Chapter Summaries

After Han Mengqi’s graduation thesis was published, Lu Zhou advised her on choosing between work and doctoral study. She decided she wanted to study Mathematics with him.

• Han Mengqi told Lu Zhou that her graduation thesis had been published in INTERNATIONAL-MATERIALS-REVIEWS.
• Lu Zhou asked Han Mengqi whether she planned to pursue a PhD or find a job and explained the difference between master's and doctoral research.
• Han Mengqi asked whether Lu Zhou ever faced problems beyond his abilities, and he mentioned unresolved personal matters before changing the subject.
• Lu Zhou recommended several Computational Materials Science fields if Han Mengqi wanted to continue in research.
• Han Mengqi declared that she wanted to study Mathematics with Lu Zhou.

Han Mengqi asked Lu Zhou to let her switch from computational materials science to pure mathematics, and he tested her resolve with a difficult problem. She left determined to solve it, while Lu Zhou explained that her answer would help decide whether she had the talent for the field.

• Han Mengqi told Lu Zhou she wanted to study pure mathematics because she had never liked chemistry and had chosen her current path after being reassigned and recruited into his program.
• Lu Zhou accepted that her interest mattered but warned that pure mathematics demanded substantial talent and offered her a place in his doctoral program if she passed an exam.
• Lu Zhou gave Han Mengqi two months to prove that ζ(2n) was transcendental, and she insisted she would solve it within one month.
• After Han Mengqi left with the problem, Lu Zhou asked He Changwen how many approaches he could devise and said the challenge would test whether she had a future in pure mathematics.

Lu Zhou prepared for his next push in mathematics while managing Jin University's Youth's Light class, then received an invitation to lecture at the 2022 International Congress of Mathematicians in Saint Petersburg. He accepted in principle and ended the chapter reminiscing about his former life at Princeton.

• Lu Zhou assigned Han Mengqi a problem about the transcendence of Riemann zeta values at odd positive integers, partly to discourage her.
• Lu Zhou reviewed the Youth's Light class meeting minutes and asked He Changwen to prepare an undergraduate discussion class.
• Lu Zhou received an email from IMU inviting him to give a 60-minute lecture at the 2022 International Congress of Mathematicians.
• Lu Zhou replied that he would attend Saint Petersburg barring unforeseen circumstances and submit his lecture content if he could go.
• Lu Zhou looked out his office window and thought about his past life and friends at Princeton.

At Princeton, Vera and Molina corrected a calculation and found that their work only reproved the existing result that 40% of the nontrivial zeros lay on the critical line. As Molina admitted her exhaustion and teased Vera about Lu Zhou, the two left their research session with their ambitions and feelings unresolved.

• Vera pointed out an error in Molina's equation, and Molina recognized that the Odlyzko Zero-Calculation Method could correct it.
• Vera explained that the revised calculation reproved the Conrey Critical Line Theorem, showing that 40% of the nontrivial zeros lay on the critical line.
• Molina wondered whether Annals of Mathematics might accept their paper and considered shifting her research toward Sir Atiyah's notes.
• Vera urged Molina to rest, and Molina admitted she had begun studying Sir Atiyah's papers despite her exhaustion.
• Molina asked why Vera remained attached to Lu Zhou, and Vera said he had given her Guangming when she was helpless.
• Molina nearly fell from exhaustion, let Vera catch her, then joked that Vera could marry her before leaving with the papers.

Lu Zhou reviewed a paper proving the Conrey Critical Line Theorem and discovered that its authors were Molina Abel and his student Vera Pulyuy. Senior Brother Luo Wenxuan returned from CERN with the engineering plan for the Lunar Hadron Collider, leaving Lu Zhou to ask about his time there.

• Lu Zhou reviewed and accepted an Annals of Mathematics paper about the Conrey Critical Line Theorem.
• Lu Zhou searched arXiv and discovered that Molina Abel and Vera Pulyuy had written the paper.
• Luo Wenxuan arrived back from CERN and gave Lu Zhou the engineering plan for the Lunar Hadron Collider.
• Luo Wenxuan described the collider’s engineering challenges, and Lu Zhou said he had a way to solve the lunar tunnel problem.
• Lu Zhou asked Luo Wenxuan how things had gone at CERN.

Luo Wenxuan told Lu Zhou about his CERN visit, where Chinese-language clubs had become popular as scholars prepared to work with the Moon Palace spacecraft’s Chinese research materials. He also passed along Frank Wilczek’s question about the 750 GeV signal, and Lu Zhou promised to settle it with the Lunar Hadron Collider.

• Luo Wenxuan described how CERN had offered engineering support and visiting places for Hua Nation’s lunar collider project in hopes of future research cooperation.
• Luo Wenxuan told Lu Zhou that many of his old CERN colleagues had left, and Lu Zhou comforted him by noting that new researchers replaced them.
• Luo Wenxuan said Chinese-language clubs had become fashionable at CERN because Moon Palace’s official working language and research materials were in Chinese.
• Luo Wenxuan passed along Frank Wilczek’s regards and said CERN’s latest experiment had found no 750 GeV signal even at one-sigma confidence.
• Lu Zhou promised to give Frank Wilczek a definitive answer about the signal after the Lunar Hadron Collider was built.

Molina warned Vera that Lu Zhou was probably uninterested in romance, while Luo Wenxuan asked Lu Zhou to help him get closer to Kong. Lu Zhou offered advice about attracting women, and a woman abruptly claimed he had gone to a horror movie with a girl.

• Molina received an acceptance recommendation for her research paper and told Vera that Lu Zhou was likely uninterested in romance.
• Molina warned Vera that marrying someone like her would make his life miserable, and Vera asked why.
• Luo Wenxuan visited Lu Zhou's office and later asked him to arrange a mixer so he could get closer to Kong.
• Lu Zhou refused to organize a mixer and advised Luo Wenxuan to attract women instead of chasing them.
• Luo Wenxuan asked whether Lu Zhou had ever gone to the movies with a girl, and an unidentified woman answered that he had gone to a horror movie.

Chen Yushan visited Lu Zhou in the cafeteria, told him BYD had gifted him a one-of-a-kind electric car, and asked him to attend a Russian delegation’s visit to his company. She left him wondering why she found his supposed hobby of barbecue rice bowls so amusing.

• Chen Yushan found Lu Zhou in the cafeteria and teased him about whether he had missed her.
• Chen Yushan offered Lu Zhou a customized Purple Lightning Max from BYD, which he eagerly accepted.
• Chen Yushan explained that the car was a gift from BYD in thanks for their Lithium-Sulfur Battery partnership and said it would arrive within a week.
• Chen Yushan told Lu Zhou that a Russian Ministry of Economic Development delegation would visit his company in two days and asked him to attend.
• Chen Yushan asked Lu Zhou about his hobbies, and he named barbecue rice bowls, making her laugh.

Lu Zhou discovered that the titanium-alloy side mission had been completed and considered the remaining lunar objectives. After an awkward encounter with students in the restroom, he resumed his Number Theory class by introducing the Riemann Hypothesis.

• Lu Zhou taught his Number Theory class and saw a system notice that the titanium-alloy mission was complete.
• Lu Zhou reviewed the remaining lunar side missions and judged which ones might be achievable.
• Lu Zhou overheard two students discussing him in the restroom, then startled them and sent them back to class.
• Lu Zhou returned to his lecture and began teaching the Riemann Hypothesis.

Lu Zhou taught his students about the Riemann Hypothesis and the distribution of prime numbers, then accepted an invitation to set the final question for the national mathematics finals. He quickly wrote a problem involving the Riemann zeta function, which Dean Qin found intriguing.

• Lu Zhou explained the prime-counting function, the Prime Number Theorem, and the origins and importance of the Riemann Hypothesis to his class.
• A student asked how a mathematician who proved the Riemann Hypothesis would compare with Lu Zhou, and Lu Zhou said that person's mathematical achievements would stand at the pinnacle of the era.
• After class, Dean Qin told Lu Zhou that the Hua Nation Mathematical Society wanted him to set the final question for the national finals.
• Lu Zhou immediately wrote a question involving the Riemann zeta function and handed it to Dean Qin to pass along.
• Dean Qin wondered whether the competition students could solve it, then decided the problem seemed interesting and hurried to his office.

Lu Zhou reconsidered the connection between the Riemann Hypothesis and the prime-counting function, then shared his conjecture with Qin Yue. He left the conversation believing the final clue might lie in π(x) itself rather than in estimates for zeros on the critical line.

• While reviewing the history of the Riemann Hypothesis, Lu Zhou concluded that the key to solving it might lie in the prime-counting function π(x).
• Lu Zhou spent an hour developing his thoughts, then asked Lin Yuxiang to bring him dinner so he could continue working.
• After eating, Lu Zhou wrote up his ideas about ζ(s) and planned to post them on arXiv.
• Qin Yue video-called Lu Zhou after noticing a Riemann Hypothesis-related entry on his academic CV and asked whether he had found clues.
• Lu Zhou told Qin Yue that improving estimates for zeros on the critical line might not solve the hypothesis and suggested returning to π(x) for the final piece.

Lu Zhou uploaded a paper arguing that the current approach to the Riemann Hypothesis might not succeed, setting off a wave of discussion across the Mathematics world. As readers debated his claims, Han Mengqi struggled with a problem he had given her but resolved to prove it anyway.

• After speaking with Lu Zhou, Qin Yue worried that Lu Zhou's doubts about the approach to the Riemann Hypothesis could unsettle Analytic Number Theory, but he kept the conversation private.
• Lu Zhou uploaded his paper to arXiv, while Han Mengqi struggled to prove that ζ(2n) was transcendental and vowed to solve the problem.
• Lu Zhou checked the paper's early downloads and MathOverflow discussions, where mathematicians debated whether the existing approach could solve the Riemann Hypothesis.
• Lu Zhou went to sleep ahead of his meeting with the Russian delegation as discussion of his paper spread across academic forums and the Mathematics world.

Lu Zhou met Russian Economic Development Minister Grudjev and his delegation at Starry Sky Technology’s Aerospace Industrial Park. After touring the facilities, Grudjev praised Hua Nation’s aerospace achievements and sought closer cooperation.

• Lu Zhou traveled to the Aerospace Industrial Park and told Wang Peng he was considering buying a fully electric car with a range of over two thousand kilometers.
• Secretary Zhong Quan welcomed Lu Zhou and explained that Grudjev had been asking to meet him since arriving in Hua Nation.
• Lu Zhou met Grudjev and agreed to join Minister Yang in taking the delegation to visit the aerospace factories.
• Grudjev toured the park on foot, marveled at its scale, and praised Lu Zhou’s role in building the Moon Palace spacecraft.
• Lu Zhou modestly credited their achievements to standing on the shoulders of giants, and Minister Yang smoothed over Grudjev’s awkward response.

Lu Zhou showed the Russian delegation the Queqiao spacecraft and explained how Hua Nation planned to assemble it in orbit, leaving the visitors impressed by Starry Sky Technology’s capabilities. At a diplomatic banquet, he discussed aerospace development with Minister Grudjev and received an invitation to visit Russia.

• The Russian delegation marveled at the Queqiao spacecraft inside the Space Shuttle Assembly Center.
• Lu Zhou told Grudjev and Academician Kaufmann that the spacecraft would be launched in three sections and assembled in orbit, and explained its electric propulsion system.
• Minister Yang led the delegation to other companies in the Aerospace Industrial Park, which failed to match Starry Sky Technology’s capabilities.
• At the banquet, Lu Zhou told Grudjev that state planning had helped Hua Nation scale up its aerospace industry and that commercialization was its next challenge.
• Grudjev invited Lu Zhou to visit Russia, and Lu Zhou said he might travel to Saint Petersburg for the International Congress of Mathematicians.

Lu Zhou escaped the banquet and spent the evening discussing the Riemann zeta function with Victoria, Grudjev’s daughter. Victoria returned to her room exhausted after Lu Zhou abruptly left when inspiration struck, while Grudjev accepted that his matchmaking attempt had failed.

• Lu Zhou left the banquet hall and met Victoria on the hotel balcony, where they ordered drinks and introduced themselves.
• Victoria told Lu Zhou about her studies in economics and trade and her interest in his research, and he agreed to discuss it with her.
• Grudjev revealed that he had been pestering Lu Zhou at the banquet to create an opportunity for Victoria to meet him.
• After the banquet, Victoria told Grudjev that Lu Zhou had spent three hours discussing the Riemann zeta function before leaving, though he had paid her bill.
• Victoria wondered if she was ugly, and Grudjev concluded that she and Lu Zhou were not fated to be together.

Vera learned that Lu Zhou was researching the Riemann Hypothesis, while Molina encouraged her to pursue it so Lu Zhou would notice her. Professors Fefferman and Deligne discussed Lu Zhou’s approach and predicted he would develop a useful new method and attend next year’s International Congress of Mathematicians.

• Vera told Molina that Lu Zhou was researching the Riemann Hypothesis, and Molina worried he might solve it before them.
• Molina reminded Vera of her agreement with Lu Zhou about the Fields Medal and urged her to work hard on the conjecture.
• Professor Fefferman brought Lu Zhou’s arXiv paper to Professor Deligne and asked how Lu Zhou might make his Prime-Counting Function approach work.
• Professor Deligne said Lu Zhou might create a new method for the Riemann Hypothesis and predicted he would attend next year’s International Congress of Mathematicians.

Lu Zhou realized that proving the Riemann Hypothesis required a new mathematical tool and developed a strategy based on narrowing the Critical Strip. He decided to work in seclusion after recognizing that the approach would take more than one night to pursue.

• After leaving the banquet, Lu Zhou told Wang Peng that he was missing a tool and hurried home to work.
• Lu Zhou cleared his desk and spent the night considering how earlier mathematical breakthroughs had advanced difficult conjectures.
• Lu Zhou decided to approach the Riemann Hypothesis by first tackling its weak form and ruling out zeros outside the Critical Line.
• Lu Zhou identified the Critical Strip Method as a possible route, starting by pushing the right boundary of the strip leftward from Re(s)=1.
• Lu Zhou searched MathOverflow for useful discussion, found little, and texted Wang Peng that he would be in seclusion for a few days.
• Lu Zhou postponed his work to catch up on sleep after realizing that one night of inspiration would not be enough.

Lu Zhou used an algebraic curve over a finite field to complete a paper on the Quasi-Riemann Hypothesis and submitted it to Mathematical Annals. After a week in seclusion, he left home and announced that he needed to pick up his car before going for his physical examination.

• Lu Zhou gathered and studied papers on Algebraic Geometry, Étale Cohomology, and the Weil Conjecture during his retreat.
• Lu Zhou found an algebraic curve over a finite field that helped him complete his proof concerning nonzero trivial points of the Zeta Function in the region Re(s)≥1-ε.
• Lu Zhou typed up the paper with Xiao Ai's help and submitted it to Mathematical Annals, naming the problem the Quasi-Riemann Hypothesis.
• Yan Yan arrived at Lu Zhou's villa after he had ignored calls and stayed inside for a week, while Wang Peng explained that he had tried entering before and Lu Zhou would get angry.
• Lu Zhou came out of the house, postponed his physical examination, and told Wang Peng he wanted to pick up his car.

Lu Zhou picked up the one-of-a-kind Purple Lightning Max and took it for a brief drive before turning his attention to the online reaction to his Quasi-Riemann Hypothesis proof. The car drew attention when he arrived home, but residents put their phones away after recognizing him.

• Lu Zhou went to the dealership with Wang Peng to collect the Purple Lightning Max and asked to drive it before Wang Peng arranged its safety modifications.
• Lu Zhou had Wang Peng drive him around Purple Mountain, but he soon decided that mathematics interested him more than luxury cars.
• Lu Zhou checked MathOverflow and saw scholars debating his Quasi-Riemann Hypothesis proof, while Terry Tao said he was checking the calculations.
• Wang Peng drove Lu Zhou back to Zhongshan International, where onlookers who recognized him put away their phones instead of photographing him.

Lu Zhou returned home after Wang Peng took his one-of-a-kind electric sports coupe to register it, then checked the Mathematical Annals’ response to his paper on the critical strip. As Lu Zhou resumed his work, a new email arrived asking whether he was studying the Riemann Hypothesis.

• Wang Peng praised Lu Zhou’s sports coupe and went to register it while Lu Zhou walked home.
• Lu Zhou told Wang Peng to keep the car’s modifications reasonable, and Wang Peng promised to return it unchanged in appearance.
• Lu Zhou read an email from the Mathematical Annals saying his manuscript had entered peer review and that the editors were seeking a qualified reviewer.
• Lu Zhou considered Professor Faltings as a possible reviewer, then thanked Xiao Ai for bringing him coffee.
• A new email arrived asking Lu Zhou, “Professor, are you studying the Riemann Hypothesis?”