--as well as those who chose to plagiarize. In some of the other literary genres in which Poe wrote, it appears he is doing the same. Poe\u27s short stories, then, were not just a means of generating revenue for himself; they were an attack and an argument against the current literary field