Chapter Summaries

Xiao Yi told Professor Liu that he had read eight advanced mathematics books in four days and understood most of their contents, astonishing Liu Bin and the professors with him. Academician Hu Guangde introduced himself and gave Xiao Yi a paper to assess, leaving Xiao Yi to examine it.

• Xiao Yi told Liu Bin he had finished seven mathematics books and started an eighth, Principles of Number Theory, in less than four days.
• Xiao Yi said he understood around eighty percent of the material, including about seventy percent of Real Analysis, and praised Fermat's Last Theorem and Andrew Wiles.
• Liu Bin and the professors at the conference were stunned by Xiao Yi's reading speed and comprehension, while Hu Guangde became interested in him.
• Liu Bin introduced Hu Guangde, an academician from USTC, to Xiao Yi over video call.
• Hu Guangde sent Xiao Yi a paper titled "The Convergence of Riemann Integrals and Lebesgue Integrability" and asked him to read it and share his thoughts.

Xiao Yi read a paper by Zeng Ang and identified an error in its application of Dirichlet's Test. He explained and corrected the proof for Hu Guangde and the other professors, who were astonished by his command of Real Analysis and looked forward to seeing him at USTC.

• Hu Guangde sent Xiao Yi a paper by graduate student Zeng Ang and asked him to read it.
• Xiao Yi found that the paper's fourth section incorrectly used Dirichlet's Test to determine the convergence of a Riemann integral.
• Xiao Yi told Hu Guangde about the error and explained how to correct the proof, using the Cauchy Criterion.
• Hu Guangde praised Xiao Yi's explanation and said he looked forward to seeing him at USTC's Academy of Mathematics and Systems Science.
• The professors marveled at Xiao Yi's ability, while Liu Bin worried that the forty books he had given Xiao Yi would not last long.

After Academician Hu challenged Xiao Yi to write a paper suitable for a domestic Core Journal before university, Xiao Yi began studying mathematics papers and improving his English. A month passed as he worked toward the goal, while Hu Guangde and Liu Bin hoped he would surprise them.

• Xiao Yi told his classmates that Academician Hu had called him for a video conversation, then recalled Hu’s requirement that he write a paper fit for a domestic Core Journal before enrolling in university.
• Liu Bin worried that the challenge was too difficult for Xiao Yi, but Hu Guangde argued that a demanding goal would motivate him and that failure would not prevent Xiao Yi from entering their school.
• Xiao Yi read Professor Liu Bin’s books and domestic core mathematics papers, studying unfamiliar material he encountered.
• Xiao Yi intensified his English studies so he could read SCI papers, and a month passed.

Xiao Yi took first place in the Nine Provinces Joint Examination with 725 points, beating senior-year legend Wang Zichao by 30 points and astonishing students and teachers. Principal Liu Songlin celebrated his achievement, then Xiao Yi asked whether he could arrange his study time freely.

• Class 1 of Science Stream saw Xiao Yi ranked first in the Nine Provinces Joint Examination with 725 points, including full marks in Mathematics and Science Comprehensive.
• The students learned from their homeroom teacher that Xiao Yi was a second-year student selected for the USTC Young Scholars Program.
• Principal Liu Songlin told Principal Chen that Xiao Yi was a second-year student and refused to introduce him to another school.
• Luo Penghua brought Xiao Yi to Principal Liu, who praised him and asked what he needed for his studies.
• Xiao Yi cautiously asked Principal Liu whether he could arrange all his time freely from then on.

Xiao Yi asked Principal Liu Songlin for more freedom to study and permission to use a computer, and Liu approved his requests while offering him a scholarship. The chapter ended as the school’s flag-raising ceremony began and Liu was invited to speak.

• Xiao Yi asked Liu Songlin to excuse him from classes so he could arrange his study time, and Liu agreed to give him access to a self-study room.
• Xiao Yi asked to bring a computer to school, and Luo Penghua explained that Academician Hu Guangde had asked Xiao Yi to write a mathematics paper before entering USTC.
• Liu Songlin allowed Xiao Yi to use a computer and his phone, and said the school would buy him a computer as a reward for his exam performance.
• Liu Songlin awarded Xiao Yi a ten-thousand-yuan scholarship and promised at least thirty thousand yuan and university expenses if Xiao Yi became Provincial Top Scholar.
• Liu Songlin arranged for the school to cover the paper’s publication fees in exchange for listing Affiliated High School as an affiliation, then headed with Xiao Yi and Luo Penghua to the flag-raising ceremony.
• The flag-raising ceremony began, and the students welcomed Liu Songlin to the rostrum to give a speech.

At the flag-raising ceremony, Principal Liu announced that sophomore Xiao Yi had placed first among 4.5 million candidates in the Nine Provinces Joint Examination with 725 points. Xiao Yi received a ten-thousand-yuan scholarship and went onstage to accept his award.

• Chen Wei guessed that Xiao Yi would receive an award, and Xiao Yi confirmed it before Luo Penghua told Chen Wei to stand properly.
• Principal Liu announced that a student had taken first place in the Nine Provinces Joint Examination, shocking students across the school.
• Principal Liu revealed that Xiao Yi had scored 725 points, five ahead of second place, and explained that he was a sophomore preparing to take the college entrance examination with the seniors.
• Principal Liu announced a ten-thousand-yuan scholarship for Xiao Yi and invited him onstage to receive it.
• Xiao Yi left Class 3 of Science Stream and walked to Principal Liu in front of the assembled students.

Xiao Yi received a 10,000-yuan scholarship for placing first in the senior-year exam, and Principal Liu let him arrange his own study schedule. He began studying alone in the library study room, drawing on the vast knowledge he had gained from reading forty books and mathematical papers.

• Liu Songlin presented Xiao Yi with a 10,000-yuan scholarship placard and told him the money would be transferred to his bank account.
• Xiao Yi returned to class, joked with Chen Wei and his classmates, and announced that he would stop attending lessons.
• Luo Penghua told Chen Wei that Principal Liu had allowed Xiao Yi to arrange his own time and study in the study room.
• Chen Wei abandoned the idea of asking for the same privilege and resolved to study harder after Luo Penghua pointed out his physics score.
• Xiao Yi studied in the library and reflected on how reading forty books and Andrew Wiles's paper on Fermat's Last Theorem had expanded his mathematical knowledge.

Xiao Yi decided to write his first mathematics paper before enrolling at USTC and asked Professor Liu Bin for advice on choosing a topic. After Xiao Yi revealed that he had read Andrew Wiles's original proof of Fermat's Last Theorem, Liu Bin agreed to recommend number theory topics.

• Xiao Yi concluded that the college entrance examination was manageable and set his sights on becoming the top scorer while preparing to write a paper before enrollment.
• Xiao Yi called Professor Liu Bin and asked for advice on selecting a paper topic.
• Xiao Yi chose number theory because reading Andrew Wiles's original papers on Fermat's Last Theorem had sparked his interest.
• Xiao Yi told Liu Bin that he had read the original papers in Annals of Mathematics and was rereading the forty mathematics books Liu Bin had given him.
• Liu Bin was astonished by Xiao Yi's preparation and offered to recommend potential number theory topics.

Liu Bin introduced Xiao Yi to number theory and sent him possible paper topics and research papers. Xiao Yi became interested in the Absolute Remote Abelian Conjecture topic, which he thought suited him perfectly.

• Liu Bin explained how number theory sought patterns in integer problems such as the Riemann Hypothesis, Fermat's Last Theorem, the Twin Prime Conjecture, and Goldbach's Conjecture.
• Liu Bin advised Xiao Yi to read number theory papers and sent him several possible topics and papers by leading researchers.
• Liu Bin reminded Xiao Yi not to pressure himself to finish a paper within four months before ending their call.
• Xiao Yi examined the topics and focused on Analytic Resolution of Nonsingularities and the Absolute Remote Abelian Conjecture.
• Xiao Yi read that the topic extended a conjecture proven by Shinichi Mochizuki and decided it suited him perfectly.

Xiao Yi chose an especially difficult mathematics topic combining number theory and algebraic geometry, while Liu Bin unknowingly sent it to him by mistake. As the 2020 Gaokao approached, Xiao Yi’s classmates wished him luck, and he waited outside Exam Room 4 for his first exam.

• Xiao Yi decided to work on a difficult topic involving number theory, algebraic geometry, and anabelian geometry.
• Liu Bin noticed he might have sent Xiao Yi the obscure topic by accident, but hurried to class without checking further.
• Luo Penghua announced the school’s Gaokao closure and told the class that Xiao Yi would take the exam with the seniors.
• Chen Wei led the class in wishing Xiao Yi success, and Xiao Yi promised he would win the Gaokao top scholar title.
• On June 7, Xiao Yi waited outside Exam Room 4 for the Gaokao to begin.

After finishing the college entrance exams, Xiao Yi devoted himself to writing his challenging mathematics paper while awaiting the results. When his 741-point score made him Hui Province’s science-stream top scorer, Shangjing University and Tsinghua University admissions teachers arrived at his home to recruit him.

• Xiao Yi continued working through difficult material for his paper, gradually making progress.
• On June 24, Xiao Guohua answered the door to teachers from Shangjing University, who congratulated Xiao Yi on becoming the province’s science-stream top scorer.
• The Shangjing University teacher revealed Xiao Yi’s 741-point score and asked whether he would apply to the university.
• Teachers from Tsinghua University arrived and argued with the Shangjing University team over who had arrived first.
• Xiao Guohua and Du Xin realized the two top universities were competing to recruit Xiao Yi, and Du Xin became tearful with excitement.

Xiao Yi’s Gaokao top-scorer result brought Shangjing University and Tsinghua representatives to his home to recruit him, but USTC’s admissions director arrived with a richer offer. The rivalry ended when Xiao Yi announced that he had already agreed to attend USTC.

• Xiao Guohua explained that Xiao Yi was a second-year high school student already committed to USTC through its Young Scholars Program.
• The Shangjing University and Tsinghua representatives proposed ways for Xiao Yi to enroll early and argued over their mathematics programs and benefits.
• Wang Enqing, USTC’s admissions director, arrived with a group and congratulated Xiao Yi on scoring 741 and ranking first among National Paper B provinces.
• Wang Enqing offered Xiao Yi tuition, accommodation, meals, monthly allowances, and competition rewards to join USTC’s Gifted Class.
• Xiao Yi said he had agreed to go to USTC.

Xiao Yi turned down recruitment offers from Shangjing University and Qinghua because he had promised to attend USTC, and his family supported his choice. After the universities’ teachers left, news of Xiao Yi’s record-breaking Gaokao score as a high school junior spread nationwide.

• Xiao Yi refused Shangjing University and Qinghua, explaining that he had promised Professor Liu he would attend USTC.
• Xiao Guohua supported his son’s decision, and the visiting teachers accepted Xiao Yi’s choice before leaving.
• Wang Enqing thanked Xiao Yi’s family and began discussing the details of his enrollment at USTC.
• Xiao Yi focused on his paper while public attention shifted to Gaokao results across the country.
• Netizens learned that Xiao Yi had scored 741 as a high school junior and had topped the science stream in Hui Province and all regions using Gaokao Exam Paper B.

Xiao Yi’s 741-point Gaokao score and decision to honor his agreement with USTC drew widespread attention, leaving him overwhelmed by reporters and messages. At a televised interview, he said he had no regrets about choosing USTC over Shangjing University and Tsinghua University because it was closer to home.

• Netizens marveled at Xiao Yi’s perfect scores in math and Science Comprehensive and praised him for keeping his promise to attend USTC.
• Xiao Yi struggled with the attention from reporters and online messages, which disrupted his work on a paper.
• Xiao Yi attended an interview at the Affiliated High School on June 26, where students, parents, teachers, and school leaders watched.
• Xiao Yi thanked his school and homeroom teacher Luo Penghua during the interview, pleasing the school leaders.
• Xiao Yi told the reporter that Shangjing University and Tsinghua University were fine, but USTC was closer to home, so he felt no regret about his choice.

Xiao Yi accepted a ten-thousand-yuan sponsorship from Anhui Provincial TV and received his school’s thirty-thousand-yuan scholarship after becoming the provincial top scholar. His classmates joined him for a graduation photo, and a month later he had returned to researching his paper.

• A reporter offered Xiao Yi a ten-thousand-yuan sponsorship, which he accepted after filling out the form.
• Principal Liu Songlin presented Xiao Yi with a thirty-thousand-yuan scholarship plaque.
• Teacher Luo brought the students of Class 3 of Science Stream to celebrate with Xiao Yi and take a graduation photo.
• Xiao Yi, Principal Liu Songlin, and the classmates posed for a photo, with Xiao Yi wearing graduation robes.
• Xiao Yi returned to researching his paper, and a month passed.

Xiao Yi completed and checked a twenty-five-page paper proving the Absolute Remote Abelian Conjecture, then learned that Ruthless Continuous Study had reached lv3. He sent the paper to Professor Liu for review, and Professor Liu was stunned by its title.

• Xiao Yi finished deriving the paper’s final conclusion and organized his work into a twenty-five-page document.
• Xiao Yi checked the derivations and received a notification that Ruthless Continuous Study had reached lv3, increasing its learning-efficiency bonus.
• Xiao Yi worried that the paper might have too little value for a Core Journal and sent it to Professor Liu for advice.
• Professor Liu opened Xiao Yi’s paper and froze when he saw its title, “Non-singular Analytic and... the Absolute Remote Abelian Conjecture.”

Liu Bin discovered that Xiao Yi had chosen a highly difficult conjecture topic and claimed to have proved it. As he carefully reviewed Xiao Yi’s rigorous paper, Liu Bin found no errors but realized the proof had exceeded his expertise.

• Liu Bin recognized Xiao Yi’s paper topic as a difficult conjecture he had once suggested and asked why Xiao Yi had chosen it.
• Xiao Yi explained that the topic interested him because it involved Algebraic Geometry and seemed harder than the others.
• Liu Bin told Xiao Yi the topic was beyond his level and tried to reassure him that researching it had still been useful experience.
• Xiao Yi said he believed he had proved the Absolute Remote Abelian Conjecture and had checked his derivation.
• Liu Bin began examining the paper and found its proof rigorous, but he could not understand parts of it because they lay outside his expertise.

Liu Bin admitted he could not evaluate Xiao Yi’s paper on Far Abelian Geometry and brought it to Academician Hu for review. Hu recognized the topic and guessed Xiao Yi might have written it, but dismissed the idea, leaving Liu Bin amused by how close he was to the truth.

• Liu Bin told Xiao Yi that he could not understand or assess the paper and would ask Academician Hu to review it.
• Liu Bin praised the paper’s rigor, calculations, methods, and writing, while Xiao Yi blamed its difficulties for calling it not very good.
• Liu Bin printed the twenty-five-page paper and took it to Academician Hu’s office.
• Hu Guangde recognized the paper’s topic as one he had once assigned to Liu Bin and asked who had written it.
• Hu guessed Xiao Yi might be the author, then rejected the possibility because he thought Xiao Yi had not studied long enough.

Hu Guangde examined a mathematics paper and judged it strong enough for leading journals, while Liu Bin revealed that Xiao Yi had written it. Hu Guangde was stunned by the revelation and kept the paper to study further.

• Hu Guangde began reading the paper, criticizing its abstract and formatting while praising its rigorous mathematical derivations.
• Hu Guangde became absorbed in the paper and worked through its calculations for about an hour.
• Hu Guangde said the paper could be submitted to leading journals, including IHES, if it contained no major errors.
• Liu Bin revealed that Xiao Yi had written the paper, leaving Hu Guangde astonished.

Hu Guangde confirmed that Xiao Yi had independently written an exceptional paper in Far Abelian Geometry and finished reviewing it. He judged it worthy of submission to IHES and told Liu Bin to ask Xiao Yi to prepare an English translation.

• Hu Guangde questioned whether Xiao Yi had written the paper and asked Liu Bin to run a plagiarism check.
• Liu Bin and Hu Guangde found the paper had a similarity rate of 3.14%, and Hu Guangde asked Liu Bin to leave the paper with him for review.
• Three days later, Hu Guangde told Liu Bin that Xiao Yi’s paper was rigorous, highly valuable, and among the best recent work in Far Abelian Geometry.
• Hu Guangde told Liu Bin to notify Xiao Yi and remind him to translate the paper into English for submission to IHES.