Loving and Hating Mathematics: Challenging the Myths of Mathematical Life
reviewed by Elizabeth de Freitas - January 20, 2012
Title: Loving and Hating Mathematics: Challenging the Myths of Mathematical Life
Author(s): Reuben Hersh & Vera John-Steiner
Publisher: Princeton University Press, Princeton
ISBN: 0691142475, Pages: 428, Year: 2010
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As guest editor of a special issue of Educational Studies in Mathematics (1996), Peter Lerman described the socio-cultural turn in the study of mathematics teaching and learning, pointing to a range of new approaches that might better capture and illuminate experiences with mathematics. Lerman and many others have since developed various kinds of socio-cultural studies of mathematics education, but there is very little research on the culture of mathematicians, and even less research that links this culture with educational trends and concerns. Reuben Hersh and Vera John-Steiner speak to this silence in their book, Loving and hating mathematics: Challenging the myths of mathematical life. The book follows the life history narratives of various nineteenth and twentieth century mathematicians, situating their stories in socio-cultural milieus, and uncovering the ways in which these contexts shaped their experiences. The authors claim that this book, unlike most books on mathematics, is about mathematicians, their extraordinary passion for mathematics and their full complexity of being (p.1).
Drawing extensively on autobiographies, biographies, and other historical documents, the authors aim to overturn common misconceptions about the field and its practitioners, first and perhaps foremost, the myth that mathematicians lack emotional complexity. Each chapter focuses on particular socio-cultural aspects of various individual mathematicians experiences, filling in the everyday details of lives lived in relation to others. The book begins and ends with chapters focused explicitly on mathematics education and its role in cultivating and inhibiting the love of mathematics. Chapter one opens with the question, how does a child first begin to become a mathematician? while chapter eight explores the impact of undergraduate education on the future of the field, and chapter nine argues for a new kind of curriculum and agenda in K-12 education.
Hersh and John-Steiner argue that the still dominant focus on drill and test leads to a population of math haters, whereas the mathematicians discussed in each chapter are clearly enamored and passionate about what they do. The strength of the book, in relation to this argument, is the focus on emotion, passion and motivation in relation to mathematics achievement. Ultimately, through its arguments and the many case studies of creative mathematicians, the book points to the incredible impact a passionate and highly motivated teacher, mentor and supportive community can have on students engagement with mathematics.
Since the field of mathematics continues to be a field dominated by while males, the chapters that trace the achievements of women in the field are compelling portraits of the need for mentoring and community support. The authors tell the stories some of them better known than others of Sophie Germain (1776-1831) posing as a man so as to study analysis with Lagrange, of Sophia Kovalevskaya (1850-1891) and her ongoing mentoring by Karl Weierstrass when the university refused to enroll her because she was a woman, of Emmy Noether (1882 -1935) who faced similar obstacles in Berlin, and of the tragic death of Bella Abramovna Subbotovskaya (1938-1982) in the Soviet Union, and her role in the creation of a Jewish Peoples University. The authors also discuss contemporary women mathematicians, recounting the case of Jenny Harrison (1949-) who successfully appealed when she was denied tenure at UC Berkeley, arguing that she had been discriminated against because of her gender: Her case raises important issues about womens determination to make a place in a traditionally masculine culture.(p. 84).
Aside from these stories of almost heroic determination, the book is committed to depicting the ways in which community and collaboration are a central part of Western mathematics culture. One chapter explores four significant community support groups that emerged at various times to sustain various movements in mathematics. The relationships (both friendships and feuds) within these communities functioned as the driving force in the development of contemporary mathematics, whether it be Felix Kleins creation of a multidisciplinary scientific center in Gottingen in the 1890s, Courants similar project at the Courant Institute at NYU in the 1930s, the Bourbaki movement begun in Paris in the 1930s by André Weil, Henri Cartan, and Jean Diedonné, the Anonymous group sparked by Paul Erdos in Budapest in the 1930s, or the Golden age at the Mechanics and Mathematics department at Moscow University in the 1960s. By focusing on these communities, and other kinds of partnerships, including the occasional marriage between mathematicians, the authors offer something like an anthropological map of the field and its practitioners. And to their credit, they also have a chapter on those famous mathematicians who have been labeled mad or insane, contesting the usual myth that it is the mathematics and its requisite abstract and absent-minded obsessive habits of thought that has driven these mathematicians mad. They tell the story of the prolific Alexandre Grothendieck, a German-born, but later somewhat stateless mathematician who from 1950 to 1970 reshaped functional analysis and algebraic geometry (p. 108). At the age of 20 he went to Paris with a letter of introduction from his calculus teacher to Henri Cartan, was there recognized for his talent and later moved to Nancy to work with Laurent Schwartz, a leading activist for human rights as well as a leading mathematician. After producing a seminal dissertation, he spent a few years in Paris, and some time in Brazil and in the US. In 1957 Grothendieck and Jean Diedonné were hired at the newly founded French Institut des Hautes Études Scientifiques (IHES), where they pumped out thousands upon thousands of pages of mathematics, including 30 volumes in the IHES blue series, as well as Élements de Géométrie Algébrique (EGA) and Séminaire de Géométrie Algébrique (SGA). Grothendieck was so prolific that a group of more or less willing and able students and colleagues acted as scribe for him. And yet in the 70s, still at the height of his creative powers, he strengthened his political resolve to not participate in a world that invested in global cruelty, and he began to show that tell-tale egotism that speaks of madness. Sadly, he left mathematics, refusing to accept honors and awards, and today lives as a pacifist hermit, at a secret address in a remote village in the Pyrenees mountains. Through their telling of this story, combined with the stories of Ted Kaczynski, André Bloch and Kurt Gödel, the authors map a terrain of madness and mathematics that doesnt mythologize the mathematics, but rather points to the ways in which a life lived in/with mathematics demands an intense emotional investment, and often takes a corresponding toll.
The focus on emotion and passion is crucial to the authors argument regarding the role of education in promoting positive experiences with mathematics. Although they admire and see a place for the work of Bob Moses and the Algebra Project, and all other attempts to bring better quality teaching to communities who have historically been denied it, they state that it is unrealistic and unnecessary to guarantee that every child pass 10th grade algebra, and have a good facility with quadratic equations or with systems of two and three linear equations (p. 322). The challenge is then to redesign school mathematics so that it functions less as a critical filter, excluding most from its upper echelons, and more as a space of passion and creativity. Citing Dudley (1997) and other data regarding the irrelevance of most mathematical procedures to everyday life, they believe that what is necessary and realistic is that every child have the opportunity to learn algebra, in a well-equipped classroom, from a qualified, highly motivated teacher(p. 322). Many arguments focusing on educational opportunity fail to grapple with the ways in which systemic racism and inequity strongly determine the outcomes of situations that appear on the surface to offer the same opportunities to all. But this book maps the complex intersection between opportunity, access and achievement in particular contexts, and points to particular practices in the history of U.S. education that have impacted the career trajectories of African-American mathematicians. For instance, in a wonderful chapter comparing the pedagogical model of Robert Lee Moore at the University of Texas with Clarence Stephens at SUNY Potsdam, the authors trace the diverse life histories of those who found themselves in these two schools, including both inspiring stories and stories that should shame any community aspiring to equity.
This book offers important insights into the socio-cultural framing of mathematics education. I believe this book will be of interest and use to both math educators and educational researchers, and to those working in any capacity with mathematics. For those wanting more than a mere anecdote from the history of mathematics, and for those needing a detailed portrait of a field and its practitioners, this book offers great insights and solid scholarship.