Love and Math: The Heart of Hidden Reality, by Edward Frenkel

“Love” and “mathematics” are words that most people would not associate with each other. Indeed, mathematicians often complain that when they first meet someone, the revelation that they teach or research mathematics will lead to their being regaled with stories of personal difficulties regarding the subject – something that rarely afflicts those in other academic disciplines.

Edward Frenkel is keen to address this challenge. Acknowledging that people do not understand what mathematics is, he blames this on mathematics teaching, which he likens to art classes that only teach students how to paint fences without ever showing the work of masters such as Pablo Picasso and Leonardo da Vinci. The problem, he says, is that while the work of the great painters is displayed for all to appreciate, mathematics at this level is locked away and inaccessible to the person on the street.

While he was still at school, Frenkel himself saw maths as “stale and boring”. But he was lucky; in his final year of high school he met a professional mathematician who introduced him to the real world of mathematics. He is now an award-winning academic (he was the first recipient of the Hermann Weyl Prize in 2002) as well as a writer and film-maker.

The problem is that while the work of the great painters is displayed for all to appreciate, mathematics at this level is locked away inaccessible to the person on the street

This inspirational book has been written to unlock the power and beauty of mathematics for the reader by weaving the ideas of sophisticated mathematics through Frenkel’s autobiography. Readers are assumed to be non-mathematicians, but are presented with enough mathematics to enable appreciation of the wonder of a major breakthrough in modern mathematical understanding and research: the Langlands Program. Proposed by Robert Langlands in the late 1960s and sometimes described as the Grand Unified Theory of mathematics, the program takes concepts and ideas in pure mathematics and uses them to further the understanding of complex physics and applied mathematical problems, bringing together the theories and conjectures of abstract algebra, number theory, geometry, analysis and quantum physics. It is an unusual mix, given that mathematics is a field in which it is rare for, say, a number theorist to read papers on quantum physics.

While some chapters of Love and Math may look heavy on the mathematics, they can easily be skipped if readers find the concepts hard to fathom. Every mathematical word is explained, and simple analogies provided, so that ideas such as groups, functions, braids and particles are quickly grasped.

What I found particularly inspirational is Frenkel’s own journey as a mathematician. Raised in Soviet-era Russia, and from a Jewish background, he decided to study mathematics but “failed” the entrance exam for Moscow State University thanks to the extreme state anti-Semitism of the period. This led him to wonder if he really was cut out to be a mathematician: even the greatest mathematicians can lose confidence in their own ability. Frenkel describes many encounters with mathematicians who encouraged him along the way, providing him with the research problems that led to his interest in many of the fundamental issues in the Langlands Program.

The book ends with two screenplays, The Two-Body Problem and Rites of Love and Math, that Frenkel co-wrote: he directed and performed in a film of the latter, which was intended as a homage to the work of Yukio Mishima. Both pieces bring love and mathematics together for a general audience, and were written in part to dispel the popular myth of the mathematician as an eccentric figure on the edge of mental illness.

Frenkel’s account of his journey from a youngster struggling to study mathematics in the USSR to an acclaimed academic at Harvard University and now the University of California at Berkeley is inspirational. I believe it has the potential to excite and motivate readers, whatever their discipline.