Chapter Summaries

After Hu Guangde praised Xiao Yi’s proof of the Absolute Remote Abelian Conjecture, he and Liu Bin urged him to submit it to a prestigious international journal. Liu Bin helped Xiao Yi prepare the paper and advised him to claim sole authorship and protect his work.

• Xiao Yi was stunned when Liu Bin told him Hu Guangde considered his paper one of the best recent works in Far Abelian Geometry, and Hu praised his talent.
• Hu Guangde and Liu Bin recommended that Xiao Yi translate the paper and submit it to Publications mathématiques de l'IHES rather than a domestic Core Journal.
• Xiao Yi translated the paper, and Liu Bin helped him revise its formatting and wording before recommending submission to IHES.
• Xiao Yi asked whether Liu Bin should be the corresponding author, but Liu insisted Xiao Yi list only himself because he had completed the paper independently.
• Liu warned Xiao Yi that academia could be unclean and advised him to protect his work and achievements.

Xiao Yi submitted his first paper to Publications Mathématiques de l'IHES and resumed studying while awaiting a decision. At the university, Hu Guangde took charge of writing the Hua Luogeng Mathematics Class entrance exam and planned to devise questions that could challenge Xiao Yi; days later, an IHES editor began work with more than fifty submissions waiting.

• Xiao Yi submitted his paper to Publications Mathématiques de l'IHES and told Liu Bin that he had sent it in.
• Liu Bin informed Hu Guangde, who said he would contact the journal's editor-in-chief and expected the paper might be published within three months if all went well.
• Dean Chen gave Hu Guangde the Hua Luogeng Mathematics Class applicant list, and Hu Guangde noticed Xiao Yi's name among the students selected for the second-round exam.
• Hu Guangde volunteered to write the written exam questions, then asked Liu Bin to help him think of questions that could stump Xiao Yi.
• Editor Evans arrived at the IHES journal office in Paris and found more than fifty unread submissions in the review system.

IHES editor Evans examined a paper on Far Abelian Geometry submitted by a Chinese high school graduate after Editor-in-Chief Bojielun asked him to review it carefully. Evans expected to reject it, but the rigorous paper impressed him as he read.

• Evans rejected several early submissions that fell short of IHES standards.
• Evans noticed that the fifth submission had been marked for the editor-in-chief’s attention and found that its author was a Chinese high school graduate.
• Evans asked Bojielun why the paper had been prioritized, and Bojielun told him to review it carefully and provide a brief evaluation.
• Bojielun explained that Mr. Hu, an old friend, had recommended the paper and bet Evans 50 euros that he would keep reading it.
• Evans began reviewing the paper, and its rigorous derivations made him abandon his plans for a tactful rejection.

Evans became absorbed in a high school student's paper on Far Abelian Geometry, recognizing its remarkable quality despite struggling to follow parts of the proof. He decided to finish reading it before speaking with Editor-in-Chief Bojielun.

• Evans studied the paper and worked through calculations until David warned him that his actions could look like plagiarism.
• Evans realized he had lost his wager with Bojielun and owed him fifty euros, but chose to keep reading the paper.
• David tried to read the paper but could not understand it, while Evans praised its methods and detailed explanations.
• Evans called the student a rising star in mathematics and said he would find Editor-in-Chief Bojielun after finishing the paper.

Evans persuaded Editor-in-Chief Bojielun that Xiao Yi’s paper on Far Abelian Geometry might be publishable, despite its author being a high school student. Bojielun sent it to Peter Scholze for expert review, leaving the paper’s merit and its possible relevance to Shinichi Mochizuki’s abc conjecture proof unresolved.

• Evans told Bojielun that Xiao Yi’s paper might be suitable for their journal and revealed he was preparing to contact Peter Scholze or Jacob Stix for a review.
• Bojielun read the paper, could not follow its mathematics, but recognized its professional writing and agreed to seek expert review.
• Bojielun called Peter Scholze, who agreed to review the paper and promised to respond within two or three weeks.
• Evans suggested Scholze might be interested because of his dispute with Shinichi Mochizuki over the abc conjecture proof, while Bojielun doubted Xiao Yi’s paper could resolve it.
• Evans left without returning the fifty euros, and Bojielun resumed his work after sending the paper to Scholze.

In late August, Xiao Yi learned that fifteen universities would hold a joint mathematics-class entrance exam, with questions set by academicians, after Academician Hu’s plan to challenge him sparked wider interest. Xiao Yi joined the exam group and opened the syllabus, where an unusual question type stopped him cold.

• Liu Bin told Xiao Yi that his paper remained under expert review and that his mathematics-class assessment would take place on August 29.
• Liu Bin explained that Academician Hu’s plan to set difficult questions had led academicians from fifteen universities to organize a nationwide joint exam.
• Xiao Yi joined the exam’s QQ group and saw applicants from several universities worrying about the abstract syllabus and their chances of admission.
• Xiao Yi opened the syllabus and froze when he discovered that it included a kind of question he had not expected.

Xiao Yi learned that the university mathematics examination would test whether students could abstract methods from research papers, then prepared for the exam and arrived at USTC. There, he met fellow examinees and was introduced to the young Ye Cheng, who insisted they address each other as scholars.

• Xiao Yi read the exam outline and realized the afternoon test would ask examinees to identify mathematical methods in papers and apply them to new problems.
• Chen Muhua recognized Xiao Yi in the group chat, praised his college entrance exam score, and exchanged good wishes with him.
• Xiao Yi accepted Chen Muhua's friend request and returned to reading Zhang Yitang's paper on the Twin Prime Conjecture.
• Eight days later, Xiao Yi arrived at USTC for the joint examination and found many young Gifted Class students among the examinees.
• Ye Cheng greeted Xiao Yi as Scholar Xiao, and Xiao Yi asked him to use his name instead; Ye Cheng proposed they call each other scholars.

Xiao Yi discussed Ye Cheng’s ambitious plans and his anxiety about the afternoon mathematics exam before finishing the test in twenty minutes and handing it in. His early departure left the other young math competitors, including Ye Cheng, stunned.

• Xiao Yi learned that Ye Cheng planned to pursue advanced mathematics and hoped to win the Fields Medal before turning forty.
• Ye Cheng admitted he was nervous about the afternoon exam, and Xiao Yi gave him an uncertain answer about his own confidence.
• The proctors distributed the exam papers, and Xiao Yi quickly saw that the three questions resembled easier Math Olympiad problems.
• Xiao Yi solved all three questions in twenty minutes and handed his paper to Professor Xu.
• Professor Xu was astonished by Xiao Yi’s completed answers, while the other examinees and Ye Cheng stared in disbelief.

Xiao Yi entered the afternoon exam as the candidates and proctors prepared for a mathematics test built around passages from research papers. While academicians argued over their students and Schultz’s claim about the abc conjecture, Xiao Yi recognized the first passage as a paper he had already read.

• Xiao Yi arrived at the examination hall, where Ye Cheng praised his performance and Xiao Yi modestly said he would wait to see the questions.
• Academicians Liao Huan and Hu Guangde argued over whether their universities had the stronger candidate as the remote proctoring meeting began.
• The academicians discussed Peter Scholze’s claim that he had found evidence against Shinichi Mochizuki’s proof of the abc conjecture, reportedly through a paper on Far Abelian Geometry.
• Hu Guangde mentioned that one of his students had recently written a paper on Far Abelian Geometry, prompting Liao Huan to tease him.
• The afternoon exam began with two questions drawn from mathematics papers, and Xiao Yi recognized the first passage as an excerpt from Chen Jingrun’s work on the Goldbach Conjecture, which he had already read.

Xiao Yi quickly understood the exam questions drawn from Chen Jingrun’s and Zhang Yitang’s papers and began solving them as soon as the exam started. Ye Cheng watched in disbelief, then refocused on his own work while the proctors gathered behind Xiao Yi to observe.

• Xiao Yi recognized the first excerpt as Lemmas 8 and 9 from Chen Jingrun’s paper and judged that its inclusion-exclusion methods made the question manageable.
• Xiao Yi identified the second excerpt as coming from page twenty-six of Zhang Yitang’s paper on the Twin Prime Conjecture and anticipated that most examinees would struggle with it.
• When the exam began, Xiao Yi immediately started answering the first question while Ye Cheng remained baffled by the excerpt.
• Ye Cheng saw that Xiao Yi had finished the first question and had already begun writing on the second.
• Ye Cheng noticed that the three proctors had moved behind Xiao Yi to watch him solve the questions, then returned his attention to his own paper.

Xiao Yi completed the afternoon exam in thirty minutes, drawing the attention of the academicians monitoring the fifteen universities. As he wandered around USTC, he realized that his thoughts on the sieve method were beginning to form a unified idea that might bring him closer to solving a problem.

• Students at the university examination halls struggled with the unfamiliar questions, while some gradually applied the Principle of Inclusion-Exclusion to the first one.
• Xiao Yi handed in his paper at USTC after thirty minutes, prompting the remote proctors to pull up the surveillance feed.
• Hu Guangde told Liao Huan that Xiao Yi had written a mathematical paper and had finished the morning exam in twenty minutes.
• Liao Huan and the other academicians grew curious about Xiao Yi’s paper, but Liu Min explained that it could not be viewed before the exam ended.
• Xiao Yi wandered around campus, thinking about the second question and the sieve methods in Zhang Yitang’s paper as his scattered ideas began to cohere.

Peking University academicians discovered that Xiao Yi’s exam paper went beyond Zhang Yitang’s method on the twin-prime problem, while IHES editor-in-chief Bojielun read Peter Scholze’s enthusiastic review of a paper whose ideas could help refute Shinichi Mochizuki. The chapter left both groups stunned by the paper’s mathematical significance.

• Liao Huan found a completed exam paper whose solutions to the first excerpt and problems were exceptionally strong, and suspected it belonged to Xiao Yi.
• Liao Huan found that the paper’s treatment of Zhang Yitang’s twin-prime method went beyond what he could understand, so he called Wang Jianxin over.
• Wang Jianxin studied the work and declared that Xiao Yi had improved Zhang Yitang’s method by approaching it from a different angle.
• Bojielun opened an email from Peter Scholze, who said the paper was unquestionably correct, highly valuable in Far Abelian Geometry, and had helped him identify a key point for proving Shinichi Mochizuki wrong.
• Peter Scholze told Bojielun he planned to discuss the matter with Jacob Stix and hoped the journal would publish the paper soon.

Bojielun and Evans learned that Peter Scholze had praised Xiao Yi’s paper on Far Abelian Geometry, which the journal accepted for publication. Xiao Yi received the news at home and told Liu Bin, who was stunned by the message.

• Bojielun learned that Peter Scholze had recognized the value of Xiao Yi’s paper and could use it in work on the abc conjecture.
• Evans confirmed Scholze’s assessment, and Bojielun instructed him to notify Xiao Yi and arrange online publication after the fee and contract were completed.
• Evans emailed Xiao Yi to congratulate him on the paper’s acceptance, explain the publication steps, and pass along Scholze’s request that Xiao Yi post future work on preprint websites.
• Xiao Yi read the email at home, realized Scholze had reviewed his paper, and sent a screenshot and message to Liu Bin.
• Liu Bin saw Xiao Yi’s message after returning from grading the joint mathematics examination and exclaimed in shock.

Hu Guangde celebrated Xiao Yi’s brilliance, then learned that Xiao Yi’s paper had been accepted by IHES. Xiao Yi paid the publication fee with funding from USTC High School and discovered that his joint-examination score was 101 out of 100.

• Hu Guangde learned that academicians had praised Xiao Yi’s paper and that Liao Huan had admitted Hu’s student was impressive.
• Hu Guangde received Liu Bin’s message that IHES had accepted Xiao Yi’s paper and reacted with shock.
• Liu Songlin and other USTC High School leaders visited Xiao Yi, thanked him for his achievement, and transferred 100,000 yuan to him.
• Xiao Yi paid IHES’s publication fee and signed the copyright transfer agreement.
• Xiao Yi checked the joint-examination results and saw that he had ranked first with a score of 101.

Xiao Yi’s perfect written-exam score and an extra point stunned the joint-exam candidates, who joked that he should act like a human being. He arrived at USTC’s interview, where Hu Guangde began by asking how he had slept.

• The candidates in the group chat struggled to explain how Xiao Yi earned 41 points on a 40-point question, and Luo Xiao said aloud that the graders must have awarded an extra point for his answer.
• Xiao Yi copied the group’s repeated message, prompting the candidates to condemn him for acting inhuman.
• Xiao Yi arrived early for USTC’s interview and heard other candidates describe the difficult questions they expected from Academician Hu.
• Hu Guangde and the other interviewers welcomed Xiao Yi, and Hu Guangde asked how he had slept the previous night.

Xiao Yi finished his brief interview and learned that his paper had been accepted by IHES and published online. News of the paper spread among the joint examination candidates, who discovered Xiao Yi was the Chinese mathematician whose work had inspired Peter Scholze.

• Hu Guangde ended Xiao Yi's interview after asking only whether he had slept well, and Xiao Yi left the examination room in under two minutes.
• Xiao Yi received an email confirming that IHES had accepted his paper and made it available online.
• Candidates in the joint examination group discussed Peter Scholze's upcoming conference and the paper that had reportedly inspired him.
• A blogger named Math and Physics Events identified Xiao Yi as the author of a newly published IHES paper and cited Peter Scholze's praise for it.
• A commenter shared a USTC High School post congratulating alumnus Xiao Yi, prompting the blogger to reply, "Huh?"

News that Xiao Yi, a seventeen-year-old USTC High School graduate and Hui Province’s top science student, had published a paper in IHES stunned students, professors, and the wider public. The story left the mathematics community buzzing as the news spread across social media and reached the trending searches.

• Netizens reacted with disbelief to USTC High School’s post about Xiao Yi’s IHES paper, then confirmed the announcement on the school’s official account.
• Luo Xiao shared the post in the Joint Examination Group, and Chen Lue and Lu Ping connected the paper’s author to USTC’s Xiao Yi.
• Professor Liu Min and other faculty members learned about the paper, and Tsinghua’s mathematical sciences faculty group erupted with questions.
• The news spread through China’s mathematics community and reached Weibo’s trending searches.
• Math and Physics Events confirmed with IHES that Xiao Yi had written the paper, noting that he was seventeen and had scored 741 on the Gaokao.

News of seventeen-year-old Yi Xiao’s paper spread from China to the international mathematics community, where Peter Scholze and Jacob Stix discussed how it had helped their work on Shinichi Mochizuki’s IUTT papers and the abc conjecture. After Gerd Faltings told them the paper was online and revealed that Yi Xiao had just finished the college entrance exam, Scholze and Stix were stunned.

• Yi Xiao’s paper became a top-ten Weibo trending topic, drawing astonished comments from mathematics students and ordinary netizens.
• At the Max Planck Institute for Mathematics, Peter Scholze explained ideas from Shinichi Mochizuki’s IUTT papers to Jacob Stix, and Stix agreed they had identified a key point.
• Scholze said they were close to proving the abc conjecture remained unproven and hoped to speak with the paper’s author, Yi Xiao, though he could not find that name in the University of Science and Technology of China listings.
• Gerd Faltings arrived and told Scholze and Stix that IHES had put Yi Xiao’s paper online.
• Scholze planned to invite the author to a mathematics conference, and Faltings revealed that Yi Xiao was seventeen, had just completed the college entrance exam, and would soon attend the University of Science and Technology of China.
• Scholze and Stix were stunned by Yi Xiao’s age and circumstances.

Peter Schultz, Gerd Faltings, and Jakob Stix discussed seventeen-year-old Xiao Yi’s mathematical paper and hoped to persuade Shinichi Mochizuki to leave his work on the abc conjecture. Schultz then wrote Xiao Yi an invitation to a Max Planck Institute mathematics conference on September 13.

• Faltings told Schultz that seventeen-year-old Xiao Yi had published a remarkable paper in IHES, astonishing Schultz.
• Schultz said he welcomed younger mathematicians who might surpass him, and Faltings hoped they would produce work he could discuss with Grothendieck.
• Faltings criticized his former student Shinichi Mochizuki’s work on the abc conjecture but hoped Schultz and Stix could convince him to return to Far Abelian Geometry.
• Schultz announced that the conference would take place on September 13 and decided to invite Xiao Yi.
• Schultz wrote Xiao Yi an invitation praising his paper and offering to reimburse all expenses for attending the conference.

After receiving Peter Scholze’s invitation to a mathematics conference about the abc conjecture, Xiao Yi traveled to USTC to register for the new semester. There, Professor Liu Bin showed him a letter from Scholze confirming the invitation, leaving the graduate students amazed.

• Xiao Yi read Peter Scholze’s email inviting him to a September 13 conference in Germany and decided to attend, despite the trip coinciding with freshman military training.
• Xiao Yi spent the following days studying the abc conjecture and Shinichi Mochizuki’s paper so he could follow the conference discussions.
• On September 4, Xiao Yi arrived at USTC to register and learned that Professor Liu Bin wanted to see him.
• The Mathematics Department upperclassmen recognized Xiao Yi as a scholar, told him his registration had been arranged, and asked him for autographs.
• Professor Liu showed Xiao Yi a letter from Peter Scholze inviting him to the conference, and the graduate students were astonished.