Love and Math: The Heart of Hidden Reality

  • Edward Frenkel
Basic Books: 2013. 9780465050741 | ISBN: 978-0-4650-5074-1

Two fascinating narratives are interwoven in Love and Math, one mathematical, the other personal. The love that Edward Frenkel alludes to in his title is the passion stirred in the mathematical heart by the extraordinary story of the research launched in the 1960s by eminent academic Robert Langlands, now at Princeton University, New Jersey. An unfinished saga, the 'Langlands program' is a far-reaching series of conjectures that connect number theory (the challenge of solving equations) with representation theory (part of the theory of symmetry) to create a “Grand Unified Theory of mathematics”.

Edward Frenkel in 2010. Credit: PEG SKORPINSKI

Frenkel grew up in Russia during the 1970s and 1980s. He initially found mathematics boring at school, and it was his fascination with quantum physics that lured him into the subject. A teacher, Evgeny Evgenievich, revealed to the youthful Frenkel that Murray Gell-Mann's prediction of quarks was actually a mathematical theory — and Frenkel's love affair with mathematics began.

Initially, it seemed his passion would be thwarted. In mid-1980s Russia, his Jewish ancestry was enough to prevent his admission to Moscow University. Frenkel's account of how his examiners at the university grilled him with increasingly difficult questions to try to provide a reason to deny him entry is as shocking as it is gripping to read.

But Frenkel was not put off. He enrolled at the Moscow Institute of Oil and Gas, which had an applied-mathematics programme. And he broke through the fences of the Moscow University compound to sneak into lectures and learn more about representation theory. Before long, he was doing his own original research. Publications developing the ideas of some of his mentors on braid groups and Kac–Moody algebras eventually provided his passport to the West. In 1989, when he was just 20 and still studying for his degree, he received an invitation to continue his research at Harvard University in Cambridge, Massachusetts.

Frenkel — now a media-feted mathematician at the University of California, Berkeley — first publicly aired his passion for the field in the 2010 short film The Rites of Love and Math, in which he tattoos formulae on a woman's naked body. His book brings out an almost symphonic aspect to the Langlands program. Through its refrains “solving equations” and “modular forms”, Frenkel deftly takes the reader from the beginnings of this mathematical symphony to the far reaches of our current understanding.

As Frenkel has found, the Langlands program is a profound endeavour (see 'Clocking on'). But his mission, as explored in this book, is much broader. He seeks to lay bare the beauty of mathematics for everyone. As he writes, “There is nothing in this world that is so deep and exquisite and yet so readily available to all”.