Chapter Summary: Stock Market Risks

Key Plot Points

• Lu Zhou, Chen Yushan, and Han Mengqi finish their cold drinks; Chen Yushan leaves for a meeting, and Lu Zhou walks back with Han Mengqi
• Lu Zhou plans to email Sarot, offering him a laboratory in Hua Nation or help finding a new employer if he declines—parting on good terms despite their differences
• Scene shifts to the Haizhou Demonstration Reactor Base, where staff have become idle after the project's conclusion
• East Asia Power begins a public stock offering: 2 billion shares at 10 yuan each (20 billion yuan total), with employee purchase limits
• Zhang Xueqian wants to buy 100,000 shares but is capped at 3,000; Su Yiwen also subscribes
• Discussion reveals that fusion reactors and electric vehicle adoption are reshaping energy policy and the economy

Character Developments

• Lu Zhou: Shows pragmatism and generosity—willing to help Sarot despite their friction; reveals a thoughtful, slightly lonely side in his assessment of friendship
• Han Mengqi: Curious about Lu Zhou's feelings toward Chen Yushan; feels sympathy for him after his answer
• Zhang Xueqian: Displays hidden wealth and sharp economic insight—understands government policy and long-term trends, eager to invest
• Su Yiwen: Risk-averse but pragmatic; pretends to complain while holding tightly to his shares

Significant Themes

• Economic transformation: Fusion energy will drive down electricity costs, accelerate electric vehicle adoption, and force oil price adjustments—phasing out gasoline cars is inevitable
• Macroeconomic regulation: Government uses policy to redirect markets (fuel taxes, new energy subsidies, standardized battery swapping)
• Investment opportunity: The stock offering is seen as a rare chance to profit; employee caps create scarcity
• Friendship and loneliness: Lu Zhou's answer that Chen Yushan is one of his few real confidants underscores the isolation of his position

Character Interactions

• Chen Yushan warmly bids farewell, promising to visit Han Mengqi's aunt; she seems revitalized since moving to Shanghai
• Han Mengqi hesitantly asks Lu Zhou what he thinks of Chen Yushan "in that sense"; his honest answer leaves her feeling sorry for him
• Su Yiwen and Zhang Xueqian debate oil prices and government policy, with Zhang revealing insider-level insight into economic planning
• Section Chief Wang distributes subscription forms matter-of-factly; both Zhang and Su immediately sign up once they understand the opportunity

Summary: "Getting a Bargain Wasn't That Easy"

1. Key Plot Points and Events

• East Asia Power's stock issuance: The chapter opens with the aftermath of East Asia Power issuing shares to the public. The shares are divided into three portions: one for the STAR Demonstration Reactor project team, one for banks and social security funds, and one public portion.
• The reality of public offerings: Ordinary people effectively have no chance to buy the stock. Private equity funds use supercomputers and high-speed internet to snatch up shares the moment they're released, leaving little for the general public.
• Haixiang Capital's poor result: After deploying a supercomputer and working overtime, Haixiang Capital's general manager Li Xiang discovers they only secured qualifications for 20,000–30,000 shares—a paltry amount for a fund managing tens of millions.
• The shareholder list revelation: The top ten shareholders are announced. The "national team" (SASAC, Three Oil Giants, State Grid, social security funds) controls over 80%. However, a mysterious company called Starry Sky Technology holds 7% of East Asia Power, shocking Haixiang Capital's team.
• Financial circle buzz: Nearly half the domestic financial world is trying to figure out where Starry Sky Technology came from. Overseas capital has also noticed. Li Xiang orders an investigation into the company's background.
• Lu Zhou's morning at Jinling University: Doctor Yan Yan delivers physical examination results for Lu Zhou's three assistants. Lu Zhou reviews a student's (Liu Siyuan) completed assignment, answers an email from Qin Yue (a lecturer at Princeton) about Analytic Number Theory, and checks arXiv for research updates.
• The chapter's cliffhanger: Lu Zhou receives an unexpected email from Professor Sarot, whose content stuns him: "[I was summoned for questioning by the FBI.]"

2. Character Developments

• Lu Zhou: Remains largely detached from the financial chaos his patent management company (Starry Sky Technology) has caused. He is focused on his academic work, mentoring students, and corresponding with colleagues. His calm demeanor contrasts sharply with the frenzied financial world.
• Li Xiang (Haixiang Capital GM): Growing increasingly frustrated and desperate. His reaction to losing out on the stock allocation—and to Starry Sky Technology's sudden appearance—reveals both his ambition and his willingness to use intimidation ("If it had no real backing... he would not mind having a talk with him").
• Yan Yan (Doctor Yan): Shows a subtle personal interest in Lu Zhou, hesitating as she considers inviting him to lunch but ultimately deciding not to. Her curiosity about his young assistants suggests some wariness or observation.
• Liu Siyuan (student): Demonstrates strong work ethic and dedication, arriving early with completed work because he feels pressure to "keep up."

3. Significant Themes

• Financial inequality and access: The chapter highlights how ordinary people rarely benefit from valuable investment opportunities—the "soup" is drained by insiders and connected funds before the public even sees it.
• The murky world of finance: The use of "white gloves," private placements, and backdoor deals is presented as normal practice. Starry Sky Technology's 7% stake is legal but opaque, raising questions about how it was obtained.
• The contrast between academia and finance: Lu Zhou's quiet, intellectual world in Jinling University stands in stark opposition to the cutthroat, high-stakes maneuvering of the financial sector.
• The reach of state power: The FBI questioning hinted at the end suggests that even Lu Zhou's academic work is not beyond the scrutiny of government institutions.
• The "national team" dominance: The state's overwhelming control of East Asia Power (80%+ of shares) underscores themes of state capitalism and monopoly power.

4. Character Interactions

• Li Xiang, Tang Guang, and Secretary Zhang: The Haixiang Capital team reacts to their poor allocation results. Tang Guang voices outrage at Starry Sky Technology's 7% stake, while Secretary Zhang speculates about its background. Li Xiang orders an investigation, showing his authoritative leadership style.
• Yan Yan and Lu Zhou: A somewhat awkward interaction. Yan Yan delivers the physical exam reports, notes how young Lu Zhou's assistants are, and considers inviting him to lunch but leaves without doing so. Lu Zhou seems oblivious to her interest.
• Lu Zhou and Liu Siyuan: A brief but positive mentor-student exchange. Lu Zhou reviews Liu's work, offers suggestions, and lets him go. Liu's early arrival and eagerness to work reflect well on both of them.
• Lu Zhou's correspondence: He exchanges emails with Qin Yue (a former colleague at Princeton) about Analytic Number Theory and receives the shocking email from Professor Sarot about FBI questioning.

Key plot points

• Chen Yushan advises Lu Zhou to sever ties with the Sarot Laboratory after its director is questioned by the FBI. She warns that investigators need not find real evidence; it could be fabricated.
• Lu Zhou decides to sell the laboratory and relocate its research and development work from North America, while retaining only the legal and management support needed to protect Starry Sky Technology’s patents there.
• The lab attracts eleven bids. Lu Zhou selects ExxonMobil and, with Chen’s help, raises its offer from $45 million to $50 million.
• He also secures the return of a Carbon Nanosphere patent from ExxonMobil for an extra $1 million. Woods agrees, considering the patent nearly worthless.
• At the Jinling Hilton, Lu Zhou and ExxonMobil CEO Woods sign the agreement. Woods appears delighted with the deal, while Lu Zhou jokes that he may have sold too cheaply.
• Lu Zhou informs Sarot that ExxonMobil is the laboratory’s new owner. Sarot replies with a brief, grateful “Thanks…”

Character developments and interactions

• Lu Zhou accepts that politics can no longer be kept separate from his research. Though the sale is emotionally complicated, he acts pragmatically to protect his work and personnel. His focus remains on research rather than personal leisure, even when Woods invites him for a drink.
• Chen Yushan takes a protective, practical role, urging Lu Zhou to reduce his exposure and helping him negotiate the sale. Their café conversation briefly turns awkward when she explains why she has switched from iced to hot coffee.
• Woods is an enthusiastic negotiator who initially resists returning the patent but quickly changes his mind when Lu Zhou offers more money. His cheerful reaction after signing suggests ExxonMobil believes it secured a favorable deal.
• Sarot is mostly absent from the negotiations, but his brief email conveys gratitude toward Lu Zhou for arranging the transition.

Significant themes

• Research under political pressure: Lu Zhou’s decision reflects the growing impossibility of insulating scientific work from geopolitical scrutiny.
• Pragmatism and self-protection: Selling the lab and relocating research are presented as necessary safeguards, not a rejection of the work itself.
• The uncertain value of knowledge: ExxonMobil sees the Carbon Nanosphere patent as nearly useless, while Lu Zhou’s insistence on reclaiming it hints that its true potential may be greater than the company realizes.

Key plot points

• In Shanghai, Haixiang Capital general manager Li Xiang learns from Chairman Wu that Starry Sky Technology has powerful backing. He abandons any plan to challenge or exploit the company.
• Deputy Manager Tang Guang proposes smearing Lu Zhou and triggering an investigation to disrupt the company’s funding and reclaim its share quota. Li Xiang angrily rejects the scheme, recognizing that neither he nor his firm could safely pursue it.
• Lu Zhou arrives at the Jinling Institute for Advanced Study to review results from tests of the lpc-1 reactor material at the Tianwan Nuclear Power Plant.
• The material withstands neutron irradiation well, but the tests expose a serious obstacle: a fusion reactor would generate more heat than a spacecraft could readily dissipate. In space, heat can escape only through radiation, and ordinary cooling panels would be inadequate.
• The researchers discuss whether slowing the fusion reaction could make heat transfer manageable, but no solution emerges. Lu Zhou ends the late-night meeting to consider the problem further.

Character developments and interactions

• Li Xiang shifts from contemplating a predatory move against Starry Sky Technology to fearful restraint. He reprimands Tang Guang for proposing a reckless smear campaign, then reflects that powerful backing makes the company untouchable.
• Tang Guang shows ambition and opportunism, suggesting a calculated attack on Lu Zhou’s reputation and finances. His confidence collapses when Li Xiang turns on him.
• Lu Zhou remains focused on research, carefully examining the disappointing test results and recognizing a possible direction in the idea of slowing the reaction.
• Sheng Xianfu explains the heat-dissipation challenge and dismisses cold fusion as an unrealistic answer for now. Professor Li Changxia raises the possibility of a slower reaction, prompting Lu Zhou to think more deeply about it.
• Wang Peng offers to wait while Lu Zhou works late; Lu Zhou accepts without making a fuss.

Significant themes

• Power and caution: Li Xiang’s predicament illustrates that people may be willing to act corruptly but dare not challenge forces beyond their reach.
• Ethics versus opportunism: Tang Guang treats slander as a business tactic, while Li Xiang recognizes the danger and refuses to proceed.
• Scientific progress and limits: Strong materials alone cannot solve fusion engineering; heat management remains a critical obstacle, especially in space.
• Persistence amid uncertainty: The researchers end without an answer, leaving Lu Zhou to seek a solution beyond the group’s current discussion.

Key plot points and events

• After emailing news that his lab had been sold to ExxonMobil, Professor Sarot drinks heavily. His assistant, Paul, tries to reassure him that the sale’s money and resources could be useful, but Sarot says Paul does not understand what is at stake.
• Sarot reflects that academic freedom changes when research begins to influence the world. He considers emigrating, perhaps to the Netherlands, and regrets not accepting a professorship at Utrecht years earlier.
• Lu Zhou’s Fusion Battery project has reached a serious bottleneck: the reactor core is too difficult to cool, and the team is questioning whether inertial confinement can make fusion compact enough for spacecraft.
• Reviewing research on thermoelectric conversion and spacecraft cooling gives Lu Zhou no practical solution. He suspects the obstacle is theoretical rather than engineering-related.
• While walking across campus, Lu recalls how earlier mathematical and physics breakthroughs enabled progress in controlled fusion. Near a classroom, he spots words on a blackboard that trigger a flash of inspiration, and he enters to investigate.

Character developments and interactions

• Sarot reveals disillusionment with the direction his work and career have taken. He values intellectual independence and is troubled by the consequences of research becoming part of larger forces. Paul’s well-meant reassurance cannot reach him.
• Paul tries to comfort Sarot and understand his distress, but Sarot’s comments about freedom and influence leave him confused.
• Lu Zhou grows frustrated as his research runs ahead of the available theory. Though he remains confident that he has chosen the right direction, he recognizes that engineering alone cannot overcome the barrier.
• Zhao Huan delivers Lu Zhou’s teaching schedule and notices his bad mood. Their brief exchange ends with Lu going out for a walk.

Significant themes

• Academic freedom and responsibility: Sarot questions whether scholars can remain free once their work begins shaping the world.
• The limits of resources: Money and institutional support may not resolve deeper conflicts of purpose or belief.
• Theory and technological progress: Lu Zhou’s experience suggests that ambitious engineering depends on foundational scientific understanding.
• Research ahead of its time: Working beyond the field’s theoretical groundwork creates an “efficiency penalty” and an apparent bottleneck.

Plot points and events

• Lu Zhou quietly attends Professor Zhang Zhongqing’s Quantum Mechanics lecture, hoping that revisiting basic questions might spark new ideas.
• Professor Zhang draws the class in by discussing the recently activated STAR-2, now called the Pangu Reactor, and asks why fusion requires such high temperatures.
• A student explains that positively charged nuclei repel one another and need enough kinetic energy to approach closely enough for the Strong Interaction to bind them.
• Professor Zhang then moves from the familiar explanation to the deeper question of why the Strong Interaction has such a short range, introducing particle exchange and a scattering calculation.
• The mathematics quickly overwhelms most of the class. Professor Zhang offers full participation credit—and exemption from future attendance—to anyone who can complete the derivation. Lu Zhou asks to use the blackboard.

Character developments

• Lu Zhou is quiet and observant, attending class to seek inspiration rather than recognition. He remains curious and confident enough to offer help when others are confused.
• Professor Zhang comes across as an engaging teacher who uses humor and a topical example to motivate the lesson. He challenges students to understand the reasons behind physical laws, not just memorize them.
• The sleepy student beside Lu Zhou wakes up during the reactor discussion but becomes bewildered when the lecture turns mathematical. He is interested in Lu Zhou’s offer to explain.

Significant themes

• Seeking insight in basic questions: Revisiting apparently simple ideas can open a path toward harder problems.
• Understanding versus memorization: Professor Zhang emphasizes asking why a force behaves as it does, rather than settling for a textbook description.
• The gap between theory and accessibility: Advanced physics depends on mathematics that many students—even graduate students—struggle to follow.

Character interactions

• Professor Zhang engages the class with questions, rewards participation, and tries to make difficult material approachable.
• A front-row student answers the initial fusion question, prompting Zhang to push the discussion deeper.
• Lu Zhou quietly offers to teach the confused student beside him, then volunteers to take on the derivation—surprising Professor Zhang and setting up the chapter’s cliffhanger.

Key plot points and events

• Lu Zhou attends Professor Zhang Zhongqing’s class and unexpectedly steps up to the blackboard to address a question about the nuclear force’s short range.
• He derives the relevant interaction from quantum field theory, using Feynman diagrams and an inverse Fourier transform. His calculation shows how massive mesons mediate the nuclear force, making it effective only at extremely short distances—around (10^{-14}) in the passage’s stated scale.
• The class applauds, but Lu Zhou is already thinking beyond the original question: could the Strong and Electromagnetic Interactions be described within a concise, unified mathematical framework?
• Lost in thought after the bell, Lu Zhou asks how to explain the existence of the mass gap mathematically. He then leaves, recognizing that this is an exceptionally difficult problem and one of the Millennium Problems.

Character developments

• Lu Zhou displays extraordinary speed and command of advanced physics, but his main development is intellectual: a routine derivation sparks a larger research question about unification and the mass gap. He is absorbed enough to ignore the applause and the end of class.
• Professor Zhang Zhongqing shifts from delighted disbelief at having a Nobel laureate in his classroom to deep respect—and some embarrassment—at Lu Zhou’s impromptu derivation. He admits he cannot answer Lu’s mass-gap question.
• The students move from confusion at Lu’s supposedly “simple” calculations to admiration, though most grasp the performance more than its full significance.

Significant themes

• Curiosity leading to discovery: A practical calculation opens the way to a much deeper theoretical problem.
• Intellectual humility and limits: Lu Zhou’s brilliance does not make the mass-gap problem easy; it remains beyond the classroom’s reach.
• Theoretical physics and practical applications: Unifying forces may not immediately improve controlled fusion, but could provide a path toward future progress.
• Knowledge over status: Lu Zhou treats the classroom as a place for academic exchange, not ceremony.

Character interactions

• Zhang respectfully yields the lecture to Lu Zhou, who gently brushes aside the formalities and begins teaching.
• Lu Zhou’s rapid derivation leaves both Zhang and the students struggling to keep up; their applause contrasts with Lu’s continued concentration.
• When Lu asks about the mass gap, Zhang initially thinks he has been addressed and admits he does not know. Lu clarifies that he was thinking aloud, then leaves the room with the question unresolved.

Summary: "Going Bald"

1. Key Plot Points & Events

• After Lu Zhou's guest lecture in Zhang Zhongqing's Quantum Mechanics class, Jin University's social media (Moments) floods with excited posts from students—many lamenting that they missed the chance to hear the "big shot" teach.
• Lu Zhou leaves the classroom and heads straight to his School of Mathematics office, eager to record ideas triggered during the lecture.
• The problem he tackles is the Millennium Prize problem: proving the existence of a mass gap for quantum Yang-Mills theory. He writes it formally: For any compact simple group G, there exists a massive quantum Yang-Mills field on R⁴ with gauge group G, and the mass gap > 0.
• He mentally splits the problem into two parts: (1) mathematically proving the existence of solutions to the Yang–Mills equations, and (2) proving the mass gap itself—the more central issue.
• Lu Zhou considers whom to consult: Princeton colleagues Edward Witten and Dean Goddard are experts, but email is insufficient for such deep discussion. He rules out bothering the nearly 100-year-old Yang Chen-Ning, recalling that even Professor Atiyah (at advanced age) failed with his Riemann Hypothesis paper, concluding that "age was practically a curse for scholars."
• Resolving to work alone, he sits silently for half an hour, leaving only a few lines of complex equations on paper, then leaves at around 6 PM.
• After Lu Zhou departs, his PhD student Feng Jin tries to peek at the draft out of curiosity. He is baffled by the advanced equations.
• Senior doctoral student He Changwen catches him, warning, "Don't poke around in your advisor's things. You'll go bald."

2. Character Developments

• Lu Zhou: Shows the mindset of a top researcher—he immediately transitions from teaching to tackling an open problem. He is self-aware about the difficulty (admitting he's not fully certain), pragmatic about its two-part structure, and considerate (not wanting to burden the elderly Yang). He acknowledges that theoretical physics is not his specialty, yet is determined to push forward alone when no suitable domestic collaborator exists.
• Feng Jin: A competent but ordinary PhD student. He is eager to prove himself by helping his advisor, but the reality of the mathematical gap between them hits him when he fails to comprehend even the opening lines of Lu Zhou's work.
• He Changwen: Appears more seasoned and street-smart. He casually warns the junior against overstepping boundaries, using humor ("You'll go bald")—a light counterpoint to the chapter's heavy intellectual weight.

3. Significant Themes

• The gap between genius and ordinary scholars: The chapter contrasts Lu Zhou's effortless lecture and deep research with students' inability to even read his drafts, emphasizing how vast the distance is between a Fields Medal-level mind and standard academic performance.
• The difficulty of frontier research: The mass gap problem requires both new mathematics and new physics. Even Lu Zhou struggles, spending long minutes without writing a single formula. The chapter suggests that true breakthroughs may require working alone when no adequate collaborator exists.
• Aging and intellectual decline: Lu Zhou's reflection on Atiyah's failed Riemann Hypothesis paper introduces a sobering theme—advanced age can curtail even the greatest minds, making him reluctant to ask the elderly Yang for help.
• Opportunity and seizing it: The students' online reactions highlight how rare and valuable exposure to a top scholar is, and how academic communities track such events closely.

4. Character Interactions

• Students (online): An excited, informal exchange of posts about Lu Zhou's surprise lecture, with some frustrated at missing it.
• Lu Zhou ↔ (imagined) Witten/Goddard/Yang: Internal deliberation about potential collaborators, ultimately settling on working independently.
• Feng Jin ↔ Lu Zhou (indirect): Feng Jin observes Lu Zhou's concentrated "daydreaming" for half an hour, then later tries to inspect his work—a one-sided attempt at connection that fails intellectually.
• He Changwen ↔ Feng Jin: A brief, witty exchange in which He Changwen warns the junior off, mixing practical advice with humor, reinforcing the office's informal senior-junior dynamic.

• Power-grid breakthrough: East Asia Power and State Grid Su Province reached an agreement, and all twelve generator units at Tianwan Nuclear Power Plant began supplying the grid. The resulting drop in industrial electricity rates—nearly half in Su Province—promises a major boost for manufacturers, especially energy-intensive industries. Residential rates also fell modestly in several cities. The chapter presents cheaper energy as a gradual force for industrial modernization and wider adoption of electric vehicles, appliances, and automation.
• Lu Zhou’s research: After reaching Mathematics LV8, Lu Zhou spends a week absorbed in work on the Yang–Mills Equations. He notices that his improvement has changed not his calculation ability but the speed and quality of his thinking; he loses track of time while researching. He is close to proving the existence of solutions, though the final step remains difficult. His earlier work on Navier–Stokes and the L-Manifold approach has helped him make faster progress.
• Neglected responsibilities: Lu Zhou has barely left home and has lost track of the week. He must return to teaching Computational Materials Science because his doctoral student, Wu Shuimu, is not yet ready to handle the class independently.
• Character interactions: Lu Zhou asks his AI assistant Xiao Ai to clean his study, and its drone and robot vacuum promptly get to work. As he prepares to leave for class, Yan Yan arrives to confront him about missing a medical exam. She has brought the necessary test supplies, and her blunt, practical manner clashes humorously with his distracted confusion. Lu Zhou realizes he has not even had breakfast—and the tests put him off eating.
• Themes: The chapter contrasts sweeping technological change with its slow, almost unnoticed effects on everyday life. It also highlights Lu Zhou’s exceptional intellectual focus, the cost of that focus in neglected routines and obligations, and the growing role of automation in daily life.

Chapter Summary: "Proof of the Existence of Solutions"

Key Plot Points & Events

• Lu Zhou teaches his first Computational Materials Science class at Jinling University; attendance is packed with students and even professors from other universities, despite the course's difficulty
• After class, he visits the School of Mathematics office where he retrieves scratch paper containing his earlier work on the Yang-Mills Equations
• He completes a proof demonstrating the existence of solutions to the Yang-Mills Equations using his L-Manifold method (developed during his Navier-Stokes work)
• He identifies the next challenge: seeking the general solution to the Yang-Mills Equations, which will be far more difficult

Character Developments

• Lu Zhou: Shows his dedication to advancing mathematical physics; maintains a mentorship style that encourages independent thinking. He briefly reflects on his Princeton past and former students (Qin Yue as a lecturer, Vera), showing nostalgia
• Feng Jin: A graduate student who spent a week trying to solve the problem Lu Zhou left on scrap paper. His initial confidence is humbled, but Lu Zhou validates his self-study effort and the general direction of his thinking
• Zhao Huan (Assistant): Learns not to tidy Lu Zhou's desk, as he prefers his workspace left as-is

Significant Themes

• The difficulty of mathematical discovery: Even bright graduate students find core problems intractable; solving millennium problems requires extraordinary insight
• The gap between physics intuition and mathematical rigor: Feng Jin's idea (introducing a scalar field) is "not wrong" but not necessarily correct either—a key lesson about theoretical work
• Building on prior work: Lu Zhou's Yang-Mills progress directly leverages his L-Manifold method from the Navier-Stokes problem, showing how breakthroughs compound

Character Interactions

• Lu Zhou ↔ Feng Jin: A mentoring conversation where Lu Zhou probes Feng Jin's week of thinking, praises his attitude (not his idea) for self-studying quantum mechanics, and compares him to a competitive former Princeton student now studying under Witten. Lu Zhou delivers the philosophical point that "absence of flaws doesn't mean correctness"
• Lu Zhou ↔ Zhao Huan: Brief exchange about desk organization; Lu Zhou politely but firmly establishes boundaries about his workspace
• Lu Zhou's internal reflections: Thoughts about Qin Yue (still lecturing at Princeton, exchanging number theory emails) and Vera (causing slight discomfort)

Key Takeaway

This is a transitional chapter showing Lu Zhou in his element—teaching, mentoring, and making steady progress on the Yang-Mills Millennium Problem, with the completion of the existence proof serving as a major milestone forward.

Here is a concise summary of the chapter:

Key Plot Points / Events

• Wei Wen, a postdoc at Princeton's Institute for Advanced Study and former student of Lu Zhou, struggles with a difficult mathematical problem.
• Professor Fefferman brings him coffee and offers help, but Wei Wen insists he is near a breakthrough.
• An assistant from Mathematical Annals delivers a paper to Fefferman for review, sent by editor Sanak. Fefferman reluctantly accepts after being told he is the only suitable reviewer.
• The anonymous paper is titled "Proof of the Existence of Solutions to the Yang–Mills Equations." Fefferman immediately identifies Lu Zhou as the author based on his signature use of L-Manifolds and differential geometry.
• Wei Wen is stunned that Lu Zhou is tackling a second Millennium Problem.
• Fefferman cancels his upcoming class, asking his teaching assistant to substitute, and eagerly prepares to review the paper, wondering whether Lu Zhou's mathematics has improved since leaving Princeton.

Character Developments

• Wei Wen: Still adjusting to independent research under Witten's sparse mentorship; appreciates Lu Zhou's past guidance but feels ashamed of relying on favors. He is persistent and eager to solve problems on his own.
• Fefferman: Shows kindness and generosity toward Wei Wen, though initially bothered by the unsolicited paper. His reluctance gives way to genuine excitement when he realizes the author is Lu Zhou, revealing his competitive respect for a mathematical rival.

Significant Themes

• Academic mentorship and the long shadow of a brilliant former student.
• The rigorous, competitive nature of top-tier mathematical research.
• The pursuit of major open problems (Millennium Prize Problems) as a measure of greatness.
• The value of intellectual challenge for its own sake.

Character Interactions

• Wei Wen and Fefferman: A supportive, mentor-like exchange; Fefferman offers help without pressure, Wei Wen politely declines but appreciates the gesture.
• Fefferman and the assistant: A slightly tense interaction—the assistant pushes the review request in person, Fefferman complains about the lack of tact but eventually complies.
• Indirect references to Lu Zhou and Witten: Wei Wen recalls Witten's frequent absences and Lu Zhou's more hands-on guidance; Fefferman recognizes Lu Zhou's mathematical style without needing a name. Both center on Lu Zhou's influence and reputation.

Chapter Summary

Key Plot Points

• Professor Fefferman reviews a paper on the Yang–Mills Equations, becoming deeply engrossed in its mathematical brilliance
• Despite the demanding nature of peer review, he finds the work remarkably sophisticated for a theory only two years old
• Lu Zhou submits his paper "A Proof of the Existence of Solutions to the Yang–Mills Equations" to Mathematical Annals
• After submission, Lu Zhou refocuses on the next challenge: finding a general solution to the equation (beyond just proving existence)
• Lu Zhou is invited to give a guest lecture on Quantum Mechanics for the School of Physics, which he agrees to
• Academician Lu arrives excitedly, asking Lu Zhou if he wrote a paper on the Yang–Mills Equations, seemingly confirming the paper's significance

Character Developments

• Professor Fefferman: Initially views review work as a "thankless task" but becomes completely absorbed in Lu Zhou's paper, earning his intellectual respect
• Lu Zhou: Demonstrates high confidence in his proof (90%+ certainty), remains productive after submission, and shows willingness to teach undergraduates despite his demanding research
• Academician Lu: Appears excited and possibly surprised, suggesting the paper may not have been expected from Lu Zhou

Significant Themes

• The rigorous nature of academic peer review
• The gap between proving existence and finding solutions in mathematics
• The collaborative and interconnected nature of academic communities
• Academic reputation and intellectual curiosity

Character Interactions

• Fefferman & Wei Wen: Wei Wen asks about the paper's validity; Fefferman cautiously acknowledges Lu Zhou "probably did it"
• Lu Zhou & Zhang Zhongqing: A courteous professional exchange inviting Lu Zhou to lecture physics students
• Lu Zhou & Academician Lu: An excited, abrupt approach with the pivotal question: "Was that paper written by you?"

Summary: "This April Was Far from Peaceful"

Key Plot Points and Events

• Late April: A major event shakes the academic world. Lu Zhou publishes a forty-page paper in Mathematical Annals proving the existence of solutions to the Yang–Mills Equations (one of the Millennium Problems).
• The paper is reviewed by Charles Fefferman and creates a sensation across the international mathematics and physics communities.
• Discussion explodes on MathOverflow, with scholars noting the paper's use of "L-manifolds" (from the author's 2018 work); many note the high barrier to entry for verification.
• Mainstream news outlets push headlines about the Millennium Problems; reactions on Twitter/Facebook are highly emotional, with many recalling that Lu Zhou solved Navier–Stokes two years earlier (presented at the Rio ICM) and also worked on controllable fusion.
• Nature gives the paper a "Highlight" with a two-hundred-word excerpt from the abstract on its cover.

Character Developments

• Lu Zhou (protagonist, off-page): Now has tackled two Millennium Problems in under two years, cementing his reputation as a leading mathematician. His earlier creation of the L-manifold theory (2018) is extended and strengthened in this paper.
• Charles Fefferman (reviewer): Publicly and emphatically endorses the work, defending both its originality and its value; becomes a key voice validating Lu Zhou's significance.

Significant Themes

• The nature of mathematical value: Debated whether value requires creating entirely new tools or whether refining/strengthening existing ones (like L-manifolds) equally counts.
• The fusion of disciplines: Partial Differential Equations, Differential Geometry, and Topology are combined into a unifying method ("bridging" equation and geometry; the "auxiliary line" metaphor) — potentially paving the way toward the general solution of Yang–Mills.
• Public fascination vs. expert caution: The gap between sensationalized media coverage and the patient, technical reality of verifying and building on a major proof.
• The ascent of a mathematical giant: Fefferman's closing remarks suggest Lu Zhou is already the century's greatest mathematician (unless the Riemann Hypothesis is proved).

Character Interactions

• Fefferman × Science reporter: The bulk of the chapter is an interview in which Fefferman rebuts critics (who claim Lu Zhou merely reused his Navier–Stokes tools), explains the "L-manifold" method in accessible terms, and ultimately affirms Lu Zhou's dominance.
• MathOverflow users: Mixed reactions — some skeptical (waiting for the presentation), most impressed; Terence Tao and Scholze are noted as active users (background detail).
• General public/commenters: Excited, reverent commentary referencing Lu Zhou's past achievements.
  Note: The final paragraph is an unrelated promotional blurb for another novel ("Sorry, Having a System Really Is Amazing") and can be disregarded.

Summary of "A Letter from the Clay Mathematics Institute"

1. Key Plot Points and Events

• Lu Zhou's paper on the Yang–Mills Equations is published in Mathematical Annals, but he initially underestimates its significance. Academician Lu's excited reaction reveals that the work is a major breakthrough—the first step toward a Grand Unified Theory in theoretical physics.
• The paper's importance spreads rapidly: Science magazine publishes an interview with reviewer Professor Fefferman, and even non-physics students in the cafeteria are discussing Lu Zhou.
• After a Number Theory class, reporters ambush Lu Zhou, asking sensational and poorly informed questions (e.g., whether he has solved the Millennium Problem and how he would spend the $1 million prize). Lu Zhou's attempts to clarify that his result is "preliminary" are ignored. Wang Peng and university security escort the reporters out.
• Lu Zhou escapes to his office. He checks arXiv and finds a flood of low-quality papers opportunistically claiming to use his "L-Manifold" theory, which annoys him.
• He receives an email from Professor Carlson of the Clay Mathematics Institute, inviting him to give a lecture explaining his proof. Initially reluctant, he agrees after realizing the need to correct misunderstandings and attract serious researchers.
• Principal Xu visits and suggests holding the lecture in the old campus's large auditorium. Lu Zhou agrees and sets the date for May.

2. Character Developments

• Lu Zhou: Shows humility and scientific rigor—he stresses his work is only a preliminary result, not a full solution. He is also somewhat socially oblivious, misreading Lin Yuxiang's flirtation and responding with logical literalism. He is practical in managing his academic reputation (accepting the lecture as a way to improve the quality of related research).
• Lin Yuxiang: Attempts to flirt with Lu Zhou (offering to make him coffee daily). Her subtle approach fails completely when he takes her literally, leaving her baffled and defeated.
• Principal Xu: Eager to capitalize on the university's prestige, gently pressuring Lu Zhou to hold the lecture on campus.

3. Significant Themes

• The gap between scientific nuance and media sensationalism: Reporters reduce complex mathematics to prize money and "solved problems," ignoring Lu Zhou's careful qualifications.
• The reality of academic hype: Physicists and mathematicians rush to post preprints to claim priority, resulting in a flood of low-quality papers.
• The weight of the Millennium Problems: Even modest progress in fundamental physics triggers outsized attention, highlighting the field's long drought of breakthroughs.
• Loneliness of research: Lu Zhou finds few papers worth referencing, reflecting isolation at the frontier of theoretical work.

4. Character Interactions

• Academician Lu (mentioned): Excitedly interrogates Lu Zhou, alerting him to the paper's enormous physics implications.
• Reporters/Media: Badger Lu Zhou with aggressive, misinformed questions; their behavior contrasts sharply with his calm, precise demeanor.
• Wang Peng: Acts as a protector, physically shielding Lu Zhou and clearing a path through the crowd.
• Lin Yuxiang: Engages in warm, informal interaction with Lu Zhou; her romantic overture is unintentionally rebuffed, creating a comic moment.
• Clergy Mathematics Institute (Professor Carlson): Professional, respectful invitation via email; Lu Zhou's response is measured and cautious.
• Principal Xu: Supportive and eager, negotiating the lecture logistics; Lu Zhou cooperates readily.

Summary: Can We Still Have a Proper Conversation?

Key Plot Points & Events

• Arrangements begin: After Lu Zhou verbally agreed, Jin University treats the Yang–Mills presentation as a top priority, holding days of meetings on details like venue security and banquet menus.
• Wang Shicheng's visit: Academician Wang Shicheng (chairman of the Hua Nation Mathematical Society, Yanshan University faction) visits Principal Xu Jian, pretending it's a friendly stop, but clearly aiming to move the presentation to Yanshan University.
• The negotiation fails: Xu Jian deflects Wang's hints for half an hour. When Wang openly asks to host the event in Shangjing, Xu Jian refuses, directly rejecting each of Wang's arguments.
• The deciding exchange: Xu Jian asks whether Yanshan has a Fields Medal or Crafoord Prize; when Wang admits they don't, Xu Jian reminds him Jin University has both. Wang leaves in frustration, going to find Lu Zhou directly.
• Xu Jian's warning: After Wang departs, Xu Jian sternly instructs his staff that the presentation concerns Jin University's honor and future, and warns anyone who fails will answer to him.

Character Developments

• Lu Zhou – Appears only indirectly. He prefers delegating logistics to others and focuses on academic matters, consistent with his pragmatic, non-political nature.
• Principal Xu Jian – Shrewd, politically astute, and fiercely protective of Jin University's interests. Displays blunt humor and a willingness to offend in service of his institution's prestige.
• Wang Shicheng – Represents the established academic old guard; tries to leverage personal connections but is outmatched. His repeated failures highlight a slightly comical desperation to claim the event for Yanshan's reputation.

Significant Themes

• Institutional prestige and rivalry – The competition between universities over hosting a major academic event reflects how such achievements are used to advance institutional standing.
• Academic politics – The chapter shows how scientific work becomes entangled with bureaucratic maneuvering, personal networks, and status claims rather than purely scholarly concerns.
• Bragging rights through prizes – Xu Jian's pointed comparison of awards (Fields Medal, Crafoord Prize) underscores how symbolic credentials define a university's place in the academic hierarchy.

Character Interactions

• Xu Jian and Wang Shicheng – A prolonged verbal duel beneath polite surface behavior. Wang tries to approach via friendship and flattery; Xu Jian sees through it, deflects, then openly defeats him with a blunt rebuttal ("Does Yanshan University have a Fields Medal?"), ending Wang's leverage.
• Xu Jian and his staff – Brief but sharply hierarchical; the principal lays down a firm expectation of flawless execution, hinting at the pressure placed on the organizing team.
• Wang Shicheng and Lu Zhou – Not directly depicted; Wang intends to approach Lu personally, implying the conflict may continue.

Chapter Summary: "They Were All the Same to Me"

Key Plot Points & Events

• Academician Wang Shicheng visits Lu Zhou's office at Jinling University, requesting that the Yang-Mills Equations presentation be moved to Yanshan University, arguing Yanshan's mathematical school is stronger and this is a chance for China's mathematical community to integrate with the world.
• Lu Zhou declines, arguing that where a presentation is held matters less than the quality of the research itself.
• Jinling University begins extensive preparations for the upcoming presentation: renovating the old Sixth Dormitory, installing air conditioners, improving campus appearance, and conducting safety inspections.
• Lu Zhou continues researching the general solution to the Yang–Mills Equations but finds himself at a complete dead end, lamenting how difficult the equations are.
• Han Mengqi submits her first original paper: "A Theoretical Model of Semiconductor/Electrolyte Solution Interfaces Based on the Schottky Barrier."

Character Developments

• Lu Zhou: Demonstrates firm principles—he values the substance of research over institutional prestige, holds loyalty to his alma mater, and reveals strategic thinking about avoiding intellectual monopolization (Yanshan's dominance already stifles academic diversity). He maintains a patient, growth-oriented mentorship style.
• Wang Shicheng: Proud and stubborn (refuses to ask Jinling professors for help), yet pragmatic enough to ask students for directions. He is genuinely baffled by Lu Zhou's refusal, revealing his institutional-rivalry mindset.
• Han Mengqi: Shows initiative by writing her own paper in just two months, and expresses a quiet desire to become capable enough to genuinely help her mentor.

Significant Themes

• Substance over prestige: Lu Zhou's "window vs. the house" analogy—real academic advancement depends on achievements, not venues.
• Academic diversity vs. dominance: Lu Zhou chose Jinling not because Yanshan was weak, but because it was too dominant; different voices are needed for academic progress.
• Alma mater loyalty and personal choice: "This is simply my alma mater"—personal ties can be legitimate reasons for institutional decisions.
• The daunting difficulty of frontier mathematics: Even Lu Zhou finds the Yang-Mills equations nearly impossible to further advance.
• Nurturing the next generation: Lu Zhou's belief that students mastering fundamentals is the greatest help they can offer.

Character Interactions

• Lu Zhou ↔ Wang Shicheng: The central confrontation. Wang appeals to institutional rivalry and national interest; Lu Zhou dismantles his argument with philosophical reasoning, then ends the debate with an unanswerable personal statement ("They are all the same to me"). Wang is left stunned, unable to respond.
• Lu Zhou ↔ Han Mengqi: Brief but warm. She submits her first paper and offers help; he accepts the paper, redirects her desire to help into mastering her studies, and she leaves with quiet motivation mixed with self-doubt.

Key events

• At the Jinling Institute for Advanced Study, fusion researchers Sheng Xianfu and Li Changxia struggle with their stalled project to miniaturize controlled fusion. Their reactor designs keep failing from heat dissipation problems, and their best attempt melted down after 34 seconds.
• Sheng worries that Lu Zhou’s sudden focus on the Yang–Mills equations has left the fusion project without direction. He and Li consider whether lowering the temperature required for fusion could be more promising than their current approach, but neither sees a clear path.
• Sheng goes to Jin University to speak with Lu, but finds him lecturing on quantum mechanics. During the question period, Lu gives the students an impromptu explanation of the Yang–Mills equations.
• Lu’s explanation develops into an advanced calculation related to the strong interaction’s mass gap. He stops before reaching a conclusion, apologizing for getting carried away, much to the frustration of professors who hoped to see the result.
• Though Sheng barely follows the mathematics, the lecture sparks an idea: bringing nuclei close enough might make fusion possible at temperatures below 100 million degrees. He leaves with a potential new reactor model to investigate.

Character developments and interactions

• Sheng Xianfu moves from frustration and doubt toward renewed hope. Lu’s lecture unexpectedly gives him the inspiration he needs for the fusion research.
• Li Changxia remains cautious and uncertain. He acknowledges that theoretical work on fundamental forces might help, but doubts how soon it could become practical.
• Lu Zhou appears absorbed in his mathematical work, improvising a deep explanation for the class and stopping only when he can go no further.
• Sheng and Li discuss their project’s setbacks and uncertainty; Sheng then observes Lu’s lecture from the back of the hall, where Lu’s ideas indirectly influence his thinking.

Significant themes

• Inspiration is contagious: Lu’s mathematical exploration sparks a breakthrough in a seemingly unrelated engineering problem.
• Theory and application: The chapter highlights the uncertain, sometimes indirect path from abstract physics to practical technology.
• Persistence amid failure: Repeated reactor failures leave the researchers discouraged, but an unexpected insight offers a reason to continue.

Key plot points and events

• Sheng Xianfu considers whether a low-temperature fusion approach might help miniaturize controlled fusion. The chapter reviews Cold Fusion’s troubled history: early claims were retracted, and the celebrated Fleischmann–Pons experiment sparked a global research rush before failing to hold up.
• Sonofusion is presented as a possible technical route, though it carries the same stigma. Sheng visits Professor Chen Weizhong, whose team studied it decades earlier and concluded that it produced light but not fusion.
• Chen initially refuses to share the old research, fearing Sheng will repeat his costly failure. Sheng argues that the work may still be useful for a different purpose. Chen gives him his battered notebook of experimental data.
• Back at the Jinling Institute for Advanced Study, Sheng struggles through theoretical material he has not used in years. After ten days, he completes a paper arguing that fusion reactions at relatively low temperatures may be technically feasible.
• Sheng brings the paper to Lu Zhou, nervous that his idea will seem foolish. Lu reads it and reveals that he and Sheng have been thinking along similar lines.

Character development

• Sheng Xianfu moves from engineering-focused plasma work toward theory, showing persistence, humility, and willingness to revisit a discredited research area.
• Chen Weizhong is burdened by the failure of his earlier project, but Sheng’s reframing of the old data gives him a reason to pass it on and hope it may yet matter.
• Lu Zhou responds as an open-minded colleague, treating the proposal as a legitimate subject for discussion rather than dismissing it.

Significant themes

• Scientific failure and renewed purpose: Old research may become valuable when viewed from a new angle.
• Skepticism versus possibility: Cold Fusion’s history encourages caution, but does not entirely eliminate the value of further inquiry.
• Intellectual humility and collaboration: Neither researcher can assume they already know the truth; productive work depends on examining ideas fairly.

Character interactions

• Sheng persuades Chen not to regard his past work as wholly wasted, and Chen entrusts him with the experimental notebook.
• Sheng approaches Lu with a tentative proposal, expecting ridicule. Lu’s reassurance—and his admission that their ideas align—turns the exchange into a moment of mutual recognition.

Summary of Chapter: "Something Only I Could Do"

1. Key Plot Points and Events

• Sheng Xianfu presents a paper on Cold Nuclear Fusion to Lu Zhou, expecting ridicule, but instead gains his approval.
• Lu Zhou explains the theoretical basis for fusion inside stars using the Quantum Tunneling Effect, arguing that Cold Nuclear Fusion is feasible even if not yet practically achievable.
• Lu Zhou reveals his ongoing work on miniaturizing Controlled Nuclear Fusion, noting the key bottleneck is the need to unify Strong Interaction and Electromagnetic Interaction through a definite model (linking to his work on Yang–Mills equations).
• Time passes to May; Lu Zhou finishes teaching his courses and plans to claim a system mission reward based on his students' published papers.
• Three days before a lecture, Professor Klaus von Klitzing arrives in Jinling and meets Lu Zhou.
• Von Klitzing delivers a message from Professor Kleiber (Wendelstein 7-X lab), who calls Lu Zhou a "terrifying opponent" — Kleiber's lab is now under pressure from German bureaucrats who assume fusion is easy after Lu Zhou's breakthrough.
• Von Klitzing mentions that ITER member states have reached a 5-year agreement with China, exchanging industrial concessions and technology. Both sides accept this as the best compromise given that fusion technology cannot remain permanently secret.

2. Character Developments

• Lu Zhou: Demonstrates scientific humility and theoretical depth. He encourages rather than dismisses "impossible" ideas. He shows strategic pragmatism regarding the fusion timeline and a desire to return to active research after a rest period. He also feels mild guilt about the international consequences of his discoveries.
• Sheng Xianfu: Displays ambition and nervousness in proposing a radical idea; his growth lies in receiving validation rather than criticism.
• Klaus von Klitzing: Acts as a friendly colleague, showing respect for Lu Zhou and conveying diplomatic—yet humorous—news from Europe.

3. Significant Themes

• Advancing the impossible: The chapter challenges the concept of "impossible" in science; breakthroughs require exploring theories beyond classical mechanics.
• Quantum mechanics vs. classical intuition: Using the Quantum Tunneling Effect to explain stellar fusion illustrates how deeper scientific understanding changes assumptions.
• Practical vs. theoretical research: Lu Zhou's position—that theoretical unification is required before engineering solutions—discusses the relationship between pure and applied science.
• Geopolitics of technology: The 5-year deal between China and ITER members addresses the tension between national advantage and inevitable technological leakage—highlighting how scientific progress transcends borders.

4. Character Interactions

• Sheng Xianfu ↔ Lu Zhou: A student presenting bold ideas to an open-minded mentor; the interaction is supportive and intellectually stimulating.
• Lu Zhou ↔ Klaus von Klitzing: A welcoming, warm exchange between peers. Von Klitzing pokes fun at Lu Zhou's impact on international fusion research but also reassures him that Kleiber is grateful, not angry—closing with an offer of future cooperation.

Key plot points and events

• Jinling prepares for a major international lecture at Jinling University, drawing more than a thousand mathematicians and physicists. The university, city government, and hotel coordinate to ensure the event runs smoothly and present Jinling well.
• Mathematicians Faltings and Kliqing arrive at the InterContinental Hotel. Kliqing has already visited Lu Zhou at the university and seen his Institute for Advanced Study. Faltings is chiefly focused on the coming lecture.
• The auditorium fills with prominent scholars, including Deligne, Witten, and Wilczek. Deligne reveals that Lu Zhou was his student, surprising Witten.
• University staff and administrators work behind the scenes to manage the event. Principal Xu and Dean Qin recognize that the lecture is a milestone for the School of Mathematics and the university.
• With half an hour remaining, Lu Zhou quietly reviews calculations in the lounge. Lin Yuxiang reminds him of the time and offers to tie his necktie; he declines. Han Mengqi wishes him luck as he leaves.

Character developments and interactions

• Faltings appears reserved and focused on the lecture, while Kliqing is more relaxed and welcoming, teasing him about arriving late.
• Faltings observes that mathematics is becoming younger—and considers this a good thing, hinting at respect for the new generation.
• Deligne and Witten exchange friendly teasing. Deligne’s connection to Lu Zhou becomes clear when he calls Lu his student.
• Principal Xu and Dean Qin show the institutional pressure surrounding the event: its success matters to the university’s reputation and future.
• Lu Zhou remains composed and self-assured before his lecture. Lin Yuxiang and Han Mengqi offer support, though in different ways.

Significant themes

• International recognition: Jinling University is stepping onto the world academic stage.
• A new generation of scholars: Established mathematicians acknowledge the growing prominence of younger researchers.
• Collective effort behind achievement: The lecture depends not only on its speaker but also on city officials, university staff, and organizers.
• Quiet confidence under pressure: While the event’s significance weighs heavily on others, Lu Zhou approaches it calmly.