Chapter Summaries

Xiao Yi continued planning how to adapt his precision magnetic-levitation fluid control furnace for Project H-20 while proving the Hailstone Conjecture. After finishing the proof, he began preparing it for publication, and Liang Qiushi discovered that his teacher had solved the conjecture.

• Wang Changhong agreed to pursue using Xiao Yi’s precision magnetic-levitation fluid control furnace to synthesize TA1203, pending approval for Project H-20.
• Xiao Yi returned to Shanghai and worked on the furnace modifications while continuing his research on the Hailstone Conjecture.
• By mid-May, Xiao Yi completed a proof of the Hailstone Conjecture and concluded that every positive integer eventually entered the 4-2-1 cycle.
• Xiao Yi began organizing his proof on his computer for his personal website.
• Liang Qiushi brought Xiao Yi his finished paper, saw the Hailstone Conjecture proof on the screen, and learned that Xiao Yi had solved it.

Xiao Yi approved Liang Qiushi’s paper proving the inhomogeneous Baker-Sprindzuk Conjecture and uploaded his own paper proving the Hailstone Conjecture. News of Xiao Yi’s achievement spread through Chinese mathematics circles and began reaching overseas, setting off another international stir.

• Xiao Yi reviewed Liang Qiushi’s paper, confirmed that it met the graduation requirements, and told him to prepare for his defense.
• Liang Qiushi told Xiao Yi that he would marry Chen Chunhua on August 8 and asked about Xiao Yi’s paper on the Hailstone Conjecture.
• Xiao Yi finished and uploaded his Hailstone Conjecture paper to his personal website that night.
• Liang Qiushi found the paper while out with Chen Chunhua, explained the conjecture, and shared the news in mathematics-related groups.
• Chinese mathematics scholars confirmed that Xiao Yi had published a proof using Representation Theory, and news of the result spread toward the international mathematical world.

After Xiao Yi published a proof of the Hailstone Conjecture using Representation Theory, Terence Tao read the paper and praised its proof and its contribution to the Langlands Program. Tao posted a review declaring the conjecture proved, and the mathematical world discussed Xiao Yi’s latest achievement.

• News spread that Xiao Yi had solved the Hailstone Conjecture, while Xiao Yi slept through the late-night discussions.
• Terence Tao learned of the proof, downloaded Xiao Yi’s paper, and discovered that it used Representation Theory to approach the conjecture.
• Terence Tao recognized the paper’s connection between Diophantine theory and Representation Theory as a major contribution to the Langlands Program.
• Terence Tao finished reading the proof, found no errors, and published a blog post praising Xiao Yi’s methods and declaring the Hailstone Conjecture proved.
• Mathematicians discussed Tao’s review and debated whether anyone could stop Xiao Yi from solving more problems.

After proving the Hailstone Conjecture, Xiao Yi received approval to support Project H-20 with his precision magnetic levitation fluid-control furnace. He introduced the furnace to Wang Changhong and the authorized researchers, then began planning its development at the Jinling institute.

• Cody Brian told Steven Cowley that Xiao Yi had proved the Collatz Conjecture, and Cowley cursed over the contrast with JNEO’s stalled progress.
• The president called Cowley to demand updates on JNEO and complained that Xiao Yi’s achievements made America look bad; Cowley said Xiao Yi was exceptional.
• The president asked the Secretary of State about the mission in China, and the Secretary of State reported that it had made little progress.
• Xiao Yi told Director Liu that Project H-20 should proceed and endorsed the precision magnetic levitation fluid-control furnace’s potential to create stronger materials.
• The higher-ups formally approved Xiao Yi’s cooperation with Project H-20, and he traveled to the Jinling research institute to meet Wang Changhong and the team.
• Xiao Yi explained the furnace to the authorized researchers, agreed to modify it and write its program, and heard Wang Changhong mention the June 24 science and technology awards conference.

Xiao Yi welcomed Luo Mingya to Science Island Laboratory to study the precision magnetic levitation fluid control furnace, while his three students graduated and settled their PhD plans. At the National Science and Technology Awards Conference in Shangjing, Xiao Yi and more than two hundred Sun-Making Plan contributors gathered, poised to receive recognition together.

• Xiao Yi welcomed Luo Mingya to Science Island Laboratory, where she planned to learn about the precision magnetic levitation fluid control furnace and share her notes with Li Zhenhai's team.
• Xiao Yi's students Sun Yuan, Chen Muhua, and Liang Qiushi passed their graduation defenses with praise from a panel of academicians.
• Sun Yuan chose to study Theoretical Physics at the University of Cambridge, Chen Muhua chose Mathematics at Princeton University, and Liang Qiushi asked to pursue a PhD under Xiao Yi.
• Xiao Yi gave Sun Yuan and Chen Muhua recommendation letters and told Liang Qiushi that his own letter would depend on his PhD performance.
• On June 24, Xiao Yi and more than two hundred Sun-Making Plan contributors took their seats at the National Science and Technology Awards Conference in Shangjing.

At the National Science and Technology Awards Conference, Xiao Yi received the State Supreme Science and Technology Award for his scientific achievements and leadership of the successful fusion project. The ceremony then honored the Sun-Making Plan, awarding Xiao Yi the Sun Medal and recognizing the project’s other contributors.

• Li Jiangan told Xiao Yi that construction of their reactor foundation was complete and estimated the reactor would be finished in about nine months.
• The conference announced Xiao Yi as the first recipient of the State Supreme Science and Technology Award, citing his breakthroughs in mathematics, physics, and commercial nuclear fusion.
• An elder leader presented Xiao Yi with the award medal and certificate, then invited him to sit on the podium and present awards to other recipients.
• The host described the Sun-Making Plan’s successful fusion power generation and announced the plan’s special commendations.
• Xiao Yi received the Sun Medal for his leadership and outstanding contributions to the Sun-Making Plan.
• Li Jiangan, Zhao Zhanyou, eighteen other principal contributors, and more than two hundred plan members received the Solar Ring Medal and Sun Creation Medal.

After the Sun-Making Plan team received their Sun Creation Medals and the awards ceremony ended, Xiao Yi became the focus of public attention and celebrated with the team at a banquet. He got drunk and was taken back to his hotel room, where Luo Mingya came to look after him while Wang Li left them alone.

• The old leader and Xiao Yi presented Sun Creation Medals to all 225 members of the Sun-Making Plan, and the old leader pinned the final medal on Xiao Yi.
• News of the awards ceremony spread, and netizens discussed Xiao Yi's State Supreme Science and Technology Award and the designs of the Sun, Solar Ring, and Sun Creation Medals.
• At the official banquet at Diaoyutai State Guesthouse, Xiao Yi drank heavily while celebrating with the team and became drunk.
• Wang Li helped Xiao Yi back to the hotel, where Luo Mingya arrived with Hangover Relief Oral Liquid and told Wang Li to let her care for him.
• Wang Li left to find Hangover Tea, privately hoping Xiao Yi would take the opportunity to get closer to Luo Mingya.

After getting drunk, Xiao Yi lost the study BUFF and spent its seven-day cooldown adjusting to his ordinary thoughts, while Wang Li revealed that his superiors had asked him to help bring Xiao Yi and Luo Mingya closer. When Xiao Yi’s slower responses alarmed researchers and leaders, they brought him to Shangjing for examinations; he waited at the sanatorium, expecting the BUFF to return the next morning.

• Xiao Yi woke with a headache, realized oversleeping had ended his study BUFF, and found Luo Mingya had watched over him while Wang Li was away.
• Xiao Yi confronted Wang Li, who explained that his superiors had asked him to create an opportunity for Xiao Yi and Luo Mingya to grow closer; Xiao Yi called the leaders and told them not to interfere.
• Xiao Yi spent several days without the BUFF and grew comfortable with being able to relax, though Luo Mingya noticed his distracted behavior and slower responses.
• Luo Mingya told Li Zhenhai and the other researchers that Xiao Yi had been in poor condition since drinking, and they informed Wang Changhong and the leaders.
• The leaders brought Xiao Yi to Shangjing for medical examinations, but doctors found nothing wrong and could not explain his condition.
• Xiao Yi stayed at the Peking Union Medical College Sanatorium and planned to sleep ten hours before his BUFF cooldown ended the next morning.

Xiao Yi recovered his usual absolute rationality, returned to Science Island Laboratory, and resumed teaching Luo Mingya while preparing to develop TA1203. Three months later, his new control furnace produced material that exceeded expectations, bringing Project H-20 closer to flight.

• Xiao Yi refused further examinations, left the sanatorium, and returned to Science Island Laboratory, where his colleagues welcomed him back.
• Xiao Yi resumed teaching Luo Mingya and said he would soon design a control furnace for producing turbine-blade-sized components and then develop the TA1203 program.
• Luo Mingya agreed to stay at the laboratory and continue learning from Xiao Yi.
• Xiao Yi completed the new precision magnetic levitation fluid control furnace design, and the classified factory began producing it.
• Three months later, researchers tested the first TA1203 sample and found it could withstand 1303 degrees Celsius while its coefficient of thermal expansion had improved by around 50 percent.
• Xiao Yi told Wang Changhong the mission was accomplished, and Wang Changhong ordered the team to manufacture the blades, modify the engines, and prepare Project H-20 for flight.

Project H-20’s WS-20S engine passed testing with record-breaking thrust and temperature figures, and later estimates gave the H-20 exceptional speed and range. After deliberately leaking fabricated lower performance numbers, China sparked alarm among foreign leaders, including the US president, who debated how to respond.

• Wang Changhong and Xiao Yi watched the WS-20S engine reach a turbine inlet temperature of 2,027 degrees, 26 tons of thrust, and a 16:1 thrust-to-weight ratio during its test at the JF-22 base.
• Wang Changhong thanked Xiao Yi for helping resolve the turbine blade material problem, and the team began compiling test data and tuning the engine.
• Further tests and calculations suggested the upgraded H-20 could reach Mach 2.5, fly up to 19,000 kilometers, and remain airborne for as long as 30 hours.
• News of the WS-20S’s supposed 23 tons of thrust and 13.8:1 thrust-to-weight ratio spread through aviation circles, prompting rumors about Xiao Yi’s involvement.
• The US president and his advisers assessed the leaked figures as likely real, and the president asked whether they should fight China directly.

The United States condemned China’s powerful new engine as foreign and Chinese netizens reacted to the leak, while China celebrated its technological and economic gains. Xiao Yi and Luo Mingya later walked together at Science Island Laboratory, and Wang Li wondered whether he could use their closeness to test if Xiao Yi was human.

• The President considered starting a war over China’s technological advances, but the secretary of state persuaded him to focus on developing American technology instead.
• The United States condemned China’s new engine, and China’s defense ministry confirmed figures exceeding the leaked specifications as netizens debated its capabilities.
• China celebrated National Day amid rapid growth around Fei City, while news coverage predicted that China could surpass the United States in GDP by 2029.
• Xiao Yi again missed the Nobel Prize, and netizens mocked the awards after the American President received the Peace Prize despite reportedly wanting to start a war.
• Xiao Yi and Luo Mingya discussed her new research project and funding during a walk, while Wang Li watched and wondered how to determine whether Xiao Yi was human.

Xiao Yi debated whether to pursue theoretical mathematics or applied technology before teaching a class on prime distribution and analytic continuation. While demonstrating a new explanation using elliptic curves, he realized it might help transform the Riemann Hypothesis into an algebraic geometry problem.

• Xiao Yi walked alone along Shushan Lake and weighed whether to focus on theoretical research or practical technology.
• Xiao Yi went to USTC and answered mathematics questions from students before his number theory class.
• Xiao Yi taught the students about prime distribution, the Prime Number Theorem, and the role of the Riemann zeta function.
• Xiao Yi explained analytic continuation using elliptic curves, modular forms, and L-functions.
• Xiao Yi realized his explanation might let him recast analytic continuation, and possibly the Riemann Hypothesis, as an algebraic geometry problem involving elliptic curves.

Xiao Yi taught his students about the Riemann Hypothesis and the distribution of prime numbers, then developed a new approach combining elliptic curves and modular forms. He began considering whether the Geometric Langlands Conjecture could take the method further and lead him toward a proof of the Riemann Hypothesis.

• Xiao Yi explained the Riemann Hypothesis, its use in estimating prime distributions, and why mathematicians seek proof rather than simply assuming it is true.
• Xiao Yi joked that he would prove the Riemann Hypothesis tomorrow, then told his students he had no plans to study it for now.
• While answering students' questions, Xiao Yi explored using elliptic curves for analytic continuation and considered combining them with Riemann surfaces before turning to modular forms.
• Xiao Yi taught a second class on methods for studying prime distributions and reminded students that their midterm exam was the following week.
• Xiao Yi refined his approach into a method he named Elliptic Inverse Analytic Continuation and combined it with modular forms.
• Xiao Yi considered using the Geometric Langlands Conjecture with his new methods, sensing that the idea might lead toward proving the Riemann Hypothesis.

Xiao Yi expanded his Elliptic Inverse Analytic Continuation method while his recorded lecture introduced it to mathematicians at Princeton. Manuel Balgava and Andrei Okounkov recognized its potential for studying the Riemann Hypothesis, leaving Chen Muhua and Sanjay Khan reflecting on their plans to return to their home countries.

• Xiao Yi researched extending Elliptic Inverse Analytic Continuation using modular forms and the geometric Langlands Program.
• Chen Muhua watched Xiao Yi’s lecture with Sanjay Khan and explained the new method to him and the students in their lab.
• Manuel Balgava and Andrei Okounkov entered the lab, examined Chen Muhua’s blackboard, and learned the equations came from Xiao Yi’s lecture.
• Manuel Balgava and Andrei Okounkov discussed how the method might help researchers study the Riemann Hypothesis by combining it with modular forms and the Taniyama-Shimura theorem.
• Sanjay Khan told Chen Muhua he planned to return to India to teach, and Chen Muhua said he would return to China because it was his homeland.

Princeton mathematicians formed the Prime Pioneer Program to pursue the Riemann Hypothesis using Xiao Yi’s Elliptic Inverse Analytic Continuation method, drawing worldwide attention and setting up a supposed contest with Xiao Yi. Xiao Yi responded by publishing a paper that laid out his current work on the method, while continuing to reject interview requests.

• Manuel, Andrei Okounkov, Peter Sarnak, and other Princeton mathematicians spent two days discussing how Xiao Yi’s method could aid a proof of the Riemann Hypothesis, then agreed to form a team.
• The mathematicians invited others to join the Prime Pioneer Program, including Terence Tao and Peter Scholze, and their collective effort became a major news story.
• Xiao Yi learned that Princeton’s team had been inspired by his method, rejected requests for interviews, and warned his university students to focus on their midterm exams.
• Luo Mingya asked Xiao Yi why he had not responded to the team, and Xiao Yi showed her the paper he had uploaded, titled “Elliptic Inverse Analytic Continuation and Extended Applications.”
• Xiao Yi said he had published his current research so both sides could start from the same point and rely on their own abilities.
• Wang Hao told Xiao Yi that Anhui Television wanted an interview, and Xiao Yi ordered him to reject every interview request about the Riemann Hypothesis.

Xiao Yi’s paper on Elliptic Inverse Analytic Continuation drew attention, and many interpreted it as his answer to the Prime Pioneer Program’s challenge. At Princeton, Terence Tao and the other mathematicians took it as a sign that Xiao Yi had accepted the contest and prepared to pursue the Riemann Hypothesis.

• Xiao Yi published a detailed paper explaining Elliptic Inverse Analytic Continuation, without directly mentioning the challenge.
• Liang Qiushi posted online that Xiao Yi’s paper was effectively an acceptance of the challenge, and his answer gained widespread attention.
• Xiao Yi summoned Liang Qiushi, warned him not to answer questions about him online, and said no problem was unsolvable if it was understood thoroughly enough.
• At Princeton, James Maynard asked whether Xiao Yi had responded, and Terence Tao suggested that the new paper was his response.
• The Prime Pioneer Program members agreed to work harder on proving the Riemann Hypothesis, while Faltings said he hoped to see it solved in his lifetime.

The U.S. president visited Princeton to rally the Prime Pioneer Program and declared that American mathematicians would defeat Xiao Yi in the race to prove the Riemann Hypothesis. Meanwhile, Xiao Yi used Elliptic Inverse Analytic Continuation to pursue the Artin Conjecture as a possible route toward the Riemann Hypothesis, and the mathematical contest continued.

• The U.S. president praised the Prime Pioneer Program at Princeton and promised government support, while declaring that its mathematicians would surpass Xiao Yi.
• Terence Tao criticized the president for turning mathematics into politics and encouraged Xiao Yi to succeed.
• Wang Hao teased Xiao Yi about dating, and Xiao Yi returned to studying the Riemann Hypothesis.
• Xiao Yi found that Elliptic Inverse Analytic Continuation could connect the Artin Conjecture to the Riemann Hypothesis and began developing a proof approach.
• Xiao Yi chose the Langlands correspondence as his angle for studying the Artin Conjecture, as mathematicians continued their long effort to solve the major conjectures.

China’s nuclear fusion expansion continued to boost the economy while JNEO struggled to develop a suitable reactor material. In the Riemann Hypothesis race, Terence Tao proposed connecting Xiao Yi’s work to the Artin Conjecture, leaving the Prime Pioneer mathematicians wishing Xiao Yi could join them.

• Nuclear fusion’s economic effects became clear in Fei City and nearby regions as China’s new reactors neared completion, while JNEO remained unable to find a suitable first-wall material.
• Media outlets mocked Xiao Yi for publishing only one recent paper, but Prime Pioneer mathematicians dismissed their criticism as uninformed.
• At a Prime Pioneer discussion, Terence Tao proposed using Elliptic Inverse Analytic Continuation and the Artin Conjecture to help prove the Riemann Hypothesis.
• Deligne, James Maynard, and Bombieri judged Tao’s approach promising but extremely difficult, and Tao suggested Xiao Yi might be the only person willing to pursue it.
• The discussion ended without another proof idea, and the mathematicians wished Xiao Yi could join their team.

During New Year celebrations, Xiao Yi’s parents teased him about marriage and learned that he was close to Luo Mingya, a researcher at his laboratory. After fleeing an awkward dinner with their neighbors, Xiao Yi made progress on an extended L-function that might help him approach the Weil Conjecture, but his mother called him to dinner before he could continue.

• At New Year’s Eve dinner, Xiao Yi told his parents he was focused on the Riemann Hypothesis, and they questioned him about finding a partner and his relationship with Luo Mingya.
• Several days later, Mother Xiao invited their elderly neighbor and Sun Lina over, and the neighbor revealed that Luo Mingya was her niece and worked at Xiao Yi’s Science Island Laboratory.
• Xiao Yi escaped to his room when the women began discussing Luo Mingya, then turned to his research to distract himself.
• Xiao Yi used p-adic étale cohomology to construct an extended L-function and analytically continued it across the complex plane.
• Xiao Yi found that the new L-function was connected to the Weil Conjecture for an elliptic curve, but encountered technical obstacles before his mother called him to dinner.

Xiao Yi struggled to connect his extended L-function to a geometric object so he could use the Weil conjecture to prove the Artin Conjecture. At Science Island Laboratory’s amusement-park outing, the roller-coaster tracks sparked new ideas about modular curves, though the ride interrupted his thinking before he could develop them.

• After the New Year, Xiao Yi focused on teaching and researching the Artin Conjecture, but remained stuck on identifying a geometric object linked to his extended L-function.
• Xiao Yi arranged a weekday team-building outing for Science Island Laboratory at Sunac Land, where researchers and their families split into groups to enjoy the park.
• Luo Mingya joined Xiao Yi at the amusement park, and Qian Wanli brought his wife and daughter, Qian Huiyin, to meet him.
• On the roller coaster, Xiao Yi compared its tracks to ellipses and began imagining an amusement park of modular curves, prompting new ideas about the geometric object he sought.
• The roller coaster began its descent before Xiao Yi could pursue his thoughts, and Luo Mingya grabbed his hand as the riders screamed.