On the morning of November 8, in an online public speech to Peking University faculty, students and the public, Zhang Yitang said, "The zero-point conjecture problem of Landau-Siegel has essentially been solved. Peers in analytic number theory will know that the solution to this problem may be of greater significance than the twin prime number conjecture. ”
On November 7, the latest paper on the Landau-Siegel zero conjecture, submitted by Zhang Yitang, entitled "Discrete mean estimates and the Landau-Siegel Zero", was officially released on the preprint website arXiv.
On the morning of November 8, Zhang Yitang gave an online public speech to Peking University teachers, students and the public.
The book "Become a Scientist" tells the "character stories" of ten internationally renowned scientists, presenting their rich and diverse growth experiences, cognitive processes of scientific enlightenment, and difficulties and breakthroughs in exploring unknown fields. This article selects the parts related to Zhang Yitang and the "twin prime number conjecture".
The following is an excerpt from "Becoming a Scientist" with permission from the publisher, and the title of this article is added by the editor.
Original author丨Zhang Rui
"Becoming a Scientist", by Tencent Youth Development Committee, illustrated by Niklas Elmehder [Sweden], CITIC Publishing Group, May 2021.
He has published very few papers
New Hampshire is located in the northeastern part of the United States, where winters are cold and long, but in the spring, the entire region is enriched with meadows and maple forests.
Early one morning in April 2013, a Chinese man walked into the office of Edward Hinson, chair of mathematics at the University of New Hampshire, handed him a manuscript across the desk, and said he was going to submit the paper to the world's authoritative academic journal, Annals of Mathematics, entitled "Bounded Distances Between Prime Numbers."
Footage from the documentary "Looking for a Needle in a Haystack: Zhang Yitang and the Twin Prime Number Conjecture" (2015).
This Chinese, Zhang Yitang, is 58 years old, has gray hair on sideburns, and has been at the University of New Hampshire for 14 years and is still only a lecturer. He has published so few papers in total, only two in all, the last time 12 years ago and again in 1985, so that his proposal to be promoted to professor was opposed by colleagues in the department. As for the Annals of Mathematics, it is the world's top professional journal, receiving 915 papers in 2013, of which less than 4% were published.
"Until that moment, I didn't even know he was working on this." Department Chair Edward Hinson later said he knew the weight of the paper and he was just a little shocked.
The "twin prime number conjecture" studied in this paper is very old, dating back to Euclid's research, which is no less difficult than the famous "Goldbach conjecture" and "Riemann conjecture". For a long time, countless people have tried to solve it, including great mathematicians, the brightest minds in the entire human race, but often taking the first step is like being in a nightmare.
Almost no one in the mathematical community at that time knew the name Zhang Yitang. He is Sven, wears a pair of glasses, has a somewhat withdrawn personality, shares a house about 13 kilometers from the University of New Hampshire, commutes by bus every day, takes 4 courses per semester, pays every day, has no research funds, and even colleagues in the mathematics department often forget his existence. The local Chinese community of less than 100 people knew very little about him, and only regarded this compatriot as an eccentric person.
After leaving the department chair's office, the eccentric, obscure lecturer, Zhang Yitang, submitted his thesis on April 17, 2013.
Soon, the editor of the Annals of Mathematics received the paper, but some were unsure. When this happens, they turn to authority figures in the relevant field.
On this day, Enrico Bombieri, an analytic mathematician at the Institute for Advanced Study in Princeton, was dining in the faculty cafeteria, when the editor of Annals of Mathematics walked straight up to him and asked in confusion: "Professor Bombieri, we have received a paper on bounded distances of twin primes, sent by an unknown Chinese mathematician." We've received too many papers like this, what should we do? ”
Stills from the movie "A Beautiful Mind" (2001).
If there is a world-recognized authority in the field of prime numbers, then Professor Bonberry is one of them: for his research on prime numbers, he won the 1974 Fields Medal – one of the highest honors in mathematics.
In fact, over the years, many math enthusiasts have emailed Professor Bonberi claiming to have found a way to solve the bounded distance of twin primes. To this, he believes that the most appropriate reply is: don't send me papers, I don't read them.
Another mathematician, Professor Daniel Goldston of San Jose State University, put it more bluntly: "I can say an expert in rejection, I have met many people who claim to prove the 'twin prime number conjecture', but what they write is rubbish. ”
Professor Goldstone has the confidence to say this, he was the closest to proving the "twin prime number conjecture". In 2003, he and two other mathematicians achieved exciting results, only a fraction of the distance from the finish line, but in the end the mathematicians were pessimistic: "At present, we are limited by knowledge and methods, and this step is impossible to cross." Goldstone said he probably won't see the answer in his lifetime.
Another mathematician, Henryk Iwaniec, who was invited to review the manuscript, soon began studying Zhang's paper. At first, he was not much interested, thinking that it was the work of some math lover, but he was gradually attracted to it. His first email to Professor Peter Sarnak, editorial board member of Annals of Mathematics, was: "This paper has a good idea. The next day, the wording of the email was "This paper has a great idea."
Ivanets passed his surprise one email after another:
"This paper has a very good idea."
"This paper may be right."
"This paper is very likely to be right."
"I think this paper is right."
During the second week of review, Professor Ivanets locked himself in his home. He no longer read Zhang Yitang's paper, but rewrote it according to Zhang Yitang's ideas, and after writing, he was sure that his results were no different from Zhang Yitang's. In the third week, Ivanets began picking out mistakes in the essay word for word. Later, Zhang Yitang said that Ivanets chose very carefully, for example, there is an English word in the text that should be plural, and he used it as singular, but the paper is correct.
The "twin prime number conjecture" is a problem that has plagued mankind for thousands of years
Zhang Yitang's "twin prime number conjecture" is a problem that has plagued mankind for thousands of years, but its basic description is actually very simple.
Prime numbers, also known as prime numbers, refer to numbers that can only be divisible by 1 and itself, including 2, 3, 5, 7, 11, 13, 17, etc., it can be said that prime numbers are the most basic concepts in the digital world. Among these primes, pairs of prime numbers with a difference of 2 are called "twin primes", such as (3,5), (5,7), (11,13), (17,19).
It has been found that as the number gets larger and the twin primes become rarer, will eventually no new twin primes be found? More than 2,000 years ago, the ancient Greek mathematician Euclid guessed that there should be an infinite number of such prime pairs, but he could not prove it. This is the "twin prime number conjecture".
Millennia later, this conjecture remains in the minds of mathematicians. In 1900, German mathematician Hilbert delivered a famous lecture entitled "Problems of Mathematics" at the Second International Congress of Mathematicians in Paris. Based on the research results and trends of mathematics in the past (especially in the 19th century), he proposed 23 mathematical problems worthy of mathematicians' consideration, and the "twin prime number conjecture" is part of the 8th problem to be solved, and it is the well-known "Goldbach conjecture" and "Riemann conjecture" that are proposed with it. They are the pinnacles of the temple of mathematics and represent the pinnacle of human intelligence. In order to prove it, mathematicians over the centuries have worked diligently and transformed many methods.
Stills from the movie "A Beautiful Mind" (2001).
In 2003, Professor Goldstone collaborated with two other mathematicians to prove that there are infinitely many pairs of prime numbers and that the distance between them is always less than a fixed value, but it is not yet certain what this constant value is. This is an exciting result, and they are only "a hair" away from the finish line. To this end, top mathematicians around the world held a week of seminars at the Institute for Advanced Study in Princeton to try to cross "this hair", but in the end they still stopped and even fell into despair.
All this ended in Zhang Yitang's "Bounded Distances Between Prime Numbers", in which he proved that there are infinite pairs of prime numbers (p, q), where the difference between each pair of prime numbers, that is, the distance between p and q, does not exceed 70 million. The method used by Zhang Yitang is a long-standing screening method, dating back to the research of the astronomer and mathematician Eratosthenes in the 3rd century BC, so it is also called the "Eratosthenes screening method".
Zhang Yitang later explained to the media that this simple screening method can be used to find prime numbers below 1000, write down all the numbers, and then delete multiples of 2, because these numbers are even and cannot be prime. Then remove multiples of 3, multiples of 5, and so on, all the way to multiples of 31. Previously, Professor Goldstone and others also used the screening method, and for the fixed value that caused them a headache and stopped moving forward, Zhang Yitang's answer was 70 million.
"It's so unusual that someone outside the math community did it." When Zhang Yitang's paper came out, the reaction was like that of Professor Goldstone, and the entire mathematical community was shocked. Although it takes 70 million to be reduced to 2 to be considered the final proof of the "twin prime conjecture", from infinity to 70 million is made from nothing, like the first ray of light in the dark. Professor Goldstone said: "The distance from 70 million to 2 is insignificant compared to that. ”
After Zhang's paper was published, mathematicians around the world rushed to compress 70 million to a smaller number, which a British mathematician named James Maynard estimated to 246. The dawn seems to be just around the corner.
Back in the spring of 2013, which belonged to Zhang Yitang, Annals of Mathematics took only three weeks from receiving the paper to publication, the fastest in nearly 130 years since its inception, and it usually takes 24 months, sometimes as long as four or five years.
When Zhang Yitang heard the good news, he called his wife Sun Yaling, who was far away in San Jose at the time. Zhang Yitang asked his wife to pay attention to media reports because "you will see my name on there", but his wife responded to him: "Are you drunk?" ”
For a while, people could not associate world-class mathematical achievements with the ordinary and even somewhat sloppy lecturer Zhang Yitang. Zhang Yitang's good friend Ziyage saw the overwhelming reports about him on the Internet and couldn't believe it for a while. He excitedly called Zhang Yitang and congratulated him after confirming the news.
The mathematics department at the University of New Hampshire, where Zhang Yitang taught, later told him that he would no longer teach, that his salary would increase, and that his position would be promoted. The secretary of the department, the old lady, is concerned about: Will Zhang Yitang change the water dispenser in the department in the future?
Footage from the documentary "Looking for a Needle in a Haystack: Zhang Yitang and the Twin Prime Number Conjecture" (2015).
Only then did people gradually understand that Zhang Yitang was once a gifted mathematical genius at Peking University, but for more than 20 years, he lived a lonely and embarrassing life that ordinary people could not understand, once living in a fixed place, and even disappeared from the world of friends and family for many years.
His sister Zhang Yingtang recalled that after losing contact for 8 years, she and her mother finally reconnected with her brother in 2001 and received a photo from him, and her mother couldn't help but shed tears when she looked at Zhang Yitang's recent photo: "The fur vest on this photo was knitted by hand for him before he went abroad, and this watch was also brought with him when he went abroad." What a life your brother has lived all these years! ”
As the media coverage deepened, people became more and more surprised by Zhang Yitang's life and the story of the first half of his life, which contained everything a person can give in the search for wisdom, truth, and, of course, the gratifying, spiritual pure reward.
The starting point of all stories, in mathematics, dreams are horses
Zhang Yitang was born in Shanghai in 1955, his father was an underground member of the Communist Party of China, and for a while after the founding of New China, he was a teacher in the radio engineering department of Tsinghua University, and his mother worked in the Ministry of Posts and Telecommunications at that time. The "Tang" in Zhang Yitang's name is his mother's surname, and the character "Yi" is homonymous with "one", which means that he is the first child in the family. Because both parents work in Beijing, Zhang Yitang has been living with his grandmother in Shanghai when he was a child.
"My grandmother's family is a very ordinary working family, my uncle and aunt have the highest education level of junior high school, and my grandmother is basically illiterate." Although his parents were both high-level intellectuals, because of the separation between the two places, the preschool Zhang Yitang was not influenced by so-called home learning, but from a very young age, his interest in books and knowledge quietly sprouted like dandelion seeds, which he usually attributed to his introverted personality, which made him tend to be alone, which he said was a natural liking and dislike: "I like to read and think, no one taught me, but I like these." ”
Zhang Yitang's earliest interest was not in mathematics, he was still in kindergarten fascinated by his uncle's geography textbooks, and even fever and nonsense, the names of capitals around the world came out of his mouth, and later his interest gradually turned to mathematics.
Zhang Yitang with his parents and sister. (Photo courtesy of Zhang Yingtang)
"My enlightenment was in the 60s of the 20th century, when there was a set of popular science books for teenagers "100,000 Whys", and then several editions were published. I remember that there were originally five volumes, and later three more were added, of which the seventh volume was about biology and the eighth was for mathematics. I was about 10 years old. Since then, Zhang Yitang has had his own "mathematical hero" - the famous mathematician Gauss, who is known as the "prince of mathematics". It can be imagined what kind of impression such a brilliant mathematical genius left in the heart of the young Zhang Yitang. The Zhang family members still like to laugh at a joke - "On the day of the uncle's wedding, the nephew cries", referring to the uncle's wedding, the children have to sit at a table alone according to custom, but the stubborn Zhang Yitang must sit with the mathematics teacher Mr. Yao to ask for math problems, and the adults do not agree, he cries at his uncle's wedding, disrupting a happy event.
Although Zhang Yitang does not want to be called a child prodigy, such stories are now handed down. As for why mathematics, he once explained: "Mathematics and literature, and even music, have a lot in common, and they are all a pursuit of beauty." We often feel a beauty when we are hazy and not very clear about the norms. ”
In addition to mathematics, Zhang Yitang did not abandon arts and sciences, he has a good foundation in ancient literature, which may be related to family learning. His father wrote well with a brush and liked "Jiaxuan Long and Short Sentences" and "Baixiang Dictionary", Zhang Yitang was able to memorize the contents of "Journey to the West" and "Dream of the Red Mansion" from an early age, and loved "Guwen Guan Zhi" and knew a lot about Western literature (including the works of Hugo, Balzac, Maupassant, and Dostoevsky). More than 40 years later, journalists interviewing him discovered that he was carrying not a math book, but Kafka's novel "The Castle."
The originally peaceful life was shattered by the Cultural Revolution, and Zhang Yitang's parents were overthrown, and he followed his mother to a cadre school in rural Hubei to participate in the transformation. It was an era when reading math books was also reprimanded, and the young Zhang Yitang had to carry hundreds of pounds of sacks on muddy dirt roads with difficulty, and no one sympathized with him. Because of his parents' political problems, he could not go to high school, and his life was almost frozen in the fate of farming. When he returned to Beijing at the end of the Cultural Revolution, he missed high school and had to work as a worker in a lock-making factory, driving a punching press to make a padlock that has now been eliminated. The future mathematician is hesitant, as if he has just escaped the fate of farming and wants to be a worker for life.
In an unpredictable life, only mathematics can give him a sense of solidity, of course, mathematics is difficult, but the world of mathematics is not unpredictable. Zhang Yitang said: "I really believe that mathematics should be very pure. I believe that mathematics has logic. When you first start thinking, everything is very unclear, but it can gradually become clear. That's an intuition, and sometimes it's hard to describe in words. ”
This is the starting point of all subsequent stories, and the young Zhang Yitang uses dreams as horses in mathematics. In 1973, Zhang Yitang read Chen Jingrun's paper "The table of large even numbers is the sum of the products of a prime number and a no more than two prime numbers" published in the journal "Science in China". Zhang Yitang said that some later reports said that he became interested in number theory after reading Xu Chi's reportage in 1978, but in fact it was not, he had already been involved before that, and he could basically understand it.
At that time, Zhang Yitang was a worker, and although he had to stay in the factory every day, his status as a worker also had advantages: he had a work permit as a worker, and he could go to the library on weekends that ordinary people could not enter. At the National Library of China, Zhang Yitang, a young worker, soaked in it alone, reading the journal of Shandong University, an important town of number theory, and reading the early articles published by Wang Yuan, Pan Chengdong and other number theorists, who was the brother of his mentor Pan Chengbiao during his master's degree.
At that time, Zhang Yitang's English level was not good, and reading an article published by an Italian mathematician in 1965 on the Great Sieve Method was basically a guess, but he was still fascinated. He said: "I can't say why I like math so much in that situation, and I can't say that I haven't gained anything, I can really read it, I just like math." ”
Her younger sister, Zhang Yingtang, who was 11 years younger than her brother, recalled Zhang Yitang at that stage: "My brother lived in a separate other room. As a young man, I only remember that my brother always worked three shifts, and my brother dedicated all his after-work time to his mathematics. He liked his cabin, quiet and undisturbed; He treasured his time, except for meal time, at most to tease a few of us little children to play, and after a while, no one was seen, and the rest of the time was spent in his small room tinkering with his math. ”
In 1977, the college entrance examination resumed, Zhang Yitang applied for the mathematics department of Peking University, and the first time he participated in the college entrance examination failed, not mathematics, English, but politics did not do well. The next year came back, but the stubborn and conceited Zhang Yitang did not want to study as an undergraduate and wanted to apply directly for graduate school. Everyone was shocked that a person who had never studied in middle school would go directly to graduate school.
His mother was resolutely opposed, and the two quarreled a lot, and no one could convince anyone. The mother had to use her hand and collapse on the bed, saying that she was angry and sick by Zhang Yitang, and said that if he did not agree, he would not go to the hospital. Zhang Yitang is a filial son, so he lost his temper and agreed to study undergraduate, and his mother's illness was suddenly cured.
Later, Zhang Yingtang said that his brother could get involved with Peking University and should also thank his mother.
In 1978, Zhang Yitang took the college entrance examination for the second time and was admitted to Peking University, with a full score of 100 points in each subject, he scored more than 90 points in mathematics and 82 points in Chinese test, both rare high scores. Although it was the second year of the resumption of the college entrance examination, Zhang Yitang became one of the first students enrolled in the mathematics department of Peking University after the "Cultural Revolution", because the previous year was in ruins, and the mathematics department of Peking University did not even have suitable teaching materials, so it had to suspend enrollment.
Zhang Yitang's class of 1978 has become the most special class since the establishment of the Department of Mathematics: there are both the "old three" high school students before the "Cultural Revolution", who were already thirty or forty years old when they were admitted to college, and Zhang Yitang, a social worker in his twenties who had been a farmer and worker, and those who wore military uniforms, of course, there were genius teenagers who were only fifteen or sixteen years old, and the most powerful of them was a student who was only in the second year of junior high school, because he won a prize in the national mathematics competition and was admitted to Peking University.
After years of lonely exploration in mathematics, Zhang Yitang was finally able to gather with the mathematical elites of the country and cherish each other. In the bumpy days that followed, Zhang Yitang said that it was a rare happy memory in his life.
He has ambitions to match, and he looks at big problems
Zhang Yitang spent 7 years at Peking University, taking classes in the Red House of Peking University and running on the shores of an unnamed lake. In the early 80s of the 20th century, most people studying in the mathematics department of Peking University had heard of Zhang Yitang's great name: he was a high-talent student, and was deeply appreciated by Ding Shisun, the president of Peking University at the time. Classmate Wang Xiaodong recalled that because of his talent in mathematics, Zhang Yitang was a prominent figure at Peking University, and "the girls who adored him lined up from the south gate of the school to the north gate."
But Zhang Yitang said that there is no such exaggeration, "In Peking University, I am not the best in the exam, everyone else scores 100 points, I only score more than 80 points, and this situation also exists." He only admits that he is more focused than other students, "except for sleeping, I am always thinking about math problems."
Later, he said that his reaction sensitivity was only average, and if he went to the middle school math Olympiad, he might not get a good grade, but one point "may be my biggest specialty, for a problem, I can think for many years as an adult".
Zhang Yitang studied for a master's degree under Professor Pan Chengbiao, who is one of the leading figures in analytic number theory in China. Analytic number theory is famous for its pure mathematical research, that is, it does not care whether the research has practical value, but persists in pursuing the beauty of truth contained in numbers. Zhang Yitang said he liked the feeling.
Peter Sanek, a researcher at the Institute for Advanced Study in Princeton and winner of the 2014 Wolf Prize in Mathematics, later met Professor Pan in Beijing, years after Zhang graduated. Professor Pan said emotionally that Zhang Yitang is one of the outstanding students of Peking University, and he has the ambition to match, and he looks at big problems.
As for what constitutes a big question, it is both a matter of professional standards and a guide for life.
Footage from the documentary "Looking for a Needle in a Haystack: Zhang Yitang and the Twin Prime Number Conjecture" (2015).
In the year he just entered Peking University, Zhang Yitang read an article in which he said: "There is a Fields Medal winner who is Deligne of Belgium, who did algebraic geometry, and then he used algebraic geometry in number theory and solved the 'Weil conjecture'. The "Weil conjecture" is part of the algebraic geometry of the "Riemann conjecture" and, like the "twin prime number conjecture," is a puzzle that plagued the mathematical community throughout the 20th century.
At Peking University, Zhang Yitang soon obtained a master's degree. Out of natural humility, his recollection is a bit of an understatement: "Mr. Pan felt that it was just a master's degree, and he asked me to get it as soon as possible, so I got it quickly, just a few months." ”
Zhang Yitang's talent in mathematics was undoubted, and he soon wrote his first paper under the guidance of Professor Pan, but instead of being complacent, he was wary. He said: "Now that I think about it, I don't even want to watch it, and then I have a feeling that the road is getting narrower and narrower, and you can't just have this one." At this time, you need to have a little courage, see whether you are bold, dare to deny the road you have traveled, ask yourself whether our field can be combined with new things, and constantly ask yourself, ask yourself every day. ”
He was eager to go abroad to see the latest research in mathematics around the world. The choice of studying abroad was in front of him, when he was a rising star in mathematics, and President Ding Shisun personally arranged his study abroad and chose his mentor - Professor Mo Zongjian of Purdue University in the United States. Professor Mo is an expert in algebraic geometry, compared with number theory, algebraic geometry has greater practical value, although Zhang Yitang is more yearning for the pure field of number theory, but the teachers believe that a mathematical genius should not only indulge in the "void", but also serve the great process of the times. Zhang Yitang, who is in his 20s, obeyed the arrangement, thinking that he would return to Peking University as a teacher after getting his doctorate, and then do his own research. He likes to be a teacher, and after getting his master's degree, he worked as a teaching assistant at Peking University for a while, teaching calculus as a younger brother and sister.
So, on June 21, 1985, young people with high ambition left Beijing to study in the United States with only a suitcase and a satchel. Everyone thought that they would see a new star in mathematics rising, and he would become famous at a young age and return to China, but slowly, year after year, Zhang Yitang, a graduate of Peking University who took a foreign land as his hometown, gradually disappeared from people's field of vision.
"Although I don't even have a job, I can still go back to analytic number theory"
"Studying for a PhD in the United States, because of some personal reasons, made me very 'miserable', of course, some of the Internet are not facts, but I also admit that it made me 'miserable'."
Anyone who is familiar with Zhang Yitang knows that he can talk eloquently about everything other than mathematics, even if it is a long period of youth into middle age.
Actually, this was not the case in the beginning.
Purdue University is a traditional famous university in the United States, which has trained 13 Nobel Prize winners, including Deng Jiaxian, the "father of the two bombs" and Liang Sili, a rocket expert, who graduated here. When Zhang Yitang first reported to the school, the tallest building on campus was the mathematics department. During the first semester, he and his supervisor Mo Zongjian met once a day to study Professor Mo's paper on the "Jacobi conjecture", sometimes until dusk.
The "Jacobi conjecture" is a classic problem in algebraic geometry, and it is also Professor Mo Zongjian's research field, as a starting point, probably also a way for instructors and students to get acquainted with each other. For the next two semesters, they worked with four other students on a difficult paper by Japanese mathematician Heisuke Hirochu on singularities. Professor Mok later said that he believed that his six people had doubled the number of people studying it in the world.
Heisuke Hirosaka won the Fields Medal for his research on the singularity. As a top mathematics award dedicated to young scholars under the age of 40, only 4 Orientals have won this honor, but there have been no scholars from Chinese mainland. More than 20 years later, Zhang Yitang said: "The Fields Medal is a heart disease for me. ”
When preparing his doctoral dissertation, Zhang Yitang chose to use the topic "Jacobi conjecture" as the title. At first, Professor Mok was surprised that the topic was too difficult for a PhD student, but later he said that he saw ambition in the young man's eyes: "Through his eyes, I saw a restless soul, a burning heart. I understand that if he were an explorer, he would go to the end of the world; If he were a mountaineer, he would climb Mount Everest, and no storm or lightning could stop him. ”
In the next 7 years, there were fewer and fewer meetings between master and apprentice, and Zhang Yitang did research alone, after all, for mathematicians, a pen, and possibly a blackboard, was enough. It seemed that everything was going well, and the news that the "Jacoby conjecture" was about to be proved spread more and more, until one day, even a professor in the chemistry department asked Professor Mo Zongjian curiously, I heard that a Chinese student in your department has made an incredible proof?
"In his doctoral dissertation, Yitang said that he proved the 'Jacobi conjecture' and that he should be awarded the Fields Medal for it."
During the defense of the doctoral dissertation, the defense committee unanimously agreed that it was a qualified thesis, but the result of the review was that Zhang Yitang was wrong, and the error was that one of the theorems he used to prove (from Professor Mok Zongjian) was proved wrong, which made his whole proof a castle in the air.
In 1992, Zhang Yitang received his doctorate and was "unemployed at the same time."
He did not receive a recommendation letter from Professor Mo Zongjian, and Professor Mo did not offer help. After graduation, Zhang Yitang was preparing to leave Purdue University, he got an interview at Rutgers University, he was going to meet the analytic number theorist Ivanets, the potential meaning of which was that he decided to return to his beloved field of number theory, for which Professor Mok Zongjian wished him good luck.
But good luck did not come at that time, the meeting with Professor Ivanets was fruitless, and it was not until 21 years later that Professor Ivanets would reacquaint himself with the young man at that time - in 2013, the Annals of Mathematics invited Professor Ivanets to serve as a reviewer for Zhang Yitang's paper, and he would become a witness to the epoch-making proof made by the latter. And that year, Zhang Yitang was 58 years old.
If life is divided into four seasons, then after leaving Purdue University, Zhang Yitang's life has entered a harsh winter. His doctoral dissertation became a bad mistake in his youth, and of course he could not be published, and there was neither a recommendation letter from his supervisor nor a representative work, and such a mathematical doctor could not be achieved in the United States.
Zhang Yitang has never been able to find a teaching position, sometimes living in Kentucky, sometimes living in New York, both overnight, living in uncertainty, sometimes sleeping on the sofa at a friend's house, sometimes even living in the car. Slowly, people said he disappeared and went into seclusion.
"He chose solitude." His friend later commented.
In New York, a friend introduced Zhang Yitang to Sun Yaling, who later became his wife, and the latter's first impression of him was not good: "As soon as I saw the dirt and wore big black-framed glasses, I said 'ugly death.'" The introducer joked: "Don't look at this, this is a talented person from Peking University, with a high IQ in terms of education and a zero index in life." Later, Sun Yaling was shocked when she first came to Zhang Yitang's house, there were no tables and chairs in the empty room, and she slept on the sofa cushions.
The only hobby the two have in common is drinking. Beer, red wine, white wine, you can drink anything, bottle after bottle, you can drink it when you sit down. Sun Yaling was born in the northeast, has a bold personality, and is also a good drinker, while Zhang Yitang drinks averagely, the wine is good, will not persuade wine, is boring to drink. Drink high, the doctor of Peking University who does not like to talk will talk more, astronomy and geography, history and humanities, poetic physics, and of course, his favorite mathematics, talk endlessly. In the adversity of life, that is the hidden edge of a Peking University talent.
From 1992 to 1999, Zhang Yitang, a doctor of mathematics, worked as an accountant in a Subway fast food restaurant, and also helped with cashiers when he was busy. Zhang Yitang said: "Later I think back, what supported me at that time? It's not that I have a strong will, but I think a lot of things lightly, and I don't value material things and money so much. Generally speaking, I have a very bad life, but I think it's not very good? I also have time. When I was a Ph.D., although I gave up analytic number theory, I always paid attention to it, and I felt that I could still do it. Although I don't even have a job, I can go back to analytic number theory. ”
According to Zhang Yitang's friend, with his mathematical ability, he can make a lot of money in the IT (information technology) and financial industries. He did have the opportunity. In early 1999, a junior disciple at Peking University approached Zhang Yitang and asked him to help solve a very difficult pure mathematical problem in network design, which Zhang Yitang solved in a week, which later became a patent. But similar things, Zhang Yitang never got involved again.
So, in the faltering middle age, Zhang Yitang still did not leave mathematics. He has such a talent, making money is just a means of knowledge, so the money is just enough. As long as he wants, the brain can turn off its outward tentacles anytime and anywhere and dive deep into the world of mathematics.
In the adversity of life, mathematics is both a reliance and a dream, a means of escaping reality and the ultimate goal, and there is no conspiracy in it, only logic and beauty.
At the beginning of 1999, a friend helped Zhang Yitang get a teaching position at the University of New Hampshire, a supernumerary lecturer, only responsible for classes, probably regarded as the "cheap labor" among teachers, but for Zhang Yitang, this was a rare opportunity to return to college. When he received the call, he immediately quit his job and flew to the interview. At the University of New Hampshire, Zhang Yitang, a lecturer who was a silent and somewhat maverick man, often paced the building alone, as if thinking or wandering, and colleagues described him most often as "shy and not talkative, always the last to leave the office."
Students liked him, and in a feedback report on teaching quality, some students praised him: "Tom (Zhang Yitang's English name) is the best!" He is the best teacher! He always talked about calculus in plain terms, he was also very humorous, and all the students loved him! The only advice was: "Tom should smoke less, that would be bad for his health." ”
In this way, Zhang Yitang, who is not good at words, can only talk eloquently in the face of mathematics, and his humor and charm come from mathematics.
Mathematics certainly has to prove, but mathematics is not exactly like that
Around 2010, Zhang Yitang decided to take the "twin prime number conjecture" as a research direction, he read the papers of professors Bonberi and Goldstone, and knew that everyone in number theory had achieved some results, but he thought that their methods were too limited and inflexible, and he thought that he could probably try again.
This is the advantage of studying number theory, many long-standing unsolved problems in the mathematical world can be classified into analytic number theory, no need to worry about no problem to solve, worry about you just don't know how to do it.
At that time, Zhang Yitang did not know Professor Goldstone's pessimistic conclusion, he said: "Later I thought that I knew, would I also be pessimistic, but I was alone, almost at the same time, I suddenly became optimistic, I found that there were some key steps in the middle, I could approach in another way, so I did it alone, strictly speaking, I did it for three years." ”
Zhang Yitang is immersed in his own world and rarely communicates with friends, and socializing seems to him to be a waste of time. However, his friend Qi Yage said that every year on his birthday, Zhang Yitang would call to greet: "I wish you a happy birthday, okay, I am Zhang Yitang." The phone hung up, and he immediately returned to the world of mathematics. Later, a reporter asked Zhang Yitang: "Do mathematicians need talent?" ”
"What is needed is focus." He replied, "And you can never give up your individuality." ”
July 3, 2012, the day inspiration finally arrived, is now a legend.
Footage from the documentary "Looking for a Needle in a Haystack: Zhang Yitang and the Twin Prime Number Conjecture" (2015).
During the summer vacation, a friend used good wine to entice him to tutor his children in calculus. Deer often pass by in the woods near a friend's house, and in the morning, Zhang Yitang originally went to see the deer, but did not see the deer, but another world suddenly appeared. Later in an interview with The New Yorker, he recalled the moment: "I saw numbers and equations, though it was hard to tell what that was. It can also be hallucinations. I know there are still a lot of details to fill in, but I should prove it. Thinking of this, I went back to the house. ”
"The bounded distance between prime numbers" caused a sensation in the mathematical community, and reviewer Ivanets commented on Zhang Yitang's paper: "Crystal transparent. ”
After becoming famous, everything changed, and Zhang Yitang was no longer a lecturer who was uncared for, and he was invited to join the University of California, Santa Barbara, as a tenured professor in the mathematics department. The year after the publication of the paper, the Swedish princess personally awarded the prize in mathematics to the Zhang Yitangrov Schock Prize. The mathematicians who attended at the same time set aside time to travel to Sweden, but Zhang Yitang had no idea of this and flew back to the United States the next day to attend classes. Back in the United States, he was awarded the MacArthur Genius Award. Zhang Yitang said to his wife: "When we got married, I said I would give you a lot, but I couldn't give it at that time, now, tell me what you want?" ”
He became a hero in mathematics, from obscurity to blockbuster, and made him live a legend that the public loved. But just as people were amazed by his talent, they were also surprised by his calm attitude towards the outside.
Instead of attending dinner and receiving applause, Zhang Yitang still prefers to sit alone in his office with mathematics. His wife, Sun Yaling, said they lived by the sea, but Zhang Yitang had only visited the beach once in four years. All he thinks about every day is to go to school, on the grounds that the school's network is faster than at home, which is convenient for him to do research. The journalists who interviewed him also felt a sense of powerlessness, and he was silent, even saying that he could think about math problems while being interviewed.
Yes, it's still mathematics, as Zhang Yitang said, in the world of number theory, there is never a need to worry about having nothing to do. The outside world is still marveling at the glory he has created in the past, and he has no intention of it.
"I have new things to do, and I believe I can still make new things."
Hardy, a mathematician, once said he never knew of a major mathematical breakthrough by someone over 50 years old. In 2020, Zhang Yitang is 65 years old, and the latest goal is the "Landau-Siegel zero-point conjecture", which is an important step towards the "Riemann hypothesis". He would not be swayed by Hardy's words, he said: "These words can be heard, although I know, but I don't take them to heart." ”
After achieving fame, Zhang Yitang once again devoted all his energy to a new mathematical peak. Sun Yaling said that her wife went to school to study mathematics, and at home she still thought about mathematics, sometimes talking to herself, stir-frying, bathing, and going down the stairs, always chanting: "Zero o'clock, zero o'clock, zero o'clock..." She knew that he was fascinated again.
Zhang Yitang returned to China more often, and he returned to Peking University to give summer classes to undergraduates. He loved spending time with these young people, whose intellectual curiosity was just as eager for mathematics as he had been back then. In the face of them, the silent Zhang Yitang disappeared, but was full of desire to tell, and he wanted to tell them everything he knew.
"Ultimately, the criterion for judging whether a person can achieve anything in the field of mathematics is the depth of thought." Zhang Yitang said, "If you are determined to do mathematics, then you feel slower than others in the learning process and do not feel inferior, there are many reasons for whether you can succeed in the end." ”
"Keep a sense of freshness, a sense of dissatisfaction, and sometimes be a little bit daring. For the achievements of predecessors, whether they are authoritative or not, you want him to have limitations, and he is not the best. Because I feel that way, I can move on. ”
"Mathematics is not a simple process: theorem one, proof; Theorem two, proof. Of course, mathematics has to prove it, but mathematics is not exactly like that, and if it were just such a process, I would find it very annoying. ”
Of course, Zhang Yitang also mentioned his difficult years: "You can avoid the detours I have taken. Finally, during the Q&A session, the young students turned their interest to the legendary mathematician. A student asked him if he could have achieved such an achievement if he had been in China at that time. Zhang Yitang thought for a while and gave the answer: "My personality is relatively unique, if it is in China, it may interfere more." But I believe I can do it too. ”
In 2014, Zhang Yitang was invited to give a speech to Peking University graduates. In a flat tone, he told the crowd: "I often feel that I am doing it badly – it's true, but I'm not disappointed, I just do it." There were a lot of setbacks in between, and I persevered every time. If people ask me what the secret to success is, I can only say the truth: I just do it and keep going. I have been like this and I will be like this in the future. ”
Original author/Zhang Rui
Excerpt / He An'an
Editor/Luo Dong
Proofreading of the introduction part / Liu Baoqing