This article is transferred from Lin Kun's official account of talking about mathematics, and is organized by Lin Kun in Zhihu. It does not represent the views of this number, welcome to discuss in the comment area.
About author:Yuan Xinyi, a professor at the Beijing International Center for Mathematical Research at Peking University, is a distinguished mathematician known for his groundbreaking work in the fields of number theory and arithmetic geometry. The following is a detailed introduction to Yuan Xinyi:
Yuan Xinyi, born in 1981, is one of the members of the "Golden Generation" of mathematics at Peking University. He received his B.S. degree from the School of Mathematical Sciences of Peking University in 2003 and his Ph.D. in Mathematics from Columbia University in 2008.
Yuan's main research interests include Arakelov geometry, algebraic dynamical systems, automorphic forms, Shimura clusters, and L-functions. He was the first Chinese to receive a research award from the Clay Institute in the United States, and has made many breakthroughs in the fields of number theory and arithmetic geometry.
After receiving his Ph.D. from Columbia University, he worked as an assistant professor and associate professor at Princeton University and the University of California, Berkeley. In 2020, Yuan Xinyi returned to Peking University as a professor at the Beijing International Center for Mathematical Research, and continued to make important progress in related fields.
Yuan Xinyi won the 2022 Xplorer Award, which is a high recognition of his academic achievements and social contributions. As a member of the "Golden Generation of Mathematics at Peking University", Yuan Xinyi has had a profound impact on young mathematicians, encouraging them to explore the "no man's land" of mathematics and make breakthroughs.
Professor Yuan Xinyi has not only made outstanding academic achievements, but also had a positive impact on the younger generation of mathematicians through his teaching and research results, and is an important figure in the mathematics community in China and even in the world.
Analysis of the doubts in the Jiang Ping incident
Yuan Xinyi
On June 14, when I saw the report on the Internet that Jiang Ping won the 12th place in the preliminary round of the Alibaba Mathematics Competition, I was happy that Jiang Ping had achieved such a result, and I was excited that such a mathematical genius had been produced in China. So I immediately reprinted the news to a few of my colleagues who were engaged in mathematical research, and they were as happy as I was, and we had a lot of discussions about it.
On June 16, I opened Zhihu to continue to pay attention to Jiang Ping's incident, and I actually saw a lot of articles questioning Jiang Ping's achievements. I didn't believe it at first, but when I habitually clicked on it, I found that some of the articles did raise all kinds of doubts very rationally, so my opinion on the incident quickly changed.
After that, there were overwhelming doubts on the Internet, including Jiang Ping's high school entrance examination results, her math test scores at Lianshui Technical College, her math teacher Wang Runqiu's resume, and screenshots of many chat records related to Wang Runqiu. As a result, there are two factions on the Internet, which are those who question Jiang Ping and those who support Jiang Ping. The debate between the two factions on the Internet was very intense, and perhaps because there was no final conclusion, the debate gradually turned into a war of words and personal attacks. There are even some self-media that lack a moral bottom line to raise this matter to the height of class discrimination, gender discrimination, and academic discrimination, inciting the public's emotions and defrauding a large amount of traffic. This reminds me of the irreparable social rift in the United States today, and this rift is mainly caused by some people who take every opportunity to elevate various problems to the level of discrimination. The Chinese nation is a wise and friendly nation, and I really don't want us to follow in the footsteps of the United States in this regard.
It is reasonable that everyone has different clues about this matter, and has their own different perspectives and ways of thinking, so they will have different views. So I hope that everyone can treat this matter calmly, just talk about the matter, don't go online, don't attack each other, and don't attack Jiang Ping or other parties. Below, I will introduce my analysis of some clues in this matter, and I hope that readers can take my analysis calmly. Since it is difficult to distinguish the authenticity of most of the materials from the Internet, I will mainly analyze the video of the interview with Jiang Ping released by the Alibaba DAMO Academy, as well as Professor Yao Yijun of Fudan University commenting on her LaTex answer sheet.
(1) The preliminary round of the Alibaba Competition
The scope of the preliminary round of the Alibaba Contest is basically the same as that of the third and fourth year undergraduate students in the Department of Mathematics, and the content of the test may cover almost all the courses that students have taken at this stage, including analysis, algebra, geometry, probability, combinations, and so on. This year's preliminary round has 2 multiple-choice questions and 5 major questions, for a total of 7 questions. The duration of the exam is 48 hours, the format of the exam is open-book, and the contestants complete the reading questions and submit the answers online. The rules allow information to be checked and discussed with others, but there is no invigilation mechanism. This test format takes good care of candidates who are in different time zones around the world. Because the preliminary round is only to qualify for the semi-finals, and the final award only looks at the results of the semi-finals, and about 800 candidates enter the semi-finals every year, the results of the preliminary rounds are actually not that important.
Jiang Ping scored 93 out of 120 points in the preliminary round, ranking 12th among 50,000 participants, which is a very high ranking. Because many players feel that their scores are enough to enter the semi-finals, they do not work hard to complete all the questions, so the level of the players at the top of the preliminary round is not necessarily stronger than that of the players who are far behind in the preliminary round. If you want to correspond, the level represented by this 93 score can correspond to the middle and upper level of senior undergraduate students in the mathematics department of famous universities such as Peking University and Tsinghua University. If this score was obtained by Jiang Ping herself, then her learning talent should be very rare. After all, according to the report, Jiang Ping only began to study mathematics intensively from secondary school, which means that it took her less than two years to complete high school mathematics and undergraduate mathematics in the mathematics department.
Let's first consider a question, is a junior high school graduate able to complete high school mathematics and undergraduate mathematics in two years, and be able to score 93 points in the preliminary round? Based on my learning and teaching experience, I think that about 10 students in the country should have this talent every year. Of course, to complete this task, the student also needs to have a strong interest in mathematics, strong learning ability, and extraordinary perseverance. Therefore, just from the resume we saw of Jiang Ping, we can't conclude that she can't get this score.
(2) The board book in the video
The math in this board book proves a basic formula in mathematical analysis. Mathematical analysis, which is calculus in the Department of Mathematics, is the first mathematics course taken by undergraduate students in the Department of Mathematics, and it is generally studied for three semesters. Because it is a pose, the real mathematical content represented by this board book is not important; It doesn't matter whether the proof on the board is right or wrong, whether it's good or bad; The board book is a copied book, copied by your own notes, or copied by the teacher's notes, in fact, it is not important.
Screenshot of the board book in Alibaba's video reporting on Jiang Ping (in line with the principle of right things and not people, the screenshot dilutes Jiang Ping's figure)
In this 9-line board, I circled 13 problems that could be mistakes, clerical errors, or misunderstandings caused by writing habits. We will analyze each of these issues one by one. Here we will temporarily refer to the person who wrote this board book in reality as "the author", and then discuss whether the author is Jiang Ping.
Based on these analyses, we can conclude that the people who wrote the board were at most high school in mathematics and had no experience in mathematical analysis at all, let alone Evans' PDE textbook mentioned in the video, which is a graduate course in the mathematics department based on mathematical analysis.
Someone outside of math circles may interpret all of these problems as a problem of nervousness or writing habits. Now let me use an analogy to explain how serious this board book is in the world of mathematics. While any metaphor will have its imprecision, the role of a metaphor comes from its popularity. Suppose there is a winner of an all-Chinese Russian essay contest who copies a Russian passage on the blackboard. The onlookers, who did not understand Russian at all, felt that this board book was quite popular. Later, a Russian expert looked at the board, and here are the findings of this expert. He noticed in the first second that there were many words in the board book that had been copied incorrectly, and he felt that it might be caused by the winner's nervousness or negligence; In the third second, he noticed that there were a few very common words that he had copied incorrectly, and these common words were as common as the and is in English, and he felt that even someone who had taken a semester of Russian language class would not make such a mistake; In the 5th second, he found that there were many Russian letters in the board book, some Russian letters were written into other Russian letters, and some Russian letters were written into some symbols that did not exist in Russian; In the 7th second, he noticed that there was a Russian letter that appeared five times in the board book, but it was written in three different symbols. He concluded that the laureate did not even recognize the entire Russian alphabet. Note that I am not referring to the 33 letters of the Russian language, not the thousands of commonly used Russian words.
(3) Was this board book written by Jiang Ping?
Those who support Jiang Ping said that since this board book is a posed photo, it is likely that the staff wrote it for her to save time. However, in the video, there are several scenes that clearly show a hand writing this board book, and there are also several scenes that clearly show Jiang Ping writing this board book on the blackboard. Moreover, since it is a story about Jiang Ping, if the director has basic professionalism, shouldn't he let Jiang Ping write mathematical formulas, and then let the photographer shoot Jiang Ping write the formula, and then shoot the formula written by Jiang Ping? Filming Jiang Ping writing mathematical formulas by herself is definitely not a waste of time in this interview.
If this board book is really written by someone else, then I have two questions. First of all, who has the courage to copy a flawed advanced mathematical formula for Jiang Ping on the blackboard and use it to reprint it for major media when he doesn't understand advanced mathematics at all? Secondly, if someone really writes it, and Jiang Ping has an undergraduate mathematics level, then she must be able to see at a glance how unpopular this board book is, then she can still allow this board book to play her own board book in the video, and pose to write on it and continue to shoot?
Whether someone writes the board book on behalf of you, maybe Alibaba can come out and clarify.
(4) The necessity of using LaTex
Participants in the Alibaba Contest are required to submit their answers online, and the system will accept a photo or scanned version of the handwritten answer, or the answer written in a variety of electronic editors. Professor Yao Yijun from the School of Mathematical Sciences at Fudan University commented on Jiang Ping's answers: "The words are precise and fluent, and LaTex is proficient. If we do not discuss the level of mathematics, but only look at the level of the answer sheet, it can be said (conservatively) that 95% of mathematics students in China cannot write such an answer sheet within the specified time. ”
LaTex is a mathematical formula typesetting software commonly used in academia, which is widely used to write professional papers in mathematics and physics. Under the guidance of the teacher, it usually only takes a few hours for a student to learn the software to do some basic editing; However, in order to be proficient in the use of this software, it is generally necessary to have written a total of nearly 100 pages of papers using this software. Copying a page of complex mathematical formulas may take only 5 minutes to write by hand; It can take up to 40 minutes for a LaTex master to transcribe in LaTex; A LaTex beginner can take up to 3 hours to copy. This shows that LaTex is so time-consuming and labor-intensive. Therefore, in most cases, mathematics students will not actively use LaTex before they have started writing their dissertation. So, what I question here is that Jiang Ping studied mathematics in secondary school and never wrote a thesis, what motivation does she have to practice LaTex so proficiently? Note that the key here is not the difficulty of learning LaTex, but the necessity of learning LaTex. Also, as a secondary school student, how many opportunities are there to sit in front of a computer and write such time-consuming and labor-intensive LaTex without promoting math proficiency?
(5) Other minor questions
At the beginning of that interview video, Jiang Ping was incredulous when she learned that she had won such a high ranking, saying that she thought she would be a "card tail" in the finals, that is, just a few points above the score line. In fact, Jiang Ping scored 93 points, which is a lot more than the score line of 45 points. In this math competition with plenty of time, an excellent contestant should definitely know how many points he can score. Based on the experience of the cut-off score in previous years, or the experience of his teacher, it seemed illogical that she didn't know where her score might be. Perhaps, this can be explained as a plot designed by the director to add to the legend.
In the first version of the video released by Alibaba, Jiang Ping described Xie Huimin's "mathematical analysis" as "mathematical aspects". Mathematical analysis is a very large part of the curriculum, usually in the first three semesters of mathematics undergraduate admission, and Xie Huimin's two books are more than 700 pages long. If she had taught herself a thorough course, the word "mathematical analysis" would have been in her head all the time for a few months, and this mistake could not be explained by a nervous slip of the tongue. I borrow a netizen's analogy here: a person who is familiar with "Romance of the Three Kingdoms" will not say "Romance of the Three Kingdoms" as "Three Kingdoms World" when he is nervous and stuttering.
Alibaba later released a revised video, which changed the "mathematical aspect" to "mathematical analysis". Is this three hundred taels of silver here?
(6) Analysis of the possibility of cheating
Now let's talk about the possibility of cheating in the preliminary round. The discussion in this section lacks testable evidence, but many doubts can be explained more plausibly. I don't keep saying that these statements must be true, but I hope to use them to tell you that there are many possibilities and inspire you to think.
Some netizens on Zhihu suggested that there is a team cheating method, which is very effective in dealing with the preliminary round. This is a cheat that most people don't expect, and this is the first time I've heard of it. Below I will introduce this cheating method in combination with the form of the preliminary round.
As mentioned above, the different questions in the preliminary round involve all directions of mathematics, and it is very difficult for a single player to get a perfect score. It is noted that from the graduate level, students in the Department of Mathematics mainly deepen their own research directions, and will gradually forget most of the content in other directions, so many doctoral students do not have as much advantage as when they graduate from the undergraduate examination. However, every question in the preliminary round is not very difficult for graduate students who are familiar with the direction of the question. So, if there is a team (e.g. a WeChat group) consisting of master's or doctoral students from several mathematics departments, these graduate students cover all major directions of mathematics. During the exam, everyone works together, everyone only needs to solve the questions in their own direction, and then everyone can get the answers to all the questions (or most of the questions), so that everyone can get a good score in the preliminary round.
Jiang Ping's teacher, Wang Yanqiu, was once a master's student in the Department of Mathematics at Jiangsu University, and in Alibaba's report, he was Jiang Ping's Bole who brought him to the world of mathematics. According to Alibaba's official records, Wang participated in the Ali competition last year and this year, and entered the re-examination in both years, and did not win a prize last year.
Below, I recount some netizens' descriptions of the stories behind them, based on screenshots of many chat logs with people related to Wang Yunqiu or Jiang Ping circulating on the Internet. Again, I reiterate that the authenticity of these screenshots and stories is difficult to determine, and the purpose of this presentation is to provoke food for thought. These screenshots show that Wang Yunqiu used the team to cheat and helped him pass this year's preliminary exam. Moreover, Jiang Ping's 93 points came from another account registered by Wang Yanqiu as Jiang Ping. The answer sheet for this account was submitted by LaTex written by Wang Yanqiu to avoid exposing his handwriting, and it is even possible that Jiang Ping had not read the questions of the preliminary round from beginning to end. The purpose of Wang Yanqiu's opening of this trumpet is to have two opportunities to read and answer the questions in the finals, so as to improve his performance in the finals.
The format of the finals is that in the fixed 24 hours officially set aside, each contestant can choose 8 consecutive hours to read and answer the questions that suit him/herself. The finals will still be online, but players will be required to keep their cameras on for eight hours, and will be allowed to leave the venue for a short period of time to eat or go to the bathroom. If Wang Yanqiu can really manipulate the two accounts, then he can read the questions online with a small account at the 0th hour, and then log out, and then continue to think about the exam questions offline, or seek help from the team, and go online with his own account to answer the questions in the last 8 hours. So, why does Wang Yunqiu want to win the final so much? There are several explanations online, one of which is that he wants to apply for a PhD in the Department of Mathematics, and the award in the final can increase the success rate of his application; Another explained that he opened a graduate school entrance counseling class, and that he would increase the popularity of the tutorial class if he won the award, and if his students won the award, it would greatly increase the popularity of the tutorial class.
Let me explain here that the finals of this year's Alibaba Competition are divided into different tracks, that is, each candidate chooses a mathematics direction and only answers the questions in this direction, and then the awards are only based on the ranking in the same track. The difficulty of the final questions is equivalent to the difficulty of the qualification examination for doctoral students in the Department of Mathematics of prestigious universities, and the contestants who can win prizes in the finals are also the best among the doctoral students of Tsinghua University and Peking University. Therefore, if Wang Yunqiu wins the award in the finals, it will indeed play a great role in his application for doctoral students in 985 universities. It is worth mentioning that the above-mentioned team cheating method is not effective for the finals, because the finals are only tested in one direction of mathematics, and each problem is extremely difficult, even if 10 ordinary level graduate students in the same direction discuss together for a few hours, they may not be able to solve the most difficult 2-3 problems of the track where their direction is located.
If this speculation of Wang Yanqiu's cheating is true, then Jiang Ping's mathematics level may be the mathematics level of an ordinary secondary school student, which can also explain our large number of questions about that board book. That is to say, the board book was copied by Jiang Ping from Wang Yanqiu's notebook, because Wang Yanqiu's handwriting was a little sloppy, and Jiang Ping had never seen those symbols outside the scope of high school, so there were all kinds of extremely unprofessional mistakes in those symbols.
The doubts we raised above may confirm the famous adage that it is difficult to tell a perfect lie. Personally, I think that Jiang Ping's preliminary results are very likely not to have been tested by herself. However, because of the silence of the parties involved, the blockade of information in Lianshui, and the inability to distinguish the authenticity of the documents on the Internet, the reliable evidence we have is very limited, and the logical analysis we rely on cannot be regarded as empirical evidence. Theoretically, Jiang Ping may still have been wronged.
Many people are waiting for Jiang Ping's final results, hoping to determine whether her preliminary results are her own based on the final results, but in fact, her final results do not explain anything. Because the depth and difficulty of mathematics in the finals are much greater than those in the preliminary round, even if Jiang Ping's results in the finals are not good, it does not prove that her results in the preliminary round are fake. Even if she did well in the finals, everyone would still be caught up in the debate about whether her final results were real.
(7) If Jiang Ping was wronged
If Jiang Ping has real talent and learning, and she wants to prove her innocence, it is very easy to do, because it is very easy to determine whether mathematics will or not. Jiang Ping only needs to explain how to do the questions in the preliminary round live on the Internet, and answer some relevant questions from netizens to prove her innocence. If he doesn't like to be less serious than that, after all, there are a lot of people on the Internet, then she can find 3-4 well-known math professors and organize a formal math interview, which only takes half an hour to prove her strength. Most professors in the mathematics community (including me) would be happy to participate in this interview and help Jiang Ping in her studies after confirming her knowledge. If Jiang Ping finds the above proposals inappropriate, I will personally invite Jiang Ping to visit Peking University and discuss mathematics or future career development with her, at my expense.
(8) Conclusion
Mathematics researchers like to be quiet, and they also need to be quiet in order to concentrate on their studies. I hope that this matter can be clarified as soon as possible, and everyone will be given justice, the mathematical community will be innocent, and the mathematical community will be a pure land.
Upcoming Group Study Tour to Indonesia (7.23-31)|The pearl left by the gods, the country of ten thousand islands from the perspective of global history
Travel with Liang Yongan to Northern Xinjiang (7.12-21), enjoy the beautiful natural scenery, and taste the kaleidoscope of exotic culture
Caucasus Travel (8.1-11)|Visa-free! World heritage and fine wine, snow-capped mountains and churches, go to a cool summer