## dragonsの挑戦の歴史は、 その65%が敗北の歴史でもある。

The Singular Mind of Terry Tao

A prodigy grows up to become one of the greatest mathematicians in the world.

New York Times Magazine ? July 2015

This April， as undergraduates strolled along the street outside his modest office on the campus of the University of California， Los Angeles， the mathematician Terence Tao mused about the possibility that water could spontaneously explode. A widely used set of equations describes the behavior of fluids like water， but there seems to be nothing in those equations， he told me， that prevents a wayward eddy from suddenly turning in on itself， tightening into an angry gyre， until the density of the energy at its core becomes infinite: a catastrophic ‘‘singularity.’’ Someone tossing a penny into the fountain by the faculty center or skipping a stone at the Santa M

onica beach could apparently set off a chain reaction that would take out Southern California.

This doesn’t tend to happen. And yet， Tao explained， nobody can say precisely why. It’s a decades-?old conundrum， and Tao has recently been working on an approach to a solution ? one part fanciful， one part outright absurd， like some lost passage from ‘‘Alice’s Adventures in Wonderland.’’

Imagine， he said， that someone awfully clever could construct a machine out of pure water. It would be built not of rods and gears but from a pattern of interacting currents. As he talked， Tao carved shapes in the air with his hands， like a magician. Now imagine， he went on， that this machine were able to make a smaller， faster copy of itself， which could then make another， and so on， until one ‘‘has infinite speed in a tiny space and b

lows up.’’ Tao was not proposing constructing such a machine ? ‘‘I don’t know how!’’ he said， laughing. It was merely a thought experiment， of the sort that Einstein used to develop the theory of special relativity. But， Tao explained， if he can show mathematically that there is nothing， in principle， preventing such a fiendish contraption from operating， then it would mean that water can， in fact， explode. And in the process， he will have also solved the Navier-?Stokes global regularity problem， which has become， since it emerged more than a century ago， one of the most important in all of mathematics.

Tao， who is 40， sat at a desk by the window， papers lying in drifts at the margins. Thin and unassuming， he was dressed in Birkenstocks， a rumpled blue-gray polo shirt and jeans with the cuffs turned up. Behind him

， a small almond couch faced a glyph-?covered blackboard running the length of the room. The couch had been pulled away from the wall to accommodate the beat-up Trek bike he rides to work. At the room’s other end stood a fiberboard bookcase haphazardly piled with books， including ‘‘Compactness and Contradiction’’ and ‘‘Poincar?’s Legacies， Part I，’’ two of the 16 volumes Tao has written since he was a teenager.

Fame came early for Tao， who was born in South Australia. An old headline in his hometown paper， The Advertiser， reads: ‘‘TINY TERENCE， 7， IS HIGH-SCHOOL WHIZ.’’ The clipping includes a photo of a diminutive Tao in 11th-grade math class， wearing a V-neck sweater over a white turtleneck， kneeling on his chair so he can reach a desk he is sharing with a girl more than twice his age. His teacher told the reporter that he hardly taugh

t Tao anything， because Tao was always working two lessons ahead of the others. (Tao taught himself to read at age 2.)

A few months later， halfway through the school year， Tao was moved up to 12th-grade math. Three years later， at age 10， Tao became the youngest person in history to win a medal in the International Mathematical Olympiad. He has since won many other prizes， including a MacArthur ‘‘genius’’ grant and the Fields Medal， considered the Nobel Prize for mathematicians. Today， many regard Tao as the finest mathematician of his generation.

That spring day in his office， reflecting on his career so far， Tao told me that his view of mathematics has utterly changed since childhood. ‘‘When I was growing up， I knew I wanted to be a mathematician， but I had no idea what that entailed，’’ he said in a lilting Australian accent. ‘‘I sort o

f imagined a committee would hand me problems to solve or something.’’ But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The ancient art of mathematics， Tao has discovered， does not reward speed so much as patience， cunning and， perhaps most surprising of all， the sort of gift for collaboration and improvisation that characterizes the best jazz musicians. Tao now believes that his younger self， the prodigy who wowed the math world， wasn’t truly doing math at all. ‘‘It’s as if your only experience with music were practicing scales or learning music theory，’’ he said， looking into light pouring from his window. ‘‘I didn’t learn the deeper meaning of the subject until much lat

er.’’

Possibly the greatest mathematician since antiquity was Carl Friedrich Gauss， a dour German born in the late 18th century. He did not get along with his own children and kept important results to himself， seeing them as unsuitable for public view. They were discovered among his papers after his death. Before and since， the annals of the field have teemed with variations on this misfit theme， from Isaac Newton， the loner with a savage temper; to John Nash， the ‘‘beautiful mind’’ whose work shaped economics and even political science， but who was racked by paranoid delusions; to， more recently， ?Grigory Perelman， the Russian who conquered the Poincar? conjecture alone， then refused the Fields Medal， and who also allowed his fingernails to grow until they curled.

Tao， by contrast， is， as one colleague put it， ‘‘super

-normal.’’ He has a gentle， self-?deprecating manner. He eschews job offers from prestigious East Coast institutions in favor of a relaxed， no-drama department in a place where he can enjoy the weather. In class， he conveys a sense that mathematics is fun. One of his students told me that he had recently joked with another about the many ways Tao defies all the Hollywood mad-?genius tropes. ‘‘They will never make a movie about him，’’ he said. ‘‘He doesn’t have a troubled life. He has a family， and they seem happy， and he’s usually smiling.’’

This can be traced to his own childhood， which he experienced as super-normal， even if， to outside eyes， it was anything but. Tao’s family spent most of his early years living in the foothills south of Adelaide， in a brick split-?level with views of Gulf St. Vincent. The home was designed by his fathe

r， Billy， a pediatrician who immigrated with Tao’s mother， Grace， from Hong Kong in 1972， three years before Tao， the eldest of three， was born in 1975. The three boys ? Nigel， Trevor and ‘‘Terry，’’ as everyone calls him ? often played together， and a favorite pastime was inventing board games. They typically appropriated a Scrabble board for a basic grid， then brought in Scrabble tiles， chess pieces， Chinese checkers， mah-jongg tiles and Dungeons & Dragons dice， according to Nigel， who now works for Google. For story lines， they frequently drew from video games coming out at the time， like Super Mario Bros.， then added layers of complex， whimsical rules. (Trevor， a junior chess champion， was too good to beat， so the boys created a variation on that game as well: Each turn began with a die roll to de

termine which piece could be moved.) Tao was a voracious consumer of fantasy books like Terry Pratchett’s Discworld series. When a class was boring， he doodled intricate maps of imaginary lands.

By the spring of 1985， with a 9-year-old Tao splitting time between high school and nearby Flinders University， Billy and Grace took him on a three-week American tour to seek advice from top mathematicians and education experts. On the Baltimore campus of Johns Hopkins， they met with Julian Stanley， a Georgia-?born psychologist who founded the Center for Talented Youth there. Tao was one of the most talented math students Stanley ever tested ? at 8 years old， Tao scored a 760 on the math portion of the SAT ? but Stanley urged the couple to keep taking things slow and give their son’s emotional and social skills time to develop.

Even at a relatively deliberate pace， by age 17， Tao had finished a master

’s thesis (‘‘Convolution Operators Generated by Right-?Monogenic and Harmonic Kernels’’) and moved to Princeton University to start on his Ph.D. Tao’s application to the university included a letter from Paul Erdos， the revered Hungarian mathematician. ‘‘I am sure he will develop into a first-rate mathematician and perhaps into a really great one，’’ read Erdos’s brief， typewritten note. ‘‘I recommend him in the highest possible terms.’’ Yet on arrival， it was Tao， the teenage prodigy， who was intimidated. During Tao’s first year， Andrew Wiles， then a Princeton professor， announced that he proved Fermat’s Last Theorem， a legendary problem that had gone unsolved for more than three centuries. Tao’s fellow graduate students spoke eloquently about mathematical fields of which he had barely heard.

Tao became notorious for

his nights haunting the graduate computer room to play the historical-?simulation game Civilization. (He now avoids computer games， he told me， because of what he calls a ‘‘completist streak’’ that makes it hard to stop playing.) At a local comic-book store， Tao met a circle of friends who played ‘‘Magic: The Gathering，’’ the intricate fantasy card game. This was Tao’s first real experience hanging out with people his age， but there was also an element， he admitted， of escaping the pressures of Princeton. Gifted children often avoid challenges at which they might not excel. Before Tao went to Princeton， his grades had flagged at Flinders. In a course on quantum physics， the instructor told the class that the final would include an essay on the history of the field. Tao， then 12， blew off studying， and when he sat down for the exam， he was stunned to di

scover that the essay would count for half the grade. ‘‘I remember crying，’’ Tao said， ‘‘and the proctor had to escort me out.’’ He failed.

At Princeton， crisis came in the form of the ‘‘generals，’’ a wide-?ranging， arduous oral examination administered by three professors. While other students spent months working through problem sets and giving one another mock exams， Tao settled on his usual test-prep strategy: last-?minute cramming. ‘‘I went in and very quickly got out of my depth，’’ he said. ‘‘They were asking questions which I had no ability to answer.’’ Immediately after， Tao sat with his adviser， Elias Stein， and felt that he had let him down. Tao wasn’t really trying， and the hardest part was yet to come.

The true work of the mathematician is not experienced until the later parts of graduate school， wh

en the student is challenged to create knowledge in the form of a novel proof. It is common to fill page after page with an attempt， the seasons turning， only to arrive precisely where you began， empty-handed ? or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematical research is to be completely stuck. It is a process that Charles Fefferman of Princeton， himself a onetime math prodigy turned Fields medalist， likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special， though: The devil is vastly superior at chess， but， Fefferman explained， you may take back as many moves as you like， and the devil may not. You play a first game， and， of course， ‘‘he crushes you.’’ So you take back moves and try something different， and he crushes you again， ‘

‘in much the same way.’’ If you are sufficiently wily， you will eventually discover a move that forces the devil to shift strategy; you still lose， but ? aha! ? you have your first clue.

As a group， the people drawn to mathematics tend to value certainty and logic and a neatness of outcome， so this game becomes a special kind of torture. And yet this is what any ?would-be mathematician must summon the courage to face down: weeks， months， years on a problem that may or may not even be possible to unlock. You find yourself sitting in a room without doors or windows， and you can shout and carry on all you want， but no one is listening.

Within his field， Tao is best known for a proof about a remarkable set of numbers known as the primes. The primes are the whole numbers larger than 1 that can be divided evenly by only themselves and 1. Thus， the first few primes are 2， 3，