Because of his existence, Chinese combinatorials have an outstanding position in the world mathematical community.
In 1983, lu Jiaxi, a middle school physics teacher, solved the world-famous "Kirkman" mathematical problem and the "Steiner's large set theorem", which was called one of the great achievements in combinatorial design in the past twenty years by the international mathematical community, and completed more than 130 years of unsolved problems.
He was an ordinary physics teacher in Baotou Ninth and became a famous mathematician in the international mathematical community.
Lu Jiaxi (1935-1983)
As he continued to climb to the peak of science, he died of a heart attack at the age of 48. People's Daily wrote an article "20 years of hard work, exhausted life's work, middle school teacher Lu Jiaxi conquered the world's problems" commemoration, Lu Jiaxi's spirit of dedication to science inspired countless young people.
This great Chinese citizen scientist was exhausted alive. His deeds are unknown to many young people of the new generation. I think it is necessary to tell you about it. His tragedy, hopefully, will not be repeated.
Lu Jiaxi was born in Shanghai in June 1935. The father's job is to "run the street", relying on selling some soy sauce, monosodium glutamate and other condiments to earn a meager income to support four children. The poor life caused the first three children to die prematurely, and only Lu Jiaxi, who had a big life, survived.
When his parents found out that the old man was unusually intelligent, they borrowed money to send him to primary school. In the face of hard-won school opportunities, Lu Jiaxi cherished them. When I was in middle school, my father died of illness. Cut off from his source of income, Lu Jiaxi had to drop out of school and work as an apprentice in a hardware store.
After the founding of New China, Lu Jiaxi bid farewell to his mother and came to Shenyang alone to take the statistical training class run by the Northeast Electrical Appliance Industry Administration. It was a program aimed at cultivating quick-track practical talents, and six months later, Lu Jiaxi was assigned to work at the Harbin Electric Machinery Factory with the first place.
In the motor factory, he has worked in finance, materials, production and other positions, worked hard and complained, and was twice rated as an advanced producer. Despite his busy work, he never forgot to study. During his off-duty time, he taught himself all the high school courses, and in order to better study, he also taught himself Russian and English, and within half a year, he was able to talk to the Soviets, which surprised his colleagues.
In the summer of 1956, he stumbled upon a book about combinatorial mathematics, "Introduction to Mathematical Methods", which introduced eight interesting mathematical problems of world-famous mathematics. Lu Jiaxi has loved mathematics since childhood, and was immediately fascinated by the "Kirkman Girl Problem" and "Steiner Series".
"Interesting Introduction to Mathematical Methods", by Xu Zeying
In particular, the "Kirk Full Girl Problem" seems simple, but it is very interesting. In 1850, the English mathematician Kirkman asked an interesting question: a female teacher would lead her 15 students out for a walk every afternoon, and she divided the students into 5 groups of 3 people, how to arrange so that every two students in the same group for one day in a week.
Kirkman answered this question in the following year, but if the number of people were arbitrarily divisible positive integers, the sufficient necessary conditions for the above grouping to be achieved were not proven.
A voice poured out from the bottom of Lu Jiaxi's heart: Solve them!
But a junior high school student, if you want to solve this problem that has not been solved for more than 100 years, it is far from enough to rely on enthusiasm and impulsiveness, and you must have solid knowledge as a backing. Lu Jiaxi wanted to go to college, applied with the factory several times, and finally was admitted to the Physics Department of Northeast Normal University in the autumn of 1957.
People now can't understand what kind of determination Lu Jiaxi had at that time to abandon work and study. He gave up a high salary of 64 yuan a month and embarked on a path of study with only poor financial aid.
Since then, Lu Jiaxi's college career has been tied to this mathematical problem. Every morning I went to the library early to read a mathematical treatise, with a pen and a few pieces of paper covered with traces of calculations. After the library closed, he continued to think and calculate under the street lamp downstairs in the dormitory.
Talent and hard work have made Lu Jiaxi's physics grades still among the best, and during his four years of college, he not only earned a bachelor's degree in physics, but also was about to overcome the "Cockman Female Problem".
In 1961, Lu Jiaxi graduated from university and was assigned to The Inner Mongolia Baotou Iron and Steel Institute as a teaching assistant. At the end of the year, an answer to this question was proposed. He wrote a paper on the four years of hard work, "The Production Method of the Kirkman Series and the Steiner Series", which was submitted to the Institute of Mathematics of the Chinese Academy of Sciences, and waited for publication with hope.
A year later, he got a response, letting him verify the paper himself.
In 1963, he sent his paper to the Mathematical Bulletin, hoping to gain academic media attention. Still after a year to get a reply, it is recommended to switch to other publications. Year after year, two consecutive times hit a wall.
He immersed himself in research, changed the paper to "The Construction Method of Equilibrium Incomplete Blocks Can Decompose Incomplete Blocks", submitted it to the "Acta Mathematica Sinica", and this time replied in less than a year: There is no value.
The flowers that took five years of painstaking cultivation could never bloom, and no one could understand this depression at that time. After the ten years of turmoil began, Lu Jiaxi was not satisfied, and he submitted four papers successively, all of which sank into the sea.
During this time, Lu Jiaxi's teaching work also began to be frequently transferred. He has successively taught in the Teaching and Research Department of the Education Bureau, Bao No. 8 Middle School, Bao No. 5 Middle School, Bao No. 24 Middle School, and Bao Jiu Middle School.
Wherever he went, he still had his "Kirkman" in mind. In Bao Jiu, Lu Jiaxi is the most beloved physics teacher among students. In his spare time, Lu Jiaxi focuses on combinatorial mathematics. He thought that he must win the "Kirk full of girls problem", and over the years, with the deepening of research, he added a lot of new ideas and methods.
At that time, Baotou was a small border city with underdeveloped information. In order to get more materials, he went to Beijing alone to consult foreign language materials in the Beijing Library.
The two ears did not ask about the outside of the window, and only wanted to be full. In that sensitive decade, lu jiaxi, who had a reclusive personality, became a negative model, accused of taking the "bz road", and suffered ridicule and white eyes. In order to hide in the dormitory, he founded the "Haiyan Combat Team", which won him valuable research time.
Lu Jiaxi (right)
Until 1978 and 1979, the research efforts that had condensed for 20 years were repeatedly revised by him, written as a paper and sent out, but he learned the news of a sunny thunderbolt.
As early as 1971, the Problem of Cockman's Girls was conquered by The Indian-American mathematician Jodhrie and doctoral student Wilson, which was unheard of in closed China at the time. Lu Jiaxi suddenly felt that the belief that supported him had collapsed, and he did not want to believe it for a long time. It feels like you agreed with a girl that you would make a lot of money to come back and marry her, but when you finally returned home with all your efforts, you found that she was already married to a woman.
Originally, he basically solved the "Kirkman Girl Problem" in 1961, and even if he was able to successfully publish a paper for the first time in 1965, it was 6 years earlier than the American mathematicians. Due to the blockage of information, it is extremely regrettable that Lu Jiaxi and China have yielded to the people!
Since the connection with the "Kirk Full Girl Problem", 18 years of hard work has become his most valued child, and he did not expect that this 18-year-old child's fate would be so sad.
He loved science and never wavered in his belief in climbing to the heights of science. This blow made him confused, if there are new works, or what should happen?
But he got back on his feet and continued to climb the mathematical peaks with a tenacious will. This time, his eyes were set on the "Steiner Series" episode.
Lu Jiaxi knew this time that the "Steiner Series Collection" has been proposed for more than 130 years, and no one in the world has conquered it, which gives him sufficient confidence. He worked as a physics teacher in his graduating high school class, with heavy teaching tasks that he could only sit down and study after 10 p.m. every night, sometimes until the next day. He did not rest, went straight to class, and came back to continue his research. Such a routine became commonplace. Often the toothache is uncomfortable, simply pulled out, slowly full of teeth become lonely and bitter, the wife looks in the eyes, pain in the heart.
Because he is too immersed in the Steiner series every day, others cannot understand it, and secretly calls him "mentally ill". Once, he sent his daughter to a kindergarten, thought while walking, loaded up the kindergarten sports equipment, and returned with a few large bags, which were rumored to be jokes.
He made a major breakthrough in October 1979 and wrote a paper and sent it to the world-famous magazine on combinatorial mathematics in the United States, Combinatorial Theory.
This time, there was a quick response, saying that "if it is true, it will be an important result", at that time, there were many mathematicians in the world who were tackling this problem, but there was little success in sight.
They are looking forward to a breakthrough from the middle school teachers in Bao Jiu.
Lu Jiaxi's twenty years of hard work were finally recognized, and he wrote papers day and night. In September 1981, the Journal of Combinatorialism successively received three articles from Lu Jiaxi, "On the Disjoint Steiner Ternary Collection", which solved the worldwide combination problem and pioneered the overall solution of the problem of the existence of large sets, which caused a sensation in the mathematical community as soon as it was published, and was called "one of the great achievements in combination design in the past twenty years".
An ordinary Chinese physics teacher has become a celebrity in the international mathematical community. The president of the University of Toronto in Canada wrote a letter of enthusiastic praise to the president of Bao Jiu Middle School: "Your Lu Jiaxi is a well-known mathematician in the West. He asked me to tell you that he should be transferred to a university position, so as to better promote the development of mathematics in China. In accordance with the treatment of famous scholars, Lu Jiaxi was invited to go to Canada to give a lecture in 1984.
On this day, Lu Jiaxi waited too long, and he wrote in his diary: "There should be more, it should be earlier." ”
Lu Jiaxi authorized Columbia University to publish his paper, but he cherished his research results too much. In order to be able to publish smoothly, he did not care about anything, only worried about the recurrence of the tragedy of "Kirkman" that year.
When Lu Jiaxi was popular in the Western mathematical circles, he was not very well known in China. In July 1983, when the Chinese authorities invited two professors, Mendelson and Bundy, who were in charge of reviewing Lu Jiaxi's papers, to give lectures in China, Mendelson specifically proposed that he wanted to meet with Lu Jiaxi, and Lu Jiaxi gradually became known.
In October 1983, the 4th Chinese Mathematics Annual Conference was held in Wuhan, and Lu Jiaxi was specially invited to share the research results of the "Steiner Series" as a guest.
In order to participate in this meeting, Lu Jiaxi borrowed 400 yuan as a coil. At the meeting, the excited Lu Jiaxilian told his colleagues in the mathematical community that he was working hard to sort out the other six exception values.
This time, Lu Jiaxi's hard work was finally not in vain, and he wanted to continue to climb on this mathematical peak. He said that he is almost 50 years old, and there is not much time to really concentrate on scientific research, so he must seize the time to do it.
In order to save money on the road, Lu Jiaxi took a train from Wuhan to Beijing to change trains and then returned to Baotou. After dinner with his family, he chatted a few words, and then shouted, "Too tired, too tired, tomorrow, rest first."
Unexpectedly, at about one o'clock in the morning on October 31, he was short of breath, suddenly died of a myocardial infarction, and never woke up again, only 48 years old.
The doctor diagnosed that this was caused by the fatigue and tension accumulated over the years, and in the ups and downs of life, Lu Jiaxi's body could no longer bear it. In other words, he was exhausted alive.
Can't help but remind people that the world-famous mathematician Chen Jingrun is also tired, why is the fate of mathematicians so "coincidental"?
Nine months after Lu Jiaxi's death, his first paper in China was finally published. He won the first prize of the Third National Natural Science Award of China for his research result "Research on the Large Collection of Disjoint Stena Ternary Systems".
The domestic mathematical community is shocked by Lu Jiaxi's sudden death, and the famous mathematician Wu Wenjun said that although Lu Jiaxi's academic achievements and personality are now known, if there is no reminder from international friends, Lu Jiaxi may still be poor and sick and in a state of being buried. This phenomenon deserves our deep consideration.
The Inner Mongolia Autonomous Region posthumously awarded him a "special teacher" and awarded him a prize of 5,000 yuan, calling on young people throughout the region to learn from Lu Jiaxi.
Experts from relevant departments were re-examined and determined that Lu Jiaxi's "Structural Method for Balancing Incomplete Blocks and Decomposable Balanced Incomplete Blocks" submitted by Lu Jiaxi in 1965 could fully solve the "Cockman Girl Problem", which was 6 years ahead of the solution proposed abroad.
Mendelson, a well-known professor of combinatorial science at the University of Toronto in Canada, was very saddened by the sudden death of Lu Jiaxi, and bluntly said that this was undoubtedly a great loss to world mathematics.
Time cannot be turned back, and China has also lost an opportunity to lead the world because of the chaos and neglect of talents at that time, and the loss is not tragic.
The Slovaks are gone, but the ideals are still there. China is not without talent, but it needs to protect the soil of talent.
Because of Lu Jiaxi's outstanding scientific achievements, he was hailed as "China's greatest amateur scientist" and became a banner for Chinese citizen scientists. He won a place in the world mathematical community for Chinese combinatorials, but was not as famous as mathematicians such as Hua Luogeng, Su Buqing, and Chen Jingrun.
However, heroes don't stay in the corner forever. Since the fall of 2017, Lu Jiaxi's alma mater, Northeast Normal University, has selected no more than 40 people from the two majors of mathematics and physics to form the "Lu Jiaxi Mathematics and Physics Base Class", inviting internationally renowned professors to teach.
Practicing Lu Jiaxi's spirit of hard scientific research, cultivating talents, and protecting talents is what we should do most.
Resources:
1. "Clarification of Some Historical Facts About the Combinatorial Mathematician Lu Jiaxi", Zhu Anyuan, Guo Huazhen, Zhu Jingshu