<i>Love and Math</i>: A Modern Russian's <i>Lara</i> Poem

If you find that hard to believe in a book (ostensibly) about one of the major areas of research in contemporary mathematics, then you are missing out on one of humanity's greatest cultural creations. You are condemned to never knowing how and why math is "the poetry of the mind."
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Edward Frenkel's book Love and Math is, quite simply, a love story, one man's declaration of his love for, and romantic description of, the mistress that destiny assigned him. If I had to sum up the book in one word, that word would be passion. The romantic prose, at times poetic, the broad sweep of deep and profound human ideas, and the eternal nature of fundamental questions that continually re-emerge under new disguises, cannot help but bring to mind the great Russian novels of Dostoyevsky, Pasternak, Sholokhov, and all the rest.

With every page, I found my mind's eye conjuring up a fictional image of the book's author, writing by candlelight in the depths of the Siberian winter like Omar Sharif's Doctor Zhivago in the David Lean movie adaptation of Pasternak's famous novel. Love and Math is Edward Frenkel's Lara poems.

The reality is somewhat different from that mental image, of course. But only in what are largely irrelevant details. Though Frenkel was born in 1960s Russia, then part of the Soviet Union, since 1989 he has lived in the United States, and the book was written in Berkeley, California, where the howling wolves of the Russian night are replaced by the mountain lions and coyotes that roam the Oakland hills, and penetrating Bay Area fogs chill the body in place of the icy winds sweeping across the snowy Steppes.

But make no mistake about it: History, culture, tradition, and national character are not cast aside in the course of a ten-hour airplane ride from Moscow to the USA. Love and Math is a sweeping, romantic love story in the classic Russian tradition. If you find that hard to believe in a book (ostensibly) about one of the major areas of research in contemporary mathematics, then I am sorry for you. You are missing out on one of humanity's greatest cultural creations, and cannot experience that vast part of human culture that Frenkel, I, and many other mathematically educated citizens of the world enjoy on a daily basis. You are condemned to live your life never knowing how and why mathematics is "the poetry of the mind," as the American mathematician David Eugene Smith expressed it, completing the thought to symmetry by describing poetry as "the mathematics of the heart."

What is more, I fear your loss is far greater than the one I suffer by being unable to read Dostoyevsky in the original Russian, though Frenkel can mitigate your loss to some extent by providing you with a "translation" of his mathematics from the complex, symbolic formulas of his many research papers to the accessible prose and simple line drawings you will find in his book.

Equally, if you are a mathematician and do not recognize the sheer romance, the love, and the poetry in Frenkel's words, if you see the mathematical techniques but not the love - and I know mathematicians who almost certainly fit this description - then you too are destined to live a life of one fewer dimension than those of us who experience both on a daily basis. As the famous German mathematician Karl Weierstrass said, "A mathematician who is not also something of a poet will never be a perfect mathematician."

An easy way to describe the structure of Frenkel's book is to say it comprises two themes. One theme is a "popular science" description of an important area of modern mathematics - the Langlands Program, a sort of Grand Unified Theory of mathematics that weaves together large parts of algebra, geometry, number theory, analysis, and quantum theory, the entire tapestry explained at great length in the book.

The other theme is an autobiographic account of Frenkel's own life, first growing up as a mathematically gifted child of Jewish heritage in the then notoriously anti-Semitic Soviet Union, overcoming all the obstacles put in his way in order to secure a mathematics education, and then moving to the United States to lead the jet-setting life of a world famous mathematician.

But to view it that way, as two storylines, would be to miss what it is really about, much like Woody Allen's famous (satirical) three-word summary of War and Peace: "It involves Russia." For what Frenkel is describing is the inseparable whole that is the man and his mathematics.

Frenkel desperately wants you to "get" this mathematics that he has fallen in love with; to understand, at least to some extent, what mathematics is and why he has devoted his life to it. If he does not succeed - and the criminally poor, culturally impoverished nature of much Western mathematics education means that for many readers he will not - it will not be for want of trying.

He writes (p.7): "My dream is that all of us will be able to see, appreciate, and marvel at the magic beauty and exquisite harmony of these ideas, formulas, and equations, for this will give so much more meaning to our love for this world and for each other."

He may dream this - being a dreamer is another familiar trait of the characters in Russian novels - but he knows that for many readers his task is hopeless, and says so early on, with an edge of both despair and frustration: "Mathematical knowledge is unlike any other knowledge," he writes in his Preface. "While our perception of the physical world can always be distorted, our perception of mathematical truths can't be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere - no matter what gender, religion, or skin color ... There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It's too precious to be given away to the 'initiated few.' It belongs to all of us."

Yet for all that mathematics belongs to all Humankind, the teenage Frenkel himself was denied access to the Soviet Union's flagship institute of learning, Moscow State University, despite having aced all the entrance exams. "The doors were slammed shut in front of me. I was an outcast," he laments - but only briefly, continuing, "But I didn't give up. I would sneak into the University to attend lectures and seminars. I would read math books on my own, sometimes late at night. And in the end I was able to hack the system. They didn't let me in through the front door; I flew in through a window. When you are in love, who can stop you?"

Who indeed? When Frenkel's student papers were smuggled out to the west, they found their way to Harvard University, where the Mathematics Department persuaded the President to invite the twenty-one-year old prodigy to come over as a Visiting Professor. Putting him on a fast track to a Ph.D., Harvard provided a launch pad for what has since been a spectacular career of ground breaking, international research, based first at Harvard, then more recently at the University of California at Berkeley.

Along the way, this now Russian-American wrote a screenplay, The Two-Body Problem, published in book form and performed on the stage, but still awaiting production as a movie, and co-wrote and starred in a short art movie, Rites of Love and Math, in which he tattoos "a formula of love" on the naked body of his lover. (The film is strongly inspired by a classic Japanese film, Rites of Love and Death.)

Intrigued? I hope what little I have told you about Frenkel - the man, the life, and the mathematics - persuades you to get his book and read it. Not because I am his agent; I am not. I have only met Frenkel once, a few weeks ago, at a dinner party in Berkeley. Rather, because I share his love for mathematics, and I too have poured effort into trying to convey the reasons for my love to my fellow humans. And because he writes so well.

As is true for all the great Russian novels, you will find in Frenkel's tale that one person's individual story of love and overcoming adversity provides both a penetrating lens on society and a revealing mirror into the human mind.

To be sure, many readers may have to skim through some of the mathematical parts. If that applies to you, then as a result you will miss a lot. But you will still come away the richer.

And what of that "formula of love" that the Rites version of Frenkel engraved on his lover's body? You must surely be curious. It's a real formula that arose in Frenkel's own research, and you can find it on page 238, together with a brief explanation.

"Yes, but is it really a formula of love?" you will surely ask. "Can there ever be such a thing?"

Frenkel has an answer - the answer. "Every formula we create is a formula of love."

FOOTNOTE: This review was originally written in response to a request from a large daily print newspaper when the book first appeared last year. Unusually for me, after a long delay, they decided not to publish it. My suspicion is they did so because they felt the "romantic prose" I adopted did not fit well with their image of mathematics and how it should be portrayed. If so (and I do not know for certain), I think that is a great pity, and may reflect why many people are turned off math. Mathematicians do love their subject and that love is both passionate and romantic. One of the strengths of Frenkel's book is that he conveys that passion. Like him, I am not afraid to show it.

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