Aaron Brown What’s Love Got to Do With It? Edward Frenkel is writing a protracted Dear John letter to popular misconceptions about math and mathema- ticians…

he great popular science and science fiction author Isaac Asimov told a story about a university committee meeting in which there was much laughter and joking about a student named “Milton” flunkingT English literature, but no one noticed when a student named “Gauss” was failing in mathematics. I wish I could find the reference to this, but I read it long ago in childhood, and some Internet searching proved fruitless. I may have the details wrong – especially the name of the student date are smaller than Asimov’s. They also have cians, and writers. With these people, screenwriters flunking English literature – but I remember the a different slant. Asimov tried to show every- often assume they must be tortured to be authentic. point. Asimov complained that a scientist would be one how mathematics and science could be fun. But there are plenty of exceptions – movies built thought a Philistine if he expressed no interest in Frenkel instead celebrates the passion and inten- around well-rounded, friendly, artistic genius- music or philosophy, but that an artist could boast sity of mathematics at the highest level. He has es. And, even when artists are a bit crazy, it is an about not knowing enough arithmetic to balance done this through lectures which are a sensation excess of passion, “agony and ecstasy,” not some his checkbook. on YouTube, an erotic film, and, most recently, a incomprehensible twisted obsession from another Edward Frenkel is one of the great mathema- book, Love and Math: The Heart of Hidden Reality. dimension. The troubled artist is too human, the ticians in the world, and he made a similar point Frenkel’s film was motivated in part by the mathematician is inhuman. The artist gains relief much more recently. “Intelligent people would observation that the most popular mathematics by completing work, and that work is appreciated never say: ‘I don’t care about art or music.’ But it is movies portray: “a mathematician is on the verge by others. The mathematician’s frenzied quest just totally okay to say: ‘I hate math.’” Asimov’s solu- of a mental illness.” I assume he is thinking about drives him deeper into obscurity and incompre- tion was to give up science and devote himself to movies like Pi, A Beautiful Mind, Proof, and Good hensibility. explaining mathematics and science in an enor- Will Hunting. To be fair, there are sane mathe- It’s also interesting to think about the media mous body of fiction and nonfiction writing, as maticians in these movies (but they are never as treatment of real-life pure mathematician Grigori well as public speaking. Although he stopped doing brilliant as the crazy ones) and A Beautiful Mind Perelman, who proved the Poincare conjecture, research in 1958, he remained one of the most pop- did not exaggerate the facts of John Nash’s mental then turned down the Field’s medal and the $1 ular lecturers at Boston University until near his problems . But I agree with Frenkel that movies million Millennium Prize, among other honors. death. His stories inspired 26 movies, shorts, and are apt to suggest that mathematicians are either He explains himself clearly. He does not want to television shows. mediocre and dull, or brilliant and psychotically be a pet or celebrity, he does not want awards from Frenkel has continued his meteoric career in obsessed. people who aren’t qualified to judge his work, he mathematics, so his public education efforts to One interesting comparison is to artists, musi- is not interested in money, and he is unhappy with

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- - His autobiography is interspersed with with interspersed is autobiography His it’s Because problems? these tackle he does Why The first step in Frenkel’s unorthodox strategy strategy unorthodox Frenkel’s in step first The is another factor. His problem choices are guided guided are choices problem His factor. another is the that feel who mathematicians professional by exploration. for areas new up open will answers an on working is he that fear the keenly feels He useful or elegant no with one or problem, insoluble that Yet, solve. to unequipped is he one or answer, he when But him. daunts as much as him thrills discovered having treasures he answers, the finds of incidents like disappointing his mentor by refus by mentor his disappointing like incidents of blustering a confronting or Russia to return the ing at lecture to invited inexplicably bigot, apparatchik MIT. researches. mathematical his of some of accounts but, terms, simple in problems the explains He motivate to try not does he Epps, Charlie unlike braid of definitions his follow can Anyone them. explorations. his of discussion his and groups training, or interest mathematical no take They to have will reader nonmathematical a although unmotivat of amount unfamiliar an through plow details. ed story, whole the were that If challenging. and fun or mathematician, applied an like be would he there that clear makes He one. recreational a even put mathematics up there with great art, or with with or art, great with there up mathematics put death. and sex as human fundamentally as concepts autobiographical poignant but brief include to is is who character a sketches skillfully He details. the has He sensitive. and tough brilliant, and shy Communism, under born be to misfortune great USSR to (according Jewish be to particular in and Yet, 1980s. the in Russia in is) that rules, ethnicity and mentors his in fortunate extraordinarily is he offered being like opportunities in and colleagues, 21-year-old a as Harvard to professorship visiting a allowed being in (and degree graduate a without He 1990). in West the to emigrate and it accept to portraits sharp through personality his illustrates ------– seems to want to challenge challenge to want to seems – Numb3rs The key seems to be whether the individual individual the whether be to seems key The Michael Asimov, Isaac unlike – Frenkel Edward Malcolm is even more radically applied. He He applied.radically more even is Malcolm ically as a pure mathematician, exploring abstract abstract exploring mathematician, pure a as ically few a make does He it. of love the for relationships mathematics, some of applicability the about noises pub and physics quantum same the always it’s but he’s below, discussed as and, cryptography key lic about us tell to wants He that. about half-hearted disappoint doubt, fear, feels: he emotions fierce the to ashamed not he’s and triumph; and joy, ment, espouses are empirical, such as: “life finds a way,” way,” a finds “life as: such empirical, are espouses logical. than rather in yourself lose to okay It’s reality. to tethered is care to sees, else one no things see to abstraction, under can else one no things about passionately intelligibility general to return you as long as stand; other that works or problems, real to solutions with be can you Then understand. and see can people are you if But happy. and eccentric charmingly into journey you if explorer, than rather tourist con fiction popular the it, of joy the for abstraction misera unstable, are you that be to seems vention dangerous. unsociable,and ble, the and Malcolm), Ian Dr. of inventor (the Crichton of creators unapologet out himself holds He compromise. this has convinced himself that pure mathematics pure that himself convinced has to axioms from reasoning game, formal a just is meaning. or pattern larger no with theorems, and “chaotician” a himselfcalls he Therefore, of simulations computer with mainly works he principles The practicalinterest. of problems Among these four people, only Perelman Perelman only people, whose four lunatic these Among certifiable a as portrayed is irrational are actions ------and the Nobel Nobel the and and Ian Malcolm of of Malcolm Ian and

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A third comparison is to the personable and and personable the to is comparison third A I think in any artist or philosopher this behavior behavior this philosopher or artist any in think I m l i consciousness, either of which could be either pure pure either be could which of either consciousness, in described are they tellingly but work, applied or terms. applied their are not always integrally related to the plot, they they plot, the to related integrally always not are mathematically and interesting both usually are research noncrime-solving Epps’ Moreover, sound. of basis mathematical the and cosmology includes when he explains the advanced mathematical con mathematical advanced the explains he when television the and agents FBI the that terms in cept sidebars these While understand. can audience nomena. While he generally disappears to a com a to disappears generally he While nomena. out work to board erasable see-through or puter is point high emotional the offscreen, details the In a generica In mathematical the sees he and crime a to relating phe social or physical simple some to connection happy mathematicians in popular fiction, like like fiction, popular in mathematicians happy of Epps Charlie JurassicPark applications. from comes joy his mathematician, a mathematician must be crazy to love math and and math love to crazy be must mathematician a peace. want themselves, rock stars die of drug overdoses, polit overdoses, drug of die stars rock themselves, on themselves set or strangers up blow activists ical But reputations. their enhance things these all fire; the general ballpark of Perelman’s. Yet, among these these among Yet, Perelman’s. of ballpark general the certifi a as portrayed is Perelman only people, four kill Artists irrational. are actions whose lunatic able Prize for literature, or the credibility that George George that credibility the or literature, for Prize down turning for got Brando Marlon and Scott C. in reasons cited three All Awards. Academy their would be celebrated as authentic and simple hon simple and authentic as celebrated be would got Sartre Jean-Paul that kudos the of Think esty. the declining for peace, and share it with honest people who under who people honest with it share and peace, or math do to continues he if clear not (it’s it stand not). the extent that professional mathematics tolerates tolerates mathematics professional that extent the in math his do to wants He conduct. unethical

a pure mathematician, exploring abstract abstract exploring mathematician, pure a it of loverelationships the for He holds himself out unapologetically as as unapologetically out himself holds He w AARON BROWN

universal truth, unknown to any other human. Cryptography is actually a bad example. Yes, the shaky chain of human and computer judgments Writing up formal proofs is a tedious ordeal. initial insights were made by pure mathematicians. that make it less certain that a lot of mundane There is an underlying assumption to that But they needn’t have been; people could have come everyday things. We know of no reason why the account, which Frenkel does not discuss. It’s the up with the same algorithms from general princi- earth’s magnetic field won’t reverse tomorrow; it’s reason that the fictional Ian Malcolm left pure mathe- ples in computer science, or even by inspired trial done it often in the past, but this would surprise me matics, and to some extent the reason that I did. What and error. The actual algorithms in use are only a lot more than if I learned that a major mathemat- if the path chosen by professional mathematicians distantly and theoretically related to anything imag- ical proof that has been widely accepted turned out doesn’t lead anywhere? What if, a hundred years from ined by a pure mathematician. Pure mathematics to have a flaw. now, mathematics will still be playing with the same gives us important insights but cryptography has I feel a lot of the things that Frenkel feels when kinds of question, with millions of pages of additional been an engineering discipline for many years; it left I do applied mathematics. There is far less fear, and proofs but no more real insight into anything? What mathematics at least 50 years ago. perhaps therefore less thrill. I know it’s not as eter- if another civilization at our level of intellectual devel- Physics is a better example, but in the last 50 nal or certain, but I’m confident that it’s meaningful opment had entirely different advanced mathematics, years it’s not clear how much pure mathemat- and useful. It’s the difference between craftsman- neither better nor worse than ours? What if the whole ics has added. If string theory, or some other ship and art. thing is the equivalent of writing a computer program advanced pure mathematical grand unification Frenkel has done an extraordinary job of mak- to grind out prime numbers or digits of pi eternally? theory, proves out, then Frenkel has one modern ing his case for love and mathematics. I think a lot Except that the computer is better at it. This is not example to buttress his case. If it doesn’t, then of nonmathematicians will gain appreciation for the fear that a decade of your life will be wasted in an he has none. In my lifetime, it’s hard to come up 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 I feel a lot of the things that Frenkel feels or the skillful writing; in both cases, one of the best practitioners in the world has opened himself up when I do applied mathematics. There is personally to communicate deep ideas. I also think there are amateur and applied mathematicians who far less fear, and perhaps therefore less will come away with a refreshed understanding of the state of pure mathematics. On a lesser note, but thrill still important, it’s a nice antidote to the recent spate of Big Proof pure mathematics books that treat impossible or unproductive problem or, far worse, with an advanced pure mathematical insight that math like a treasure hunt. In that respect, I would a false proof, this is the fear that every effort in pure demonstrates practical utility. The point is not that compare it to the delightful novel, The Parrot’s mathematics is wasted. mathematics has to be useful to be worthwhile, it’s Theorem. Some people have faith in pure mathematics that practical utility gives confidence that math- This is a serious and important book. It does because results that are obscure when first proved ematics is not wandering aimlessly in an infinite not have the feel of a classic, however; it feels like have frequently turned out to be of central impor- forest with no part essentially different from any the opening chapter of a larger body of work. tance to pure or applied problems many years later, other. Isaac Asimov, another Russian nonreligious Jew, in completely unexpected ways. And, sometimes, I’m not trying to make the case against pure was born 48 years earlier and 500 miles west of scientific hypotheses made for reasons of math- mathematics; I lean in its favor, and I consider Frenkel, near the border with Belarus. He also ematical elegance have turned out to be closer to it primarily an empirical question. I don’t lean emigrated to the United States, graduated from the truth than what we learn from painstaking strongly enough to devote my life to it, but I’d bet it college at 19, and quickly earned a Masters in observation and experience, what Eugene Wigner will prove to be nonarbitrary and I certainly hope Chemistry from Columbia. If you subtract the called, “the unreasonable effectiveness of mathe- it does. I think Frenkel’s faith is different, mainly six years he took out for World War II, he got his matics.” Frenkel travels a little down this road, citing because he’s a lot better at pure math. I think he Ph.D. at the same age as Frenkel. He published non-Euclidian geometry and group theory, and also feels the connections and symmetries he and oth- his first book at age 30, five years younger than the applications of mathematics to quantum physics ers are working to prove. Where I see multihun- Frenkel, but went on to produce over 500 books, and cryptography. But these are mechanical, slap- dred-page proofs that can only be verified through stories, screenplays, and other written works. dash references compared to the vitality and inci- years of intense work by top mathematicians – or While Frenkel seems unlikely to match that total, siveness of the rest of the book (Mario Livio wrote gigantic computer computations – he seems to see given his later start and full-time research work, an excellent book, Is God a Mathematician, that pieces fitting perfectly into a jigsaw puzzle. He cel- we can hope for some more stimulating efforts to makes a much stronger case). ebrates the theoretical certainty of a proof, I see the humanize mathematics.

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