The public perception of mathematics and mathematicians can be rather depressing for those of us in the discipline. We are often regarded as highly intelligent, yet the people we meet at parties tend to change the subject when they find out what we do, and the creativity inherent in our profession is not always recognised. The actor Molly Ringwald, asked about her love life, told the interviewer, "Well, it's not really going anywhere these days. Of course you won't find me dating any mathematicians...", and the heroine of Charlotte Cory's BBC Radio 4 comedy series Thinking of Leaving Your Husband? nearly missed out on her perfect partner when he outed himself as a mathematician.
One of the aims of this provocative new book, jointly written by Reuben Hersh, a mathematician, and Vera John-Steiner, a professor of linguistics and education, is to overcome "distorted, stereotypic images of the field and its practitioners". The early chapters look at how people are drawn to mathematics; the culture of the subject; friendships and partnerships in mathematics; and the communities in which mathematics takes place. Here, the approach is largely anecdotal.
A number of these affectionate stories are very amusing. I particularly enjoyed hearing about the topologist RH Bing ("RH" were his full forenames, not his initials) driving a group of mathematicians to a conference on busy roads in bad weather. The windscreen had steamed up and the passengers were worried about Bing's inability to see, but he was more interested in talking about topology. Finally, to the passengers' relief, he leaned towards the windscreen - but only to draw mathematical diagrams to illustrate the discussion. While most of the material in this part of the book may support the authors' attack on "the myth that mathematicians are different from other people, lacking emotional complexity", the reader may not be convinced that the first clause of the "myth" is fully debunked by stories such as this.
Hersh and John-Steiner also examine the value of mathematics as solace through well-chosen examples. Chandler Davis paid a penal price for refusing to cooperate with the House Un-American Activities Committee in the 1950s: one of his papers, conceived in jail, acknowledged "research supported in part by the federal prison system". Jose Luis Massera, who spent almost 10 years in prison in Uruguay for political reasons, taught mathematics to his cellmates, and Paul Turan described the ecstasy he felt thinking about mathematics in a Fascist labour camp in Hungary.
The section "Mathematics as addiction" explores more sinister behaviour. Ted Kaczynski's mathematical papers were "paragons of precision", but he used mathematical reasoning to justify his murderous campaign as the Unabomber; Andre Bloch felt that logic compelled him to murder three of his family; and recently Walter Petryshyn, a distinguished mathematician, unhinged by discovering a minor error in a book he had written, killed his wife. The bulk of this chapter is devoted to a discussion of the career of Alexandre Grothendieck, a major figure in mathematics in the third quarter of the 20th century, who later abandoned the subject completely and now reportedly lives as a hermit in the Pyrenees. Here the authors' analysis of the personal factors inspiring apparently impersonal mathematics is illuminating, and the account is enthralling. Moreover, recent events in the UK have lent additional resonance to his story: Grothendieck, during one demonstration in the 1970s, used his boxing skills to knock out two policemen he believed were harassing peaceful protesters.
While the anecdotes in the first part provide entertainment, the authors' passion emerges more clearly in the themes of the book's second half. Here they investigate forms of discrimination that have prevented many scholars from achieving their mathematical potential. There are case studies of female mathematicians who succeeded against the odds - Sofia Kovalevskaya, Grace Chisholm Young, Emmy Noether, Julia Robinson - and the strategies they used, the support they received and the accommodations that were necessary. Much of Chisholm's work was published in her husband William Young's name, while Robinson did not get an appointment at the University of California, Berkeley until she was elected to the National Academy of Sciences.
There are also shocking accounts of the treatment of Jews in the Soviet Union, and one of the book's heroes is Bella Abramovna Subbotovskaya, killed by a hit-and-run driver in suspicious circumstances when the authorities cracked down on the underground mathematical Jewish People's University. And the accounts of the obstacles faced by black mathematicians in the US in the 20th century are horrifying.
A final theme here is the teaching of mathematics. My suspicion that reflections on education in the US might not be entirely relevant to readers elsewhere turned out to be ill-founded. Two US pioneers are presented - R.L. Moore, whose "Moore method" for training research mathematicians was enormously successful and influential, and Clarence Stephens, whose department at the tiny Potsdam College in New York state produced, in 1985, more mathematics graduates than all but two US universities. The contrasts could hardly be greater between the African-American Stephens and Moore, who on one occasion refused to teach while a black student was present.
There is insightful analysis of both the strengths and weaknesses of the Moore method, which required students to create advanced mathematics for themselves, entirely without reference to books or journals. Hersh and John-Steiner cannot hide their enthusiasm for the Potsdam method, based on high standards combined with principles such as "Students come first", "Know your students well - their names, their hopes and fears" and "Have complete confidence that every student can be successful".
The authors ponder whether too much mathematics is taught to those who don't need it. We are told the story of the mathematician, stopped at an airport security check, who is asked a series of increasingly detailed questions of no obvious relevance. When he eventually complains, the customs officer says, "Now you know how I felt when I took calculus." The issues raised are important and the discussion is helpful, even though the UK situation is not quite the same.
Mathematics is loved by many and hated by many. One of the strengths of this book is that the authors, who presumably are in the former camp, are sympathetic towards those in the latter. And while they love mathematical culture, they are far from uncritical. They are forthright in discussing recent examples of prejudice in the community, and the factors that still make careers for female mathematicians much more difficult. They look at the vexing question of age, and the "myth" that mathematics is a young man's game: indeed, a survey conducted by Hersh is encouraging for us oldies. The unifying theme in this book is that, contrary to popular belief, mathematics is a human activity and human factors are important in it, and the weight of evidence the authors have gathered makes the point very strongly.
It is the critical examination of the consequences of the human factors in the community of mathematics that makes Loving and Hating Mathematics so important. The rallying call for support for women in making mathematics careers is powerfully presented. In the UK, there is a new initiative from the London Mathematical Society and the Heads of Departments of Mathematical Sciences to help advance women's careers in university mathematics departments: this is certainly as important an issue here as it is in the US.
This thoroughly entertaining book highlights vitally important issues: it also leaves me inspired by the wonderful Stephens, whose successful approach to mathematics teaching is summed up by his slogan, "Believe in your students; everyone can do mathematics."
Upon completing his bachelor's degree in English literature at Harvard University and realising he had "just missed his opportunity to fight Fascism", Reuben Hersh signed up for 18 months in the US Army in 1945-46. Four years as an editorial assistant at Scientific American magazine, and then work as a second-class machinist, followed.
He then "took refuge in academia" and pursued a PhD in mathematics at New York University.
Hersh is currently professor emeritus in the department of mathematics and statistics, University of New Mexico.
Professor of linguistics and education at the same institution, award-winning author Vera John-Steiner loves the bridges between the shores of the Danube, and between cultures, languages and people.
Her engagement with the "life of the mind", she says, was encouraged by her teachers in her native Budapest.
She took a bachelor's degree in psychology from Columbia University and then a doctorate in the same subject at the University of Chicago.
Loving and Hating Mathematics: Challenging the Myths of Mathematical Life
By Reuben Hersh and Vera John-Steiner
Princeton University Press
Published 26 January 2011