Lu Jiaxi: China's top mathematical genius, a mediocre life but not mediocre achievements

Lu Jiaxi was born in Shanghai on June 10, 1935. He died of illness in Baotou on October 31, 1983, a modern Chinese mathematician and the winner of the First Prize of the National Natural Science Award.

Lu Jiaxi commented

He proved the "Steiner Series" and "Kirkman Series" problems in the field of combinatorial computing under difficult circumstances, and is a modern Chinese mathematician, an expert in combinatorial mathematics, and a winner of the First Prize of the National Natural Science Award. However, at the peak of his amateur research, he died suddenly and prematurely. His research results, his spirit of research, and his encounters are breathtaking.

Mendelson, a famous Canadian mathematician and professor at the University of Toronto, once praised him: "This is one of the major achievements in combination design for more than two decades." He also asked the president of the University of Toronto, Stegrainville, to write to the principal of Baotou No. 9 Middle School, suggesting that Lu Jiaxi be transferred to a university post. University of Toronto, Canada President Strandwell (D. W． Strangway) wrote to the principal of Baotou Ninth Middle School: "Lu Jiaxi in Baotou Ninth is a well-known mathematician engaged in combinatorial theory in the West."

The "Lu Jiaxi Academic Work Review Committee" composed of Chinese combinatorial mathematics experts commented: "Lu Jiaxi's achievements on large sets can be compared with two other world-renowned achievements in block design theory, and will be recorded in the annals of combinatorial mathematics with them.

World-class mathematician who solves world problems such as the Kirkman girls' problem

Life of Lu Jiaxi

Boyhood

On June 10, 1935, Lu Jiaxi was born in a poor citizen's family in Shanghai. Father Lu Baoxiang is on the beach "running street", self-produced and sold some soy sauce essence, monosodium glutamate, etc., a day does not run, the whole family will not have rice under the pot. Mother Li Yuexian took care of the housework, has raised four children, the first three are due to illness and inability to heal and died one after another, only the old four families are big, grow up.

Jia Xi has been brilliant since childhood, very strong, at the age of 6 into Shanghai Nanxun Road Zhengde Primary School, in his young mind has learned to cherish the hard-won opportunities to study, academics have remained excellent. In 1948, while he was in the second grade of junior high school at Myron Middle School, his father suddenly fell seriously ill and died shortly after he had no money for medical treatment. This was undoubtedly a heavy blow to his family. Jia Xi barely graduated from junior high school and was forced to drop out of school. In September 1950, he was introduced to the people at the age of 15 when he came to Shanghai as an apprentice in a hardware and material industry, took on the pressure of life prematurely, and experienced the hardships of life.

In 1951, the statistical training course of the Northeast Electrical Appliance Industry Administration bureau was completed

In November 1951, Jia Xi resolutely bid farewell to his family, left Shanghai, which had brought him joy and suffering, and came to Shenyang, the northern country, and was admitted to the statistical training class run by the Northeast Electrical Appliance Industry Administration. Half a year later, he finished with the first place in his studies and was assigned to work in Harbin Electric Machinery Factory.

In the more than five years of working in Harbin Electric Machinery Factory, he has been diligent and diligent, immersed in hard work, and has worked in materials, finance, planning, production and other departments, and has twice been rated as an advanced producer of the factory. In 1956, the Songhua River flooded, directly threatening the safety of Harbin City, he actively devoted himself to the front line of flood prevention and rescue, and won the honorary title of the city's second-class flood control model.

Jiaxi has strong self-learning ability and excellent perseverance. No matter how harsh the environment is, he can always systematically arrange his study schedule. He is very strict with his own requirements, starting from the bits and pieces, and studying tenaciously and steadily. In his spare time, he took all his high school courses and was particularly fond of pamphlets in the natural sciences. Winters in Harbin were unusually cold, but in order to learn Russian, he insisted on walking a long way to night school every night. According to Yuan Maoyuan, who went to night school with him, half a year later, Jiaxi could have a simple conversation with the teacher in Russian. He had a high talent for language learning, and in poor conditions he not only basically mastered Russian and English, but also taught himself Japanese in later years due to the need to view materials.

Jiaxi lost his father at the age of 13, went out alone to earn a living at the age of 16, and lost his mother at the age of 29. Due to the premature loss of family warmth, he is already introverted, gradually becoming withdrawn, willing to swim alone in the ocean of knowledge. Yet he is also a very entertaining and interested person. In his spare time, he loves to sing Peking Opera; since his youth, he has loved chess and Go; he also likes to appreciate literary masterpieces and care about the latest achievements in science and technology. While sorting out his relics, he discovered masterpieces of Chinese and foreign literature and books introducing the latest technology. Some books have his circles and simple comments, question marks, etc. There are also some original books in foreign languages.

Lu Jiaxi's youth

One day in the summer of 1957, Jia Xi bought a copy of Sun Zeying's "Interesting Introduction to Mathematical Methods". For many days, he immersed himself in more than ten interesting world-famous mathematical problems in the book. At that time, Lu Jiaxi, who was in full bloom, may not have dreamed that a thin pamphlet would change the path of his future life.

"Interesting Introduction to Mathematical Methods" that leads Lu Jiaxi to the road of mathematics

The most fascinating thing about him in "Interesting Introduction to Mathematical Methods" is the "Kirk Full Girl Problem". As early as 1850, T. C. C. Man, a district of the Church of England, was the proctigy of the Church of England. P． Kirkman) asks an interesting question in the annals of The Lady and The Gentleman: A female teacher leads her 15 girls for a walk every afternoon. She divided the students into 5 groups of 3 people each and asked how to arrange them so that every two students in the same group happened to be in the same group one day during the week. This fun math game seems simple at first glance, and Kirkman himself gave an answer in the same publication the year after he asked the question. However, the mathematician's instinct is to generalize and abstract a simple game problem. For example, we can use N instead of 15, divide N units into several groups, each group of 3 units, a division to form a series, called the Kirkman series. Suppose there are several series, Q: Divide N into series so that each unit is in exactly one of the other units in the same group. What are the charging conditions that N satisfies? How is the division of the series made up? This is a combination of designs that have been a problem of existential charge conditions that has not been solved for more than a hundred years. In honor of this self-taught man in mathematical research, people call this famous mathematical puzzle "The Cockman Girl Problem".

22-year-old Lu Jiaxi, drunk for many days in a row, he had a tenacious idea in his heart, he must overcome this problem. However, a young man with only a degree of initial Chinese to overcome such problems is, in the eyes of others, tantamount to a fool's dream. Lu Jiaxi himself also deeply understood that the cause of science cannot rely on momentary enthusiasm and impulse. He was aware of his lack of knowledge and was eager to further his education.

Things are not all smooth sailing. The leader did not understand the ambitious Young Man in Shanghai in front of him and did not approve his application for further study. Lu Jiaxi was very stubborn and stubborn, and did not hesitate after making up his mind. He resolutely gave up his monthly salary of 64 yuan and was admitted to the physics department of Jilin Normal University (now Northeast Normal University) in the autumn of 1957, and began a difficult university life with only a meager bursary.

In the four years of college, although the material life is much worse than when working, the spiritual world is completely free, which is exactly the environment that Jiaxi dreamed of. In the past four years, he has worked hard in both physics and mathematics, read a large number of mathematical monographs, taken a considerable number of notes, and achieved excellent results in professional courses. From the beginning of college until the last step of his life, because his major was to study physics and teach physics, he always regarded mathematical research as his hobby, and never delayed his own work. Later, he also talked to his relatives and friends that he really loved physics and was willing to take it as a lifelong profession in order to make more direct contributions to mankind; but physics required too many material conditions, so he could only engage in mathematics.

Impacting world-famous mathematical puzzles is no easy task. For a stubborn college student, it does not mean more than just a pen and a few calculus papers, but also a dedication. Whenever it was late at night and others fell asleep, he quietly got up, left the dormitory, and paced around the staircase under the all-night electric light, talking to his "Kirk Full Girl". This "dialogue" lasted for four full spring and autumn seasons. At the end of his stressful college life, he not only graduated with honors, but also completely solved the "Kirk Full Girl Problem" that had plagued the mathematical community for more than a hundred years.

Silent struggle

He graduated from the Department of Physics of Northeast Normal University in 1961. He has successively served as a physics teacher at the No. 24 Middle School and the Ninth Middle School in Baotou City, Inner Mongolia. Combinatorial mathematics expert of Baotou City.

Lu Jiaxi has long been engaged in combinatorial mathematics research. In 1961, he completed the "Kirkman Quadrant Series" paper, and then specialized in the "Steiner Series", created a unique recursive construction method that introduced prime factors, and completed seven papers with the total title of "Disjoint Steiner Ternary Collection", which solved the problems that had not been solved for many years in the international research on combinatorial design theory.

He graduated from the Department of Physics of Jilin Normal University (now Northeast Normal University) in 1961.

In the autumn of 1961, Lu Jiaxi graduated from university and was assigned to Baotou Iron and Steel Institute in Inner Mongolia Grassland Steel City as an assistant professor. He is full of ambition and full of infinite hope for the future. On December 30 of the same year, he sent his five-year-old debut work, "The Constructor of the Kirkman Series and the Steiner Series," as his first child in spirit, to the Institute of Mathematics of the Chinese Academy of Sciences for advice, affirmation, and publication. He also sent another paper, "Some Results of Using a Combinatorial Series to Make Orthogonal Latin Squares", and he began the difficult journey of life.

In the early summer of 1962, Baotou Iron and Steel Institute was dismissed, and Jiaxi was transferred to the Baotou Municipal Education Bureau. In the first four years of the Cultural Revolution, he successively taught in the Teaching and Research Department of the Education Bureau, Bao No. 8 Middle School, Bao No. 5 Middle School, and Bao Twenty-fourth Middle School, during which he also spent a period of training at the Administrative Cadre School of the Education Bureau. Although he had no time to take care of his marriage affairs, he continued his mathematical research with tenacious perseverance.

In February 1963, he received a reply from the Institute of Mathematics, which introduced some of the latest literature, hoping that he would verify the paper himself, and said: If the results are new, they can be submitted directly to journals such as the Acta Mathematica Sinica. So he took advantage of the Spring Festival to rewrite the paper and post it to the Mathematical Bulletin on March 12. The Mathematical Bulletin, by its very nature, does not publish long texts, especially long articles like Lu's highly specialized texts. After a difficult year, I received the following reply: "Due to the length and mathematical tools used, it is recommended to submit to another journal. ”

Of course, it is a pity to take a detour, but Lu Jiaxi is full of confidence in his paper. He rewrote the paper, named "Constructor of Equilibrium Incomplete And Decomposable Equilibrium Incomplete Blocks", which was posted to the Acta Mathematica Sinica on March 14, 1965. The revision of this paper took more than a year and was carried out under extremely difficult conditions. On the one hand, in order to add new content to the paper, he traveled to almost all the libraries in Baotou City, and used the summer vacation to go to the Beijing library to check the materials, sometimes living in the railway station. On the other hand, frequent job transfers also make it difficult for him to study with peace of mind. Also, because he worked silently and rarely interacted with people, the criticism, blank eyes and sneers he received in the case that people around him did not understand gave him a lot of mental pressure. Once upon a time, during college, he was saddled with the burden of "not asking politics" for studying the "Cockman's Girl Problem". At this time, on the eve of the "Cultural Revolution," when the ultra-leftist trend of thought was increasingly pervading the motherland, it was only natural for him to wear a hat to take the "white road" and send him to a cadre school for training and labor reform.

The paper was returned in February 1966. History is just and does not bury pearls in the soil forever. In 1987, four years after Lu Jiaxi's death, Chinese combinatorial mathematics experts reviewed and concluded that the paper announced the first solution to the "Kokman problem" . Of course, for historical reasons, this achievement is recognized in the mathematical community as belonging to R. Chadhari. Chaudhuri) and R. Wilson M． Wilson) as they were the first to publish this result in 1971. This is also beyond reproach. Here we quote a report by Professor Chen Jie of Inner Mongolia University to the Science and Technology Commission of the Inner Mongolia Autonomous Region: "In accordance with the request of the September 1984 Lu Jiaxi Academic Work Review Conference, I accepted the commission of the conference and continued to invite experts to review Comrade Lu Jiaxi's posthumous work on the Kirkman issue. We invited Professors Wu Lisheng and Zhu Lie of Soochow University and Professor Kang Qingde of Hebei Normal University (both experts in combination design) to do this work. In the past year, they have repeatedly reviewed and discussed, and believe that Comrade Lu Jiaxi's 1965 posthumous work "The Construction Method of Balancing Incomplete And Decomposable Equilibrium Incomplete Blocks" (there is definite evidence that this article was indeed written by Lu in 1965) has indeed solved the famous Kirkman problem at least 6 years before Chad Harley and Wilson. That is to say, on the Kirkman issue, Comrade Lu Jiaxi's work is also leading in the world. "This conclusion was only made 22 years later, giving China one less chance of leading the world for a landmark achievement in combinatorics.

He then continued to work hard and completed four more papers in just half a year[5-8] as a development of the previous paper.

In the summer of 1966, the "Cultural Revolution" began, and in the face of disaster, Lu Jiaxi was a little desperate. In a letter to a friend after the end of the Cultural Revolution, he wrote: "After reading the reply to the Acta Mathematica Sinica, this work (referring to the Korkman problem) I stopped the idea of submitting papers... Soon it was the Cultural Revolution, all stranded. "These things seem to sink in the depths of memory, sinking, sinking." From the beginning of 1966 to the fall of 1977, he did not submit a single paper for 11 years.

Good luck and late knots

After the "Cultural Revolution" began, Lu Jiaxi did not give up the study of combinatorial mathematics. Once, at a meeting criticizing the so-called "bourgeoisie", he hid in a corner of the unobtrusive venue and performed in Xiao Ben. At first he was vigilantly watching left and right, but soon entered the realm of self-forgetfulness. Towards the end of the battle, people finally discovered his behavior, which at the time was a matter of principle of "what class to stand on". Fortunately, his family origin saved him, and the radical rebels only wanted to pull off his "white flag" and return the son of a poor citizen to the "revolutionary ranks". At night he lay in bed, thinking about it, and almost all night he could not close his eyes. The next day, a conspicuous large-character poster appeared on the campus, and Lu Jiaxi, a typical representative of the "White Road," took the lead in setting up a "Haiyan Combat Team," appointed himself as the commander-in-chief, and declared war on the "earth, the rich, the anti, the bad, the right, and all the reactionaries" in fierce language. Since then, other rebel organizations have looked at him differently and stopped looking for trouble for him. As the days passed, people could no longer see Lu Jiaxi, nor did they find any "revolutionary action" in the "Haiyan Combat Team". Finally the truth came out, the so-called "Haiyan Combat Team" was a light rod commander. This is also the countermeasure he was forced out, so that he could hide in the single dormitory and quietly delve into the combination design. Because his family was from a "city poor", and he usually never offended anyone, this matter did not cause a big storm.

Time flies, and in the blink of an eye he is thirty or more. He is bent on the cause of scientific research, usually does not trim the edges, cotton clothes are too lazy to remove and wash, really can be said to forget the cold and summer waste sleep, "the belt gradually widened and finally no regrets". But he is a human being after all, and sometimes he thinks of his life's events. However, he usually speaks little, has little contact with people, has no relatives in Baotou, and although he has also introduced several enthusiastic colleagues to him, he is ultimately unsatisfactory and politely rejected by him.

"Love is an alias for understanding" (Tagore), Lu Jiaxi finally met Zhiyin. In the Spring Festival of 1972, through the mediation of his friend Liu Ziyu, he became acquainted with Zhang Shuqin, a doctor at Wolf Mountain Hospital who returned to Baotou to visit his relatives. He has always been not good at words, and he has more to talk about, talking about work, talking about science, and talking about plans for the future. After a period of correspondence, the two fell in love and married in the summer of the same year. At the age of 37, he finally has a warm home. Soon, Zhang was also transferred to the First Affiliated Hospital of Baotou Medical College. In March of the following year, he was transferred to Baotou No. 9 Middle School to teach (the two units were closer together). From then on, he began a period of relative stability in life and work.

Years of single life and heavy teaching and research have made him an authentic layman in housework, so that he has made a lot of jokes. But he was happy that he had the opportunity to pour out his scientific experience and twists and turns in scientific research, and to pour out the bitterness that had been suppressed in his heart for many years to his wife. Zhang Shuqin is a wise woman, who understands him and understands him, although she does not understand the "Kirkman girl problem" and cannot understand mathematical papers, she believes that her husband's work is meaningful. She took the initiative to take on most of the housework and create a quiet environment for her husband. As soon as she had the right opportunity, she publicized her husband's scientific research work and won the understanding and support of the school, colleagues, relatives and friends.

Zhang Shuqin was married to Lu Jiaxi after the divorce. Married with a two-year-old daughter Zhang Huizhong. Jia xi likes children, is willing to play with her, amused, the child soon became intimate with him, often asking him to hug, back. Until Lu's death, the child did not know that he was the stepfather. On February 7, 1976, they had a daughter, named Lu Deng. The birth of the younger daughter not only added new joy to their family, but also made Lu's personality gradually cheerful. He is no longer so taciturn and occasionally chats and jokes with his colleagues. As his daughter grows up, he has to squeeze out time to tease her, tell them stories, teach them to sing, draw, and play Rubik's Cubes. The wife said: "Jiaxi and her daughter together are like a changed person. "Old Lu sheng is not fond of asking for people; in order to teach Dengdeng a children's song, he also asked the music teacher to learn the song first. He is not financially wealthy, but he must buy his daughter a toy piano. A small bag of oranges was given to him at the end of the Wuhan Mathematics Conference, and he did not eat a single one along the way, and all of them were brought back to the children. Lu Deng has graduated from high school and continues his studies. Huizhong graduated from the University of Electricity and Power in 1989 and worked in the classroom of Baojiu Zhongdian, zhang Shuqin is still working at Baotou Medical College and has been promoted to associate professor.

Conquer the large set theorem in the "Steiner series"

Smash the "Gang of Four" and usher in the spring of science. Lu Jiaxi felt that the future was bright, so he returned to his old business. On September 4, 1977, he sent a revised version of the article "Equilibrium Incomplete Blocks of k=5, λ=1, v=141" to the Acta Mathematica Sinica. In March of the following year, with the help of his comrades, he borrowed a copy of Hall's "Combinatoric Theory" from the Loan Department of the Beijing Library, from which he learned that the "Kirkman Girl Problem" had not yet been generally understood. This is really good news for Lu Jiaxi, who has been immersed in the problem for more than 20 years and is confident that he has completely solved it. But he is the main physics teacher in Baotou Ninth Middle School, one of the first key middle schools in Inner Mongolia, and he has an excess of class hours every week. In 1978, he crossed the junior year of junior high school and the first year of high school, with 7 lesson plans, 14 classes per week, and 3 evening self-study. Where is the time for scientific research! He usually immersed himself in hard work, never picked and chose, and never made any demands on the leader. He only takes advantage of holidays and evenings to engage in scientific research. Every night at nearly 10 o'clock, he began "formal amateur work" and even stayed up all night. The next morning I went to the podium as usual. From May 6 to July 2, 1978, in less than two months, he wrote four papers on the "Kirkman Problem" in addition to his busy teaching.

In April 1979, he borrowed the Journal of Combinatorics, a world journal on combinatorial mathematics published in the United States in 1974 and 1975. It was unexpectedly discovered that the Kirkman problem and the generalization of the quad series had been solved abroad in 1971 and 1972. This fact hit him too hard. At that time, he wrote in a letter to Comrade Fang Yi, who came to Baotou City to inspect the work: "... These are seven to 10 years later than I am, and my manuscript is still unattainable. The original text has not been seen, and it cannot explain the similarities and differences in methods, but in any case, foreign countries are ahead in the publication time! ...... It also shows that my past work is meaningful. This is 18 years old, my first child, the spiritual child, she is 18 years old. But her fate is really not good, 18 years, in a person's life is not short, for modern science, it is a long period, is there no lesson here? I love science, no matter what the public opinion environment, no matter what the working conditions, I have never wavered, and I am worried about what will happen if there are new works! ”

The honor of climbing the world's mathematical peak was buried, lu Jiaxi was heartbroken, but instead of falling, he plucked up more courage to impact another peak of combinatorial mathematics, the "Steiner Series", which is his new work.

As early as 1853, the Swiss mathematician Steiner encountered a (v, 3, 1) block design when studying the double tangent of quadratic curves, which is the so-called Steiner ternary system. The study of block design plays an important role in the fields of digital communication theory, rapid transformation, and finite geometry. The Steiner ternary system has fundamental significance in the theory of block design. The set composed of the ternary system of steiner that reaches v-2 and satisfies a certain charging condition is called a large set. The so-called "large set problem" is the existence problem of large sets; the so-called "big set theorem" is to prove the sufficient conditions for its existence. For more than 130 years, many mathematicians have been attracted to this problem and racked their brains and labored for it, but the results are still fragmentary. The May 1981 issue of the Journal of Combinatoric Theory said: "This problem is still far from being completely solved. ”

After the Third Plenary Session of the Eleventh Central Committee, the spring breeze of reform and opening up blew to Saiwai Steel City, and Lu Jiaxi began the most tense stage of his life. He teaches during the day and conducts scientific research at night. Opening his December 1979 diary, 21 of the 31 days recorded: "night work", "night make-up class", "night writing papers", "night thinking Bays conjecture" and "night playing English manuscripts". Every Spring Festival, he always let his wife take her children to his mother-in-law's house for the New Year, while he wandered in the mathematical kingdom in the streets and alleys all night under the sound of firecrackers.

Although the wife supports her husband's scientific research, she is also worried about his health. He was advised to go for a walk every day after dinner and stay up late not more than 12 o'clock. But he studied mathematical problems, and once the idea was developed, it was not easy to end up casually. Therefore, I often have to violate my wife's rules and work hard. From February 24, 1979 to July 20, 1979, Lu Jiaxi submitted three papers to the Acta Mathematica Sinica, one of which, "Theory of the Existence of Decomposable Equilibrium Incomplete Block Design", was published in the 4th issue of the Acta Mathematica Sinica in 1984. This was his first and final paper published in a national journal. He had been dead for more than 9 months at the time of publication.

In October 1979, Lu Jiaxi's scientific research made a major breakthrough. In a letter to the Journal of Combinatoric Theory, he predicted that he had basically solved the "great collection of disjoint Steiner ternary systems". The journal's reply said: "If true, it would be an important result. He added: "Many experts in the world are studying this problem, but it is still far from being completely solved. "What they didn't expect was that this problem would be basically solved by a Chinese middle school physics teacher.

Since September 18, 1981, the Journal of Combinatorialism has successively received a series of articles by Lu Jiaxi entitled "On the Great Collection of the Disjoint Steiner Ternary System" [18, 19]. Western combinatorialists were amazed, with Mendelson, a renowned Canadian mathematician and professor at the University of Toronto, saying: "This is one of the major achievements in combinatorial design for more than two decades. "The President of the University of Toronto, Canada, D. S. W． Strangway) wrote to the president of Baotou Ninth High School: "Dear sir: Professor Mendelson said: Lu Jiaxi in Baojiu is a well-known Mathematician in the West who works on combinatorial theory, and said that it is necessary to agree to transfer him to a university post. He wants me to tell you that such a transfer will play an important role in the development of Mathematics in China, and he hopes that the will expressed will be approved. Your sincere D. W． Strangway． Retrieved 30 September 1983. On September 15, 1984, the Lu Jiaxi Academic Work Review Committee, composed of Chinese combinatorial mathematics experts, made the following evaluation:

Lu Jiaxi solves the "disjoint Steiner ternary system of the great set"

“...... Comrade Lu Jiaxi originally introduced auxiliary designs such as AD, AD*, AD**, LD and LD* and related large sets LAD1, LAD2 and LAD3, creatively used the results of predecessors, cleverly designed a series of recursive structures, and rigorously proved that the large sets of the disjoint v-order Steiner ternary system, in addition to the six values, existed for all v≡ 1 or 3 (mod 6), v>7, thus announcing the overall solution to this problem (regarding the exception value, he has an abdominal draft, However, he died in the process of writing, leaving only an outline and some results).) As we all know, in 1960, Bose et al. proved that when t > 1, the Euler conjecture about the 4t+2 order orthogonal Latin square does not hold; in 1961, Hanani gave and proved that the (b, v, r, k, λ) design of k = 3 and 4 was an adequate condition, which are two world-famous achievements in block design theory, and Lu Jiaxi's achievements on large sets can be compared with the above two major achievements, and will be recorded in the history of combinatorial mathematics with them. ”

Looking at the proof of ancient and modern mathematical theorems, depending on the difference in objects, there are both grand and huge works of grand view, and there is no shortage of short and concise works, and with the arrogance of building from a lofty height, according to the original 55 theorems and lemmas, with 100 printed pages and 100,000 words to prove a theorem, it is really rare, which can be called a large-scale project. Lu Jiaxi's proof is structural, which is in line with the ancestral tradition of the ancient Chinese arithmetic tradition, which is characteristic and glorious of Oriental mathematics.

Lu Jiaxi's last years

In October 1983, Lu Jiaxi participated in the 4th Annual Meeting of the Chinese Mathematical Society held in Wuhan as a specially invited middle school teacher. The conference fully affirmed his achievements and commended his spirit of struggle to climb the peak of science. He was very excited to report his work at the meeting and told everyone that six of the exception values had been solved and that they were taking the time to sort them out.

He succeeded, but he did not revel in the joy of victory, and a new plan was conceived in his heart. He's going to go to new heights. I remember how happy he was when he received a sample of his first three papers from the Journal of Combinatorics from the United States. Shortly thereafter he would give the author a thesis as a souvenir. The author said to him: "I can't understand your mathematical paper, and there are many people who want your paper, so you should give it to them." But can you give me a general idea of the origin, status, and value of this mathematical problem? He smiled and thought for a moment before saying, "Your problem is too difficult, and I can't say it clearly, but the mathematical problems I study can be said to be both old and young." Research in this area is in the ascendant and will have a climax. The author said: "Lao Lu, since the mathematical problem you are studying has been basically solved, you should take a good rest and pay attention to your body. He replied, "I'm almost 50 years old, I don't have much time left, and I still have to hurry up and do it." ”

After the Wuhan meeting, in order to return to school, Lu Jiaxi only waited for a few short hours when he transferred trains in Beijing, and then returned to Baotou at about 6 p.m. on October 30. As soon as he entered the house, he excitedly said to his wife: "This time I can see the world. After dinner, I chatted with my family for a while and said, "Too tired, too tired, rest early." "The accumulated fatigue and long-term latent illness have far exceeded the limits of his physiology. At about 1:00 a.m. that night, he had a heart attack and died suddenly. Not a last word was left before his deathbed. He is only 48 years old.

Lu Jiaxi is an ordinary person who has been working silently before his death. The persistent quest for his career made him obsessed. Once upon a time, people regarded his act of lying in a single dormitory, lying on the bed and counting the grids on the ceiling, as "mental illness"; after sending his children to kindergarten, he came back to the school's joint apparatus in broad daylight and had several stitches on his forehead as a laughing stock. His formal profession is a middle school physics teacher, the basic knowledge of physics is solid and systematic, mathematical knowledge is proficient and comfortable, and solving physics problems is his favorite strength. The more senior the student, the more capable the student is, the more he loves to listen to his lessons. If the teaching and research group has any theoretical problems that are not accurate, please consult him. I remember once talking about "rectification and filtering", when preparing for the lesson, the oscilloscope interference was large, and the normal waveform could not be displayed. Several physics teachers adjusted for a long time, or the tune is not good, and can not find anything wrong. Please ask Lao Lu to help, he adjusted for a while or not. He said, "I'll go back tonight and look up the information. The next morning he said: The output is connected in parallel with a high-value resistor and it will probably be stable. I tried it and it worked.

Lu Jiaxi is engaged in scientific research in his spare time, and the people in his physics teaching and research group have heard about it slowly, and slowly, he has received admiration and support from teachers. In 1980, Baotou City established the Physics Association to appoint a director from Baojiu, and everyone agreed to recommend him. He attended the annual meeting of the Inner Mongolia Mathematical Society, and the whole group of comrades helped him bind it. The English version of his thesis, two foreign language teachers helped him revise the text, print. Unfortunately, when he received everyone's understanding and support, and his career had just entered the golden age, he died prematurely.

After Lu Jiaxi's death, the Baotou Municipal Party Committee and the Baotou Municipal Government called on the city's scientific and technological workers to learn from him and issued a special science award of 2,000 yuan. On the first anniversary of Jiaxi's death, the party committee and government of the Inner Mongolia Autonomous Region held a "meeting to learn from comrade Lu Jiaxi, an outstanding intellectual" in Baotou. He called on the people of all ethnic groups in the region to learn from him and dedicate themselves to the "four modernizations". He was posthumously awarded the title of "Special Teacher" and awarded a special prize of five thousand yuan.

Lu Jiaxi's achievements and unfortunate death shook society. Wu Wenjun, Cheng Minde, Duan Xuefu, Xu Lizhi, Chen Jie, Zhang Dianzhou in the Chinese mathematical circles, and Zhong Ji, Zhu Lie, Wei Wandi, Kang Qingde, Wu Lisheng, Chen Ziqi, Gu Tongxin, and Luo Jianjin in the field of combinatorial mathematics have all attached great importance to them. After learning the true situation of Lu Jiaxi, Mr. Wu Wenjun wrote in a letter on November 3, 1984: He was "deeply touched by Lu's life experience, academic achievements and qualities. Although recently the great contribution of society to land has finally been recognized and confirmed, the loss has become irreparable. It is worth pondering that this matter has to be brought to the attention of foreign scholars (they are real international friends), otherwise Lu may still be poor and sick and buried. How to avoid the recurrence of such incidents should be deeply considered".