his 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 Monica 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 blows 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 ‘‘Poincaré’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 taught Tao anything, because Tao was always working two lessons ahead of the others. (Tao taught himself to read at age 2.)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 taught 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 of 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 later.’’
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 Poincaré 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 father, 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 determine 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 mak
เมษายนของเขา เป็นสูง ๆ strolled ไปตามถนนนอกสำนักงานของเขาเจียมเนื้อเจียมตัวในวิทยาเขตของมหาวิทยาลัยแคลิฟอร์เนีย ลอสแอนเจลิส นักคณิตศาสตร์เต่า Terence mused เกี่ยวกับความเป็นไปได้ที่ธรรมชาติสามารถกระจายน้ำ ชุดที่ใช้กันอย่างแพร่หลายของสมการอธิบายพฤติกรรมของของเหลวเช่นน้ำ แต่ดูเหมือน จะไม่มีอะไรในสมการเหล่านั้น เขาบอกฉัน ที่ทำให้เอ็ดดี้ wayward ก็เปิดในตัวมันเอง ขันเป็นการโกรธเขาผิดพลาด จนกระทั่งความหนาแน่นของพลังงานที่เป็นหลักกลายเป็นอนันต์: ความรุนแรง "ภาวะเอกฐาน '' เห็นได้ชัดว่าคน tossing เงินเป็นน้ำพุตามศูนย์คณะ หรือข้ามหินหาด Santa Monica สามารถตั้งค่าออกจากปฏิกิริยาลูกโซ่ที่จะแกะแคลิฟอร์เนียภาคใต้นี้ไม่มีแนวโน้มที่จะเกิดขึ้น และยัง เต่าอธิบาย ไม่มีใครสามารถบอกได้แม่นยำว่าทำไม มันเป็น conundrum ทศวรรษ และเต่ามีการทำงานมีวิธีการแก้ไขปัญหาล่าสุด — fanciful ส่วนหนึ่ง ส่วนหนึ่งจัดไร้สาระ เช่นบางพาสหายจาก ''อลิซท่อง ''จินตนาการ เขากล่าวว่า คนฉลาดชะมัดสามารถสร้างเครื่องจักรน้ำบริสุทธิ์ มันจะสามารถสร้าง ของก้านและเกียร์ไม่ แต่ จากกระแสโต้ตอบรูปแบบ ขณะที่เขาพูด เต่าแกะสลักรูปร่างในอากาศกับมือ เช่นเป็นนักมายากล ตอนนี้คิด เขาไป ว่า เครื่องนี้ได้จะมีขนาดเล็กกว่า เร็วคัดลอกของตัวเอง ซึ่งสามารถทำอีก และอื่น ๆ จนกว่าหนึ่งนิ้วมีความเร็วไม่จำกัดในพื้นที่เล็ก ๆ และพัดขึ้น '' เต่าได้เสนอการสร้างเครื่องจักร — '' อย่าว่า!'' พูด หัวเราะ มันเป็นเพียงการทดลองทางความคิด การเรียงที่ไอน์สไตน์ใช้ในการพัฒนาทฤษฎีสัมพัทธภาพพิเศษ แต่ อธิบาย ถ้าเขาสามารถแสดง mathematically ว่า ไม่มีอะไร หลัก ป้องกัน contraption โหดร้ายจากการปฏิบัติ แล้วมันจะหมายถึง ว่า น้ำสามารถ ในความเป็นจริง เต่ากระจาย และในกระบวนการ เขาจะมียังแก้ไข Navier-สโตกส์ความสากลปัญหา ซึ่งได้กลายเป็น เนื่องจากมันเกิดเมื่อกว่าศตวรรษที่ผ่านมา หนึ่งสำคัญสุด ของคณิตศาสตร์เต่า ที่ 40 นั่งที่โต๊ะโดยหน้าต่าง นอนใน drifts ที่ระยะขอบของเอกสาร บาง และน่า เขาได้สวมใส่ในกางเกงยีนส์ และมีเสื้อโปโลสีฟ้าเทา rumpled, Birkenstocks กับ cuffs ที่เปิด หลังเขา โซฟาอัลมอนด์มีขนาดเล็กต้องเผชิญเป็นสัญลักษณ์ครอบคลุมกระดานดำใช้ความยาวของห้อง โซฟามีถูกดึงออกจากผนังรองรับจักรยาน Trek beat-up ที่เขาขี่ไปทำงาน ที่ห้อง ของอีกฝ่ายยืน bookcase แผ่นใยไม้อัดที่ผิด ๆ ถูก ๆ ชั้นกับหนังสือ รวมถึง '' Compactness และแย้ง '' และ ''ของ Poincaré มรดก ส่วน '' สองไดรฟ์ข้อมูล 16 เต่าได้เขียนมาตั้งแต่วัยรุ่นFame 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 taught Tao anything, because Tao was always working two lessons ahead of the others. (Tao taught himself to read at age 2.)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 taught 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 of 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 later.’’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 Poincaré 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 father, 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 determine 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 mak
การแปล กรุณารอสักครู่..
