Some graduate students are not likely to find their own topics to do research, but "wait for the rice to go to the pot". Ding Jiu, a professor in the Department of Mathematics at the University of Southern Mississippi, recalled his special experience in studying, selecting and writing papers.
Written by | Ding Jiu (Professor, Department of Mathematics, University of Southern Mississippi, USA)
Before the outbreak of the pandemic, when I returned to China for academic visits and exchanges with professors, they mentioned that some graduate students were not likely to find their own research topics, but waited for their supervisors to assign a research topic like they did in class exams and other examination papers. "Delicious food" is not as comfortable as a buffet. We all know that the free-range grass chickens in the farmhouse are delicious and juicy, and they are far from being comparable to the broilers raised in collective captivity. Guy has a monotonous recipe because of the broiler rice, while the grass chicken forages everywhere and is rich in nutrients. The market price of grass chickens is therefore much more expensive than that of broilers. When I was a child, I lived in my parents' dormitory, and before the rain I loved to use a big broom to catch dwarf dragonflies and feed the chickens because they laid eggs for us. Just like when studying, your vision should not be limited to the pages of a textbook, and when choosing a dissertation research topic, it is best to pay attention everywhere and take the initiative. As far as I am concerned, although the choice of the topic for my doctoral dissertation was chosen by chance, and I may not have thought of it in advance by my supervisor, Professor Li Tianyan (1945-2020), it was the result of "learning everywhere with attention". In fact, the first research article I wrote after I went to the United States benefited from the pioneering work of my old classmate Dr. Wei Musheng at NTU, and had nothing to do with the fields in which my supervisor was involved. Although it didn't make it into my doctoral dissertation, it was born by the same circumstances as my later dissertation.
For the sake of accuracy, some mathematical concepts will be introduced in this article. I'll use elementary or geometric language, as well as metaphorical analogies, to describe concepts, even if the reader doesn't fully understand the mathematical implications. Impatient readers need not be intimidated to keep reading, hoping that the drama and inspiration of the story will ignite a greater flame of reading.
"Find rice to cook"
My first research during my Ph.D. was on perturbation theory of least squares solutions for deficit matrices. Carl Friedrich Gauss (1777-1855), one of the patriarchs of least squares, had the idea of the method at the age of eighteen. As director of the Observatory at the University of Göttingen, he invented the method of least squares while studying astronomical observations. This is geometrically related to the curve fitting of a given test data point on a flat surface. For example, suppose there are ten points on the Cartesian coordinate plane, which can be seen as ten sets of data for a certain test result. They generally don't happen to line up in a straight line. But can we draw a straight line so that it minimizes the sum of the squares of the "perpendicular distances" of these points? This is a simple example of a "least squares problem". The answer is yes, and the solution is "least squares". The least-squares problem is determined by a matrix, which is a set of numbers arranged in several rows and columns. For "full-rank" matrices (i.e., the "rank" of the matrix is equal to the lesser of the number of rows and columns), the theory and algorithm of least squares are well established and form part of numerical linear algebra in the subdiscipline of computational mathematics.
My college classmate Wei Musheng, who ranked first in mathematics in the province in the seventh-level Jiangsu college entrance examination - full marks for the main topic and additional questions, went to study at Brown University in the United States at public expense after graduating from the bachelor's degree, and obtained a doctorate degree in 1986. His doctoral dissertation was on scattered wave calculations, which required consideration of the least squares problem. But at this point, the matrix is no longer full rank, but "deficit rank", that is, the rank of the matrix is less than the number of rows and columns of the matrix. He could not find a ready-made perturbation theory of the deficit problem in the literature. At an academic conference, Wei Musheng met Professor Gene Howard Golub (1932-2007), a great figure in numerical algebra, a dual academician of the American Academy of Sciences and Engineering, and a professor of computer science at Stanford University, and asked him for advice. The answer of the other party surprised him considerably: no one has seriously studied such a question yet. So Wei Musheng decided to lay the first pile in this new field by himself. In 1989, his first paper on the theory of least squares perturbation of deficit-rank matrices was published in the journal Linear Algebra and Its Applications.
In the 1986-87 academic year, he was a postdoctoral fellow at the Institute of Mathematics and Applications at the University of Minnesota. In the fall of 1987, Wei Musheng came to the Department of Mathematics at Michigan State University, where I studied for his Ph.D., to continue his postdoctoral research. Professor Li Tianyan selected him out of six or seven applicants because Professor Peter Lax (1926-), a great mathematician at the Courant Institute of Mathematical Sciences, had written a strong letter of recommendation. The person who can make Lax write a letter is certainly not an idle person. Indeed, Wei Musheng won this honor because in his doctoral dissertation, he overturned a point of view in a monograph on the theory of Lax scattering waves. Throughout the school year, our two old classmates often drove to go shopping with their families and spent many pleasant times together. In that autumn school season, I read a few articles written by Wei Musheng, and I found them very interesting.
Dr. Wei Musheng's pioneering work is essentially to demonstrate the "upper semi-continuity" of the general least squares solution by estimating the upper error bound of the perturbation solution of the deficit-rank least squares problem. Many phenomena in nature are continuous, such as the continuous flow of water. "Continuity of solution" probably means that when the data of the solved problem changes slightly, the solution does not change much. In order to be able to apply the famous "singular value decomposition theorem" in matrix theory, he had to use a matrix norm named after the German mathematician Ferdinand Georg Frobenius (1849-1917) a hundred years earlier. This norm is to arrange all the elements of the m-row and n-column matrices into a vector with mn components, and then calculate the Euclidean norm of the vector (i.e., the sum of the squares of all components, and then open the square root). After reading the full text, a strong feeling quickly came over me: the conclusion of the article is naturally beautiful, and the mathematical analysis is also incisive, but the use of this norm is not as natural as the vector Euclidean norm used in the definition of the least squares problem itself. So I took the initiative, concentrated on it, and soon had a clue, using only the Euclidean norm, to obtain a more concise perturbation world.
Because this is the first article I have written since I came to the United States, I was a little excited when I finished it. My master's thesis was never submitted for publication, on the one hand, because my wife was pregnant at the time, of course, I had to do my duty, and I was too busy studying abroad to organize it, and on the other hand, I had long since lost my attention to that work, and after Guy came to the United States, he found that the international research on simple fixed point algorithms based on triangulation had fallen silent, and was not as prosperous as it was in the 70s and early 80s. However, the modern homotopy algorithm based on the idea of differential topology has always been vigorous. The doctoral dissertations of several of my brothers and sisters are closely related to this method. Later, I also applied the idea of the Tonglun extension method to the study of optimization.
In addition to the excitement, I sent the first draft of the article to my supervisor Li Tianyan, who was then a chair professor at the Institute of Mathematical Analysis at Kyoto University in Japan, and asked him to give advice. Professor Li Tianyan quickly replied, giving specific opinions on the main theorems of my article in a three-page long letter, and gave enlightening comments on the methodology of reading and research. He usually doesn't praise students in person, but this time he encouraged me enthusiastically, because in the matter of learning, I did not "wait for the rice to go to the pot", but "find the rice to go to the pot". According to him, this is a graduate student's "obligation".
Teachers preach
As for how doctoral students do research, Professor Li Tianyan's own study experience is the best example. His three major academic contributions before the age of 30 were: the eight-page essay "Cycle Three Means Chaos", which gave the first precise definition of the concept of "chaos" in mathematics, the first computational construction of Brouwer's fixed point, which was the pioneering work of modern Tonglen extension, and the first historical proof of the Ullam conjecture in computational traversal theory. The most famous of these is his collaborative research with his doctoral dissertation supervisor, James Yorke (1941-), which has been cited more than 5,900 times. This is among the highest in the group of mathematical papers that are generally much less cited than in the fields of experimental science and engineering. The author of the second paper added Bruce Kellogg (1930-2012) in addition to York. The third project, which he completed alone, provided the inspiration for my doctoral dissertation.
Let's first review how he was "lucky" to write the world's first article on the calculation of Brouwer's fixed point using the modern Tonglen extension method. In the simplest one-dimensional case, the meso-value theorem of elementary calculus, the geometric property of this great theorem of topology, named after the Dutch mathematician, is well understood: any continuous curve connecting points on both sides of a straight line must intersect the straight line. In the two-dimensional case of Brouwer's fixed point theorem, any continuous self-mapping (i.e., the value range contained in the defined domain) on a closed disk must have a fixed point, i.e., that point is reflected to itself. Li Tianyan graduated from Tsinghua University in Hsinchu, Taiwan in 1968, and after serving as a soldier for a year, he went to the University of Maryland in the United States to study for a Ph.D. in mathematics under the supervision of Professor York. In 1973, a year before he graduated, he took Professor Kellogg's course, Numerical Solutions of Nonlinear Equations. In the lecture, the professor described the new proof of Brouwer's fixed point theorem published ten years ago by Professor Morris Hirsch (1933-) of the Department of Mathematics at the University of California, Berkeley.
The idea of this concise counterargument is that assuming that a fixed point does not exist leads to a contradiction with a theorem of topology. It follows that there is no smooth mapping that mirrors the closed disk to the periphery of its circle, so that all the points on the circumference of the circle remain motionless. These intriguing and profound theorems in topology may explain why there is a spiral socket on the top of the human head that does not grow hair. When Li Tianyan heard such a novel proof, he suddenly had a plan: he could use this idea to calculate the fixed point of the theorem to ensure the existence. Because the closed disk is a two-dimensional region, and the circumference is only a one-dimensional curve, the definition domain is one dimension more than the value range for the mapping that Hirsch considers to mirror the disk to the circumference, so there is an "inverse" curve, which starts at one point on the circumference and ends at the originally mapped set of fixed points. As long as you can follow this "homotopy curve" numerically, the fixed point can be calculated. Active and independent thinking has led to such a wonderful new algorithm! Creative thinking is a miracle unimaginable to those who rely on rote memorization of definitions, theorems, and proofs. But for explorers who like to go back to the roots and find primitive ideas, this is the most natural thing to do.
When Li Tianyan told York about his idea, the latter fully supported him, even though he had other research projects in his hands, and his far-sighted mentor knew the value of the subject. After two months of programming and calculation, Li Tianyan's algorithm idea was finally realized - a thin page of printing paper recorded the numerical results of the first modern homotopy algorithm in history. As soon as the preparatory committee for the Conference on Fixed Point Algorithms and Their Applications at Clemson University heard that they had constructed a new homotopy fixed point algorithm using differential topology ideas, rather than following the path pioneered by Yale economics professor Herbert Scarf (1930-2015) in 1967 for a simple fixed point algorithm based on simple sectioning and combinatorial techniques, they were invited to present their papers. Later, in the preface to the conference proceedings, Scarfe praised the new ideas for Kellogg-Lee-York's article. Since then, the modern Tonglen extension method has entered the big stage of computational mathematics.
"With a bull's energy"
As mentioned earlier, three of the most notable pieces of work in Professor Li's academic career were completed during his PhD studies. The third paper on the "Ulam conjecture" was written by him independently, and was published in the Journal of Approximation Theory in 1976. In 1973, York and his collaborator, Andrzej Lasota (1932-2006), a member of the Polish Academy of Sciences, published a paper in the journal Transactions of the American Mathematical Society, in which they proved an existential theorem for an absolutely continuous invariant measure. It asserts that there is an "invariant density function" for a class of slice-by-slice elongated self-mappings defined over intervals. The density function is a mathematical object that is often used in probability theory, it is a function with a non-negative value and an overall integral of 1. That is, the area of the "curved rectangle" below its image and above the interval is equal to 1. After the existence of the invariant density function was guaranteed, Li Tianyan began to think about how to calculate it. Or, in other words, how to approximate it numerically and effectively. He proposed an approximation method using a slic-by-slice constant function and demonstrated the convergence of the algorithm by mapping the kind of intervals considered by Losuda and York. As the name suggests, a slice constant function takes a constant value on those sub-intervals that are partitioned into defined domain intervals.
But Li Tianyan was completely unaware that Stanislaw Ulam (1909-1984), the father of the American hydrogen bomb and a prominent mathematician of Polish origin, had proposed this method in his 1960 book, A Collection of Mathematical Problems, which was only 150 pages long, to calculate the invariant density function. After the article was written, Li Tianyan heard that this was the Ulam method that existed more than ten years ago. And Ulam guesses in the book that as long as the invariant density function exists, the algorithm converges. The "Ulam conjecture" gave birth to the discipline of "computational ergodic theory", which has important applications in physics and engineering. The "historical coincidence" between Li Tianyan's article and the Ulam method also led to a change in the title of the article, adding "a solution to the Ulam conjecture". This landmark work in the field of computational ergodic theory culminated in "The finite approximation of the Frobenius-Peron operator: A solution to the Ullam conjecture".
Many years later, Professor Li Tianyan recalled to me the process of publishing his masterpiece and said with great emotion: "If I had known in advance that the convergence of this algorithm had not even been proved by a mathematician at the level of von Neumann, I might not have dared to gnaw this bone." However, when he was young, Li Tianyan was a warrior who was "a newborn calf is not afraid of tigers". According to his own words, he "relied on a bull's spirit, persevered in everything to the end, and never gave up easily." He believes that the problems that the big people can't solve don't mean that the little people can't solve them, and the way the big people think about the problem is not necessarily the only way to solve the problem. On the road of learning, as long as you have an independent spirit and free thought, as long as you spend one minute more thinking than others, you will be able to solve seemingly difficult problems.
Before the early summer of 1987, after passing the exams in two foreign languages (English and Chinese are not foreign languages), I continued to take courses while actively keeping up with a new field, linear programming interior point algorithms. It is related to the optimization direction of my master's degree at NTU, which began with a seminal paper published in 1984 by Narendra Karmarkar (1956-), an Indian student. At that time, this field had begun to heat up in the international optimization community, and researchers were rushing to follow up. Many even predicted that Camacca would win the Nobel Prize in Economics by the end of the last century, just as the Soviet mathematician Leonid Kantorovich (1912-1986), who first proposed an efficient method for calculating linear programming. However, this prediction did not come true. Considering that my old profession is mathematical programming, Professor Li suggested that I keep up with the rapid development of the interior point algorithm. Some of his scholarly friends, such as Professor Masakazo Kojima (1944-), a well-known scholar of optimization theory in Japan, often sent preprints of articles on this subject. Several Chinese scholars, such as Ye Yinyu, a Ph.D. in operations research at Stanford University, have also begun to emerge. I tried to learn more about these latest research results, slowly approached the academic frontier, and completed several articles on the interior point algorithm for linear complementation problems. The first article was published in the inaugural issue of the SIAM Journal on Optimization in 1991 in the new issue of the SIAM Journal on Optimization. I had planned to compile these into my doctoral dissertation, but the outcome was unexpected.
West Coast Tours
In March 1989, my three-year-old daughter followed her grandmother to the United States. It was the first time we met father and daughter, even though she met me at the Detroit airport and said in pure Yangzhou dialect, "I saw my dad in photos." In early June of that year, just after the spring semester ended, the current academic year came to an end, and Professor Li's three-quarter course "Ergodic Theory on [0, 1]" also came to a successful conclusion. Although his main interest at that time was no longer chaos and ergodic theory, but in the homotopy solution of matrix eigenvalues and systems of multivariate polynomial equations, we disciples increased our knowledge and broadened our horizons, and gained a clearer understanding of his research until the mid-eighties. In order to be a good student, you need to understand not only what the teacher is doing, but also what the teacher has done in the past, otherwise you can be called a lame disciple. It's the same as how the history of science is treated. The great all-round mathematician Henri Poincaré (1854-1912) once admonished us: "If we want to foresee the future of mathematics, the appropriate way is to study the history and present of this science." This sentence was placed at the top of the preface by Morris Kline (1908-1992), author of the famous work on the history of mathematics, Ancient and Modern Mathematical Thought. It is equally important to understand history as it is to recognize the present, because history is a mirror. Hermann Weyl (1885-1955), one of the best disciples of the German mathematician David Hilbert (1962-1943), once said that he "liked to teach the history of mathematics", and he had a good point.
While I was on my way to Northern California for a meeting, my family planned to visit the West Coast of the American continent in June, which was my first long-distance trip since coming to the United States.
During the month we traveled from Michigan to San Francisco, our family left footprints in many places along the way. I reunited with many old classmates and acquaintances of NTU. At the first stop of the trip, the University of Illinois at Urbana-Champaign, I met Hu Zhixin, a college classmate, and chatted all night, and I also reunited with Li Qiaoying, a seventh- and eighth-grade student in the Department of Chemistry of NTU who was on the same plane as me to study for a doctorate. Then my family went to Kansas City, where I was warmly welcomed by the family of my Korean brother, Lee Hong-koo, who teaches at the University of Missouri-Kansas. After arriving in Salt Lake City, the stronghold of the Mormon Church, Yin Guangyan, a Ph.D. student at the University of Utah, drove us to see the scenery of Salt Lake. Now he and the other two "champions of the Jiangsu college entrance examination" in my former classmates have begun to enjoy the retirement scenery of "the sunset is infinitely good".
When I arrived in the San Francisco Bay Area, I met Yanning Zhang, who has received her Ph.D. in statistics from Stanford University. Born in Beijing, with excellent university grades and a love for long-distance running, he was admitted to the Computing Center of the Chinese Academy of Sciences as a graduate student and stayed abroad for further study. The first letter I received from my old classmates in the United States after I came to the United States to study was his enthusiastic "welcome postcard", and in the second letter, he praised me for naming my newborn daughter "Yi Zhi": "You are worthy of your literary skills." Later, Zhang Yanning, who had a successful career, did not cool down his enthusiasm for long-distance running, and participated in several marathons, including the famous Boston International Marathon.
I also met again with Dai Jiangang, a mathematics genius in the seventh and eighth grades of NTU. He is currently working on his Ph.D. dissertation in the Department of Mathematics at Stanford University (he is currently a Chair Professor in the School of Operations Research and Information Engineering at Cornell University and Dean of the School of Data Science at Hong Kong Chinese University, Shenzhen). In early March, he went to San Francisco International Airport to pick me up and take my mother and daughter to the gate to Detroit. We walked around the beautiful Stanford campus and toured this world-renowned university. My mother took a photo in front of the famous cathedral in the middle of the campus. It was established by Mrs. Stanford in memory of her husband of the railroad king, with whom she co-founded the school in 1885. A quarter of a century later, before Thanksgiving in 2013, I went to visit my daughter, who was already working there. Under the cloudless blue sky, the two of us took a group photo in front of this beautiful church, allowing my 85-year-old mother to witness the magnificent Stanford architecture again.
Sparkle in the manuscript
Before the trip, Professor Li Tianyan asked me if I was interested in helping him complete the first draft of a Chinese book based on the ready-made lecture notes he had just finished the course. An academic foundation in Taiwan wants him to publish the book. Last year, he met Professor Mo Zongjian (1940-) of the Department of Mathematics at Purdue University in the United States, and the two discussed the matter, which was one of his original intentions for opening this course. Professor Li promised to allocate one of the summer research grants given to him by the National Science Foundation so that I could concentrate on writing the book instead of being distracted from teaching. Of course I do, this is not only a great opportunity to consolidate what I have learned, but also a training ground for my future academic writing.
When I returned to Michigan, I quickly got into the groove and began drafting the manuscript that my mentor had given me. The basic framework of the book is already in shape, with only the addition of the basic parts of the preparatory knowledge and the unification of written expression and linguistic symbols. I worked non-stop at my desk for two months. This is also the process of reorganizing my knowledge and practicing academic writing, which provides me with an excellent opportunity to practice writing books on my own in the future. What's more, at some point in the chapter on the Ullam Method for Calculation of Absolutely Continuous Invariant Measures, I had a spark for a new study.
Professor Li's planned Chinese book focuses on a class of positive operators widely used in ergodic theory, the Frobenius-Peron operator, which mirrors non-negative functions into linear operators of non-negative functions and keeps the integral unchanged, the former property is the definition of "positive operator". The name of the operator is borrowed from the names of two German mathematicians, which is actually not related to them. It is only because this infinite-dimensional operator inherited some good properties of non-negative matrices, and because Oskar Perron (1880-1975) in 1907 and then Frogbenius in 1912 established a general theory of non-negative matrices, that Ullam borrowed their name and named the operator in the Mathematical Problem Collection. This phenomenon is not uncommon in the history of mathematics, for example, Newton's method of solving nonlinear equations was not formally proposed by Newton, he only used it to approximate the root of a polynomial equation. The systematic study of Newton's theory of convergence is attributed to the twentieth-century Russian mathematician Kontonovich. Lopida's law, which finds the indefinite limit in calculus, is the result of "deceiving the world and stealing fame". This law, which Guillaume de l'Hôpital (1661-1704) put in his book of 1696, was actually discovered by the Swiss mathematician Johann Bernoulli (1667-1748). The invariant density function is the fixed point of the Frobenius-Perón operator. The first few chapters of Professor Li's manuscript deal with the existence theorems and properties of the fixed points of operators, and the last chapter deals with their calculations, entitled "Finite Approximation of the Frobennius-Peron Operator", which covers the Ullam method and Li Tianyan's conjecture on the Ullam conjecture and the beautiful proof of the convergence of the Losuda-York interval mapping family.
When I was about to finish this chapter and the whole manuscript was finished, a question popped up in my head. From the point of view of computational mathematics, it is the simplest and crudest way to approximate a general function with a slic-by-slice constant function. Common sense tells us that if you use a horizontal line to approximate a catenary line, the accuracy is much lower than that of a line segment connecting two points on a curve. So I was so curious that I immediately picked up a pen and paper, drew a picture and calculated. For more than 30 years, I have been working on computational ergodic theory, and this journey of thousands of miles began here. It has nothing to do with my previous research on the interior point algorithm, and belongs to two worlds separated by 108,000 miles. Since I have mastered the basic knowledge of the traversal theory of pure mathematics in the United States, and I have already laid a good foundation in the computational mathematics major of NTU, my thinking is relatively clear and the progress is quite smooth. I noticed that the Ulam method is not only a structure-preserving algorithm for correctness and integral, but also belongs to the category of traditional projection algorithms. So I promoted it in both directions. Soon, I was constructing two new classes of algorithms based on either slice linear or slice quadratic polynomials. The first type relies on the principle of the Carryokin projection, and the other type preserves the structure because it uses a finite-dimensional Markov operator, which I named the Markov finite approximation method. The Markov operator, named after the Russian mathematician, has a wider range than the Frobenius-Perón operator and is defined as a positive operator that keeps the integrals of non-negative functions unchanged. For the Ulam method to converge the Losuda-York class interval mapping, I have proved the convergence of the new algorithm. In order to prove that the higher-order numerical methods converge faster, I used the Sun-Workstation computer in the department (referring to the workstation provided by the computer company Sun Microsystems—editor's note) to input my own Fortran program and perform computational comparisons. Numerical experiments show that they converge much faster than the Ulam method, and the gap is as big as Lu Bu's red rabbit horse racing against Lu Bu himself. Subsequently, two Chinese professors theoretically studied the convergence rate of the piecewise linear Markov finite approximation method, and together with the follow-up article published by Professor Li and I in 1998, the convergence rate theory and error estimation of such algorithms were finally established.
At the end of August 1989, I completed the first draft of Professor Li Tianyan's Chinese monograph. As a by-product, two research articles were also taken out. Even to my surprise, I didn't even type a draft of this book, and each chapter and section was basically based on the overview of Professor Li's lecture notes, brewing it in my stomach first, and then writing it down in one go, which greatly saved writing time. Within two months, I not only drafted a Chinese book, but also did some meaningful research. When I handed the manuscript to my supervisor and presented the first draft of my dissertation, he was surprised at first, but after reading it, he felt satisfied. Since then, I have never asked about the fate of that manuscript. It is a pity that Professor Li Tianyan has been busy with the grand research project on the numerical solution of polynomial equations, and has basically left the field of chaotic dynamical systems and ergodic theory, which made him famous in his early years, so he has never had time to revise and complete this book. On the contrary, my interest in learning traversal theory from the tutor course, coupled with this unique experience of writing and research, led me to leave the interior point algorithm and devote myself to computational traversal theory, which I have enjoyed for many years, and cooperated with Dr. Zhou Aihui of the Institute of Computational Mathematics and Scientific and Engineering Computing of the Chinese Academy of Sciences to publish the graduate Chinese textbook "Statistical Properties of Deterministic Systems" through Tsinghua University Press in 2006. At the end of 2008, the English counterpart was published by the publisher in conjunction with Springer Verlag in Germany.
Graduation and work
One morning in October 1989, Professor Li Tianyan came to my teaching assistant office and said to me kindly, "You can consider graduating next year and compile these two latest articles into your doctoral dissertation." "I was grateful and agreed to his arrangement. Except for me who came to the United States in January 1986, the rest of our doctoral students recruited directly from the mainland were all from the 77th grade of the famous universities in China (the "77th grade" is the first college student after the resumption of the college entrance examination - editor's note), graduated from Jilin University, Wuhan University, Xiamen University, etc., plus a doctoral student who defected to him from Northwest University, a famous private university in the United States, and turned from a visiting scholar, all entered the university in August 1986. Naturally, I could graduate earlier than them. Last year, my sister from the 7th grade of Beijing Normal University had already graduated with a Ph.D. and found a university faculty position, and I became an assistant professor in the Department of Mathematics at Clemson University, where Professor Lee's Bloomer fixed-point computing thesis began to become famous. At that time, the economy of the United States was still relatively strong, and there were many new positions for university teaching.
The difficulty of finding a job is linearly related to the economic situation and even the social environment. In 1957, the Soviet Union's satellite went into the sky, which frightened the United States, thinking that its scientific and technological level was lagging behind the other side. As soon as the top leaders gave the order, American universities immediately began to swell, resulting in a lot of new doctors in the sixties, and everyone could get a good job teaching at the university. As a result, some of them, due to congenital deficiencies or acquired slackness, have been defeated in a highly competitive academic environment and have been poorly paid, especially in research universities. There are also such people among the professors at Michigan State University, and the proportion among the old professors is not too low. I remember one time, my tutor pointed to the office of a professor of low academic standing and joked to his disciples: When I was in high school, he was a professor, but his salary is now almost half of mine. When Professor Li received his Ph.D. in 1974, the good days of PhDs in the United States were over, and many people could not find jobs. He was fortunate enough to get a university teaching job, while many Taiwanese PhDs like him had to go home. However, many people later made a lot of money due to Taiwan's economic take-off. He also told us that when his first Ph.D. student, Zhu Tianzhao from Taiwan, got his degree in 1982, the situation was reversed again, and there were so many opportunities for campus interviews. In the end, Dr. Zhu chose North Carolina State University. His research performance was so outstanding that he was promoted to full professor six years later.
However, what I didn't expect was that I graduated in 1990, just in time for the most severe new round of the American university faculty market! Fortunately, I found a full-time assistant professor position, but that was for another time.
Written on Sunday, March 24, 2024
Summer Hills in Hattiesburg, USA
Note: This article is based on Chapter 6 of "Doctoral Dissertation" in Experiencing American Education: Thirty Years of Experience and Reflections, published by the Commercial Press in 2016.
Acknowledgments: I would like to thank Dr. Chu Wai-kin for proposing two changes that increase the accuracy of the narrative.
This article is supported by the Science China Star Program
Producer: Science Popularization Department of China Association for Science and Technology
Producer: China Science and Technology Press Co., Ltd., Beijing Zhongke Xinghe Culture Media Co., Ltd
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