Book Review: Edward Frenkel's Extraordinary Case for Love and Mathematics

By Aaron Brown,

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In Michael Crichton's book Jurassic Park , he describes "a new generation of mathematicians" who "dressed and spoke with what one senior mathematician called 'a deplorable excess of personality.' In fact, they often behaved like rock stars."

Crichton's fictional Ian Malcolm could not have been based on real-life mathematician Edward Frenkel; Frenkel was a shy teenager in Russia when Jurassic Park was written. Over the intervening 25 years, however, Frenkel has become one of the most prominent pure mathematicians in the world, with personality and brashness to spare. His YouTube lectures get hundreds of thousands of views, despite covering what most people consider impossibly esoteric, boring, and impenetrable mathematical topics. He has written a screenplay and produced and starred in an erotic movie about math. His celebration of the passion and intensity of mathematics at the highest level has found new expression in his just-published book, Love and Math: The Heart of Hidden Reality .

Frenkel's film was motivated in part by the observation that the most popular mathematics movies portray, "a mathematician [who] is on the verge of a mental illness." I assume he is thinking about movies like Pi , A Beautiful Mind , Proof, and Good Will Hunting . To be fair, there are sane mathematicians in these movies (but they are never as brilliant as the crazy ones) and A Beautiful Mind did not exaggerate the facts of John Nash's mental problems. But I agree with Frenkel that movies are apt to suggest mathematicians are either mediocre and dull or brilliant and psychotically obsessed.

One interesting comparison is to artists, musicians, and writers. With these people, screenwriters often assume they must be tortured to be authentic. But there are plenty of exceptions, movies built around well-rounded, friendly artistic geniuses. And even when artists are a bit crazy, it is an excess of passion, "agony and ecstasy," not some incomprehensible twisted obsession from another dimension. The troubled artist is too human, the mathematician is inhuman. The artist gains relief by completing work, and that work is appreciated by others. The mathematician's frenzied quest just drives him deeper into obscurity and incomprehensibility, not uncommonly to the point that he disappears into some mystic dimension, lapses into catatonia, or simply dies.

It's also interesting to think about the media treatment of real-life pure mathematician Grigori Perelman, who proved the Poincare conjecture , then turned down the Fields Medal and the $1 million Millennium Prize among other honors. Perelman explains himself clearly. He does not want to be a pet or celebrity, he does not want awards from people who aren't qualified to judge his work, he is not interested in money and he is unhappy with the extent that professional mathematics tolerates unethical conduct. He wants to do his math in peace, and share it with honest people who understand it (it's not clear if he continues to do math or not).

I think in any artist or philosopher this behavior would be celebrated as authentic and honest. Think of the kudos Jean-Paul Sartre got for declining the LÃ©gion d'honneur and the Nobel Prize for literature or the credibility George C. Scott and Marlon Brando got for turning down Academy Awards. All three cited reasons in the general ballpark of Perelman's. Yet among these four people, only Perelman is portrayed as a certifiable lunatic whose actions are irrational. Artists kill themselves, rock stars die of drug overdoses, political activists blow up strangers or set themselves on fire; all these things enhance their reputations. But a mathematician must be crazy to love math and want peace.

A third comparison is to the personable and happy mathematicians in popular fiction, like Charlie Epps of Numb3rs and Ian Malcolm of Jurassic Park . Although Epps is described as a pure mathematician, his joy comes from applications. In a generic numbers plot, Epps is given a puzzle relating to a crime and he sees the mathematical connection to some simple physical or social phenomena. While he generally disappears to a computer or see-through erasable board to work out the details offscreen, the emotional high point is when he explains the advanced mathematical concept in terms the FBI agents and the television audience can understand. While these sidebars are not always integrally related to the plot, they are usually both interesting and mathematically sound. Moreover, Epps' non-crime-solving research includes cosmology and the mathematical basis of consciousness, pure or applied work, but tellingly they are described in their applied terms, and his popular lectures always involve dramatic physical demonstrations.

Malcolm is even more radically applied. He has convinced himself that pure mathematics is just a formal game, reasoning from axioms to theorems, with no larger pattern or meaning. Therefore he calls himself a "chaotician" and works mainly with computer simulations of problems of practical interest. The principles he espouses are empirical, such as "life finds a way," rather than logical.

The key to popular treatment of professional abstract thinkers seems to be whether the individual is tethered to reality. It's okay to lose yourself in abstraction, to see things no one else sees, to care passionately about things no one else can understand -- as long as you return to general intelligibility with solutions to real problems, or works other people can see and understand. Then you can be charmingly eccentric and happy. But if you are tourist rather than explorer, if you journey into abstraction for the joy of it, the popular fiction convention seems to be that you are unstable, miserable, unsociable, and dangerous.

Edward Frenkel challenges this compromise. He holds himself out unapologetically as a pure mathematician, exploring abstract relationships for the love of it. He does make a few noises about the applicability of some mathematics, but it's always the same quantum physics and public key cryptography, and he's half-hearted about that. He wants to tell us about the fierce emotions he feels: fear, doubt, disappointment, joy, and triumph; and he's not ashamed to put mathematics up there with great art, or with concepts as fundamentally human as sex and death.

Frenkel has done an extraordinary job of making his case for love and mathematics. I think a lot of non-mathematicians will gain appreciation for the field, in the way that Stephen Hawking's A Brief History of Time delivered cutting-edge cosmology to the masses. It's not just the clarity of the thought or the skillful writing, in both cases one of the best practitioners in the world opened himself up personally to communicate deep ideas. I also think there are amateur and applied mathematicians who will come away with refreshed understanding of the state of pure mathematics. On a lesser note, but still important, it's a nice antidote to the recent spate of Big Proof pure mathematics books that treat math like a treasure hunt. In that respect I would compare it to the delightful novel, The Parrot's Theorem .

Love and Math is a serious and important book that will teach you a lot about math-the real thing, not the nonsense crammed into standardized tests. It may not convince you to love math, but it should help you understand the people who do.


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