Key Plot Points and Events

• Rumors spread that Li Dong voluntarily turned down the Fields Medal due to the controversy surrounding his absence at the ICM.
• Peking University and Tsinghua University release joint statements supporting Li Dong and criticizing the International Mathematical Union's handling of the Fields Medal.
• Mathematicians like Wiles and Langlands publicly support Li Dong, with Langlands stating that Li Dong's work is too significant to be overshadowed by conference schedules.
• Li Dong expresses frustration with the public attention and the use of the Fields Medal as a political bargaining chip.
• Mr. Yang, a high-ranking official, invites Li Dong to meet him at the hospital, where he thanks Li Dong for developing the Second-Generation Single-Atom Iron Nanozyme that has improved his health.

Character Developments

• Li Dong: Becomes increasingly frustrated with the public attention and the politicization of the Fields Medal, leading him to question the purity of mathematics and research circles. He remains focused on his mathematical work despite the distractions.
• Mr. Yang: Shows improvement in his health due to Li Dong's nanozyme, leading to an increase in his vitality and spirits. He invites Li Dong to meet him to express his gratitude.

Significant Themes

• The purity and politicization of mathematics and research.
• The importance of the Fields Medal and its intended purpose.
• The impact of Li Dong's work on the lives of others, as seen through Mr. Yang's improved health.

Character Interactions

• Li Dong and Dr. Weng: Dr. Weng is warmer towards Li Dong after Mr. Yang starts using his nanozyme, and she thanks him for its development.
• Li Dong and Mr. Yang: Mr. Yang invites Li Dong to meet him at the hospital to express his gratitude for the nanozyme, showing a personal side to the high-ranking official. Li Dong remains humble and focused on his mathematical work despite the recognition.

Summary: L-Homomorphism

Key Plot Points

• Li Dong visits Mr. Yang in the hospital, who has heard about Li Dong's recent academic controversies.
• Mr. Yang reflects on how older-generation scholars (like Qian) crossed disciplines freely and compares that to Li Dong's own style.
• Mr. Yang points out that if Li Dong had stuck purely to mathematics, no one could attack him—but then tells him to simply prove he's right.
• Li Dong confesses a half-month-long dilemma: his Pairing Correspondence criterion is broken by counterexamples (functions with overlapping Pairing Correspondence but differing Euler Factors), leaving him stuck between two paths: (1) force Pairing Correspondence to bridge from finite intervals to the entire real axis, or (2) abandon it and find a more rigid constant.
• Mr. Yang offers the key insight: a dictionary is used for translation, not for recognizing words. Matching entries on the left column don't guarantee the right column points to the same thing.
• Li Dong realizes the counterexamples were never counterexamples—they were different things linked by the same bridge, i.e., an L-homomorphism. Matching Pairing Correspondence identifies not identical objects but a Functoriality Transfer between two automorphic representations.
• Both dead-end paths collapse; the correct framework is Functoriality itself. Li Dong bows in deep gratitude.
• At the moment of insight, Li Dong's base attributes surge to 0.8, then fall back to Memory 0.6 / Logic 0.5 / Focus 0.5.

Character Developments

• Li Dong: Breaks through a major mathematical impasse by recognizing his own logical error (forcing a shadow to identify a three-dimensional object). Demonstrates humility in seeking advice and depth in receiving it.
• Mr. Yang: Shown as a wise mentor who can offer decisive insight even outside his specialty—not by knowing the details, but by reframing the problem entirely.

Significant Themes

• Interdisciplinarity as strength: The wall between fields is artificial; true breakthroughs often come from crossing it (Qian, Fermi, Li Dong).
• Shadow vs. substance: Pairing Correspondence is a projected shadow; one cannot use it to reverse-identify the underlying entity.
• The dictionary/translation metaphor: Matching surface-level structures (left column) links distinct things (right column) via a shared bridge (L-homomorphism), rather than proving sameness.
• Intellectual humility and mentorship: Even a non-specialist can dissolve a specialist's deadlock by offering a fresh angle.

Character Interactions

• Li Dong is initially hesitant to burden Mr. Yang with his problem but ultimately lays it out exactly as it troubles him—showing trust.
• Mr. Yang listens without needing to know the Langlands details, draws on a simple everyday analogy, and redirects Li Dong's entire framework in one sentence.
• Their exchange ends with a formal bow from Li Dong, signaling deep respect; Mr. Yang accepts it warmly, their bond reinforced.

Chapter Summary: "I'll Wait for You, Dong"

1. Key Plot Points

• Li Dong visits Mr. Yang in the hospital. He asks Dr. Weng to notify him immediately if anything changes.
• Li Dong goes to the seminar room to meet Penrose, where he presents a new mathematical insight: the Pairing Correspondence is not sufficient as a ruler; one must establish an exact functoriality transfer between automorphic representations (via an L-homomorphism). This corrects their previous flawed premise and gives a clear path forward on the Li Conjecture.
• The two work through the night, with Penrose filling in gaps and both excitedly proving results.
• Time jumps to early 2026, during New Year's Eve. A hot pot dinner is held at Li Dong's apartment with Wang Hao, Penrose, Liu Qiang, Chen Nan, and Qi Yu.
• Qi Yu leaves to deliver dumplings to Zhang (a sick friend/colleague).
• Li Dong receives a call: he is to receive the Zhao Jiuzhang Award (postponed from the previous year due to a solar flare).
• After the dinner, a drunk Penrose tells Li Dong he plans to tackle the Riemann Hypothesis after finishing the Langlands work, and asks Li Dong to join him.
• Li Dong internally imagines proving RH and showing it off to the real Riemann in the group chat. Penrose, noticing Li Dong's grin, declares he "knew" Li Dong would be interested and says, "I'll be waiting for you, Dong!"

2. Character Developments

• Li Dong: Shows care for Mr. Yang; makes a breakthrough in his mathematical thinking; remains playful with friends but is also contemplative. He is intrigued (though initially evasive) by Penrose’s challenge about the Riemann Hypothesis, and begins to envision proving it himself.
• Penrose: Displaying obsessive dedication, he is reinvigorated by the new mathematical direction (the "Passing the Torch" effect is noted). Drunk, he reveals a deep admiration for Riemann, a personal wish to see RH become a theorem, and a strong belief that Li Dong is the one who can do it. His emotional side shows.
• Supporting characters (Wang Hao, Liu Qiang, Chen Nan, Qi Yu): They are largely unchanged—loyal, humorous, and comfortable with Li Dong. Qi Yu is caring (delivering dumplings to Zhang).

3. Significant Themes

• Mathematical obsession and collaboration: The thrill of solving a problem together, working through the night.
• Legacy and "passing the torch": Penrose, aging, sees Li Dong as the heir to great mathematical quests.
• Friendship and normalcy amidst genius: The hot pot dinner grounds the story in ordinary human connection.
• The allure of the Riemann Hypothesis: A famous unsolved problem becomes the new horizon, symbolizing the endless pursuit of mathematical truth.

4. Character Interactions

• Li Dong & Penrose: Intense collaboration (writing/checking proofs), playful banter about spicy food, and an emotional late-night conversation about the Riemann Hypothesis. Penrose expresses profound trust in Li Dong.
• Li Dong & friends: Teasing and laughter during the hot pot; Wang Hao and Liu Qiang mock each other, Chen Nan joins in. Penrose attempts spicy food and fails, to everyone's amusement.
• Li Dong & Qi Yu: Easygoing, affectionate rapport; she takes care of others, and he jokes with her.
• Li Dong & the group chat (internal): Reflects on Riemann himself, imagining future one-upmanship—this motivates his interest in RH.

Chapter Summary: “So, Li Dong Was Wrong!”

1. Key Plot Points & Events

• The Zhao Jiuzhang Young Scientists Award ceremony is held at the Chinese Academy of Sciences’ National Space Science Center.
• Chang Jin, now director of the National Astronomical Observatories, tells Li Dong about a new center for monitoring extreme space weather, set up in cooperation with the Max Planck Society; their contact is Clara Novig.
• The awards are announced:
  • Atmospheric Physics Award: Huang Ping — for calculating atmospheric expansion during the Carrington Event, helping low-orbit satellites escape.
  • Geophysics Award: Wang Xin — for mapping geomagnetically induced currents and identifying vulnerable power grid nodes.
  • Space Physics Award: Li Dong — for his early warning paper, which gave a 14-month advance notice, enabling satellite safe-mode operations, regional power grid load shedding, and undersea cable backups. His work was credited with avoiding hundreds of billions in losses.
• Li Dong receives his award and a 50,000 yuan prize from Wang Chi, who encourages him to continue.
• During the banquet, Li Dong sees a newly published Annals of Mathematics paper by Elias Weber proving that zero-pair correlation rigidity is a complete invariant for automorphic representations of GL(n), making local-global compatibility unconditional.
• This directly contradicts Li Dong’s earlier claim that the Li Conjecture’s final form might differ from what people believed. The chapter ends with the realization:

Li Dong was wrong.

2. Character Developments

• Li Dong: Though already wealthy, he feels genuine happiness holding the award. His confidence in his mathematical judgment is shaken when Weber’s paper disproves his public caution about the Li Conjecture.
• Wang Chi: Acts as a mentor figure, affirming that Li Dong’s mathematical skills were “put where they belonged.”
• Li Dong’s reputation: The “money-grubbing mathematician” joke persists, but his standing in space science is now firmly established.

3. Significant Themes

• Interdisciplinary triumph: A pure mathematician is honored for major contributions to space science.
• Science as disaster prevention: Li Dong’s warning paper is shown transforming into concrete protective measures for satellites, power grids, and communication infrastructure.
• Scientific humility: Even top mathematicians can be wrong; new results can overturn confident public assertions.
• Institutional collaboration: Cooperation between Chinese institutions and the Max Planck Society highlights global scientific exchange.

4. Character Interactions

• Li Dong and Chang Jin: Friendly reunion; Chang updates Li Dong on the new space weather center. Li Dong jokes about Clara Novig’s money-loving nature, and Chang teases him in return.
• Li Dong and Wang Chi: During the award presentation, Wang Chi grips his hand and urges him to keep applying his mathematical talents to the field.
• Li Dong and Elias Weber (indirect): Weber’s paper becomes the intellectual challenge of the chapter, forcing Li Dong to confront a direct refutation of his earlier position.

Key Plot Points and Events

• Li Dong, a mathematician, learns that a paper by Weber was featured in Annals of Mathematics, potentially challenging Li Dong's own work on the Li Conjecture.
• Li Dong attends an awards banquet where he meets other scientists who worked on mitigating the Carrington solar flare event.
• The next day, Li Dong receives an urgent call from Professor Wang Zhigang, summoning him to the research group due to an unspecified issue.

Character Developments

• Li Dong: Confident in his own work, he initially dismisses Weber's paper without reading it. He reflects on the unsung heroes who worked tirelessly during the solar flare event, showing empathy and respect for their efforts.
• Huang Ping and Wang Xin: They are award winners who approach Li Dong, expressing their admiration for his work and seeking his advice on disaster prediction and monitoring.

Significant Themes

• Recognition vs. Unsung Heroes: Li Dong realizes that while he received recognition, many others who worked tirelessly behind the scenes did not.
• Collaboration and Communication: The importance of collaboration and open communication among scientists, as seen in Li Dong's interactions with Huang Ping and Wang Xin.
• Preparedness: The need to always be prepared for potential disasters, as emphasized by Li Dong's advice to Wang Xin.

Character Interactions

• Li Dong, Huang Ping, and Wang Xin: They discuss disaster prediction and monitoring, exchanging contact information and agreeing to collaborate further.
• Li Dong and Professor Wang Zhigang: Wang Zhigang calls Li Dong, expressing urgency about an issue at the research group, hinting at a potential problem or challenge they need to address together.

In this chapter, Li Dong returns to his research group after a six-month absence. Wang Zhigang fills him in on recent events: after Li Dong had warned everyone not to attack the main lines of the Li Conjecture, some left, but those who stayed explored side directions and produced three notable papers. Wang Zhigang published a conditional construction related to local-global compatibility for GL(n) in Annals of Mathematics; doctoral students Chen Yan and Zhou Yun published numerical evidence and a weak compatibility theorem in top journals. The group celebrated, but their triumph collapses when Weber publishes a paper in the same journal claiming a complete invariance result based on Pairing Correspondence, effectively invalidating all three papers and threatening the students' early careers.
Li Dong quietly reads Weber’s paper and recognizes its quality, but he notices a subtle potential weakness in the crucial inverse Tauberian estimate, Lemma W—the whole argument's cornerstone. He then reads the three group papers and confidently reassures everyone: "Don't worry. I'll cover you on this." He tells them to wait and leaves.
Key plot points: group's recent success, Weber's paper undermining it, Li Dong identifying the possible flaw, offering protection.
Character developments: Li Dong remains calm, perceptive, and takes responsibility for the group; Wang Zhigang shows concern for his students' morale; the students are talented but vulnerable.
Themes: mentorship, intellectual risk, fragility of mathematical reputation, group solidarity, and trust.
Character interactions: Wang Zhigang explains the situation; Li Dong listens, reads carefully, reassures the group, and leaves without drama.

Key Plot Points and Events

• Li Dong decides to proceed with proving the Li Conjecture without further delay due to the bullying of his colleagues.
• Weber's paper stirs up mathematical circles, with some professors at Beijing Normal University considering responding but ultimately hesitant.
• Luo Yu, after reading Weber's paper, secretly decides to take action against Li Dong.
• Online discussions heat up, with some misinterpreting Li Dong's previous statements and criticizing him for being selfish and narrow-minded.

Character Developments

• Li Dong: Becomes more determined to prove the Li Conjecture after his colleagues are bullied.
• Wang Zhiqiang: Still bitter from past humiliations by Li Dong, he remains silent when his colleagues suggest responding to Weber's paper.
• Luo Yu: Sees Weber's paper as an opportunity to settle his score with Li Dong.
• Weber: Gains recognition for his paper, but his methods are criticized for being too mechanical by Penrose.

Significant Themes

• Competition and Collaboration in Mathematics: The tension between Li Dong and Weber highlights the competitive nature of mathematics, while Li Dong's determination to prove the conjecture himself raises questions about collaboration and sharing of ideas.
• Perception vs. Reality: Li Dong's words are taken out of context and misinterpreted, leading to a distorted perception of his character and intentions.

Character Interactions

• Li Dong and Penrose: Their banter and mutual understanding continue, with Penrose offering both support and critique.
• Li Dong and Wang Hao: Wang Hao expresses his frustration and support for Li Dong, while Li Dong reassures him and remains confident in his abilities.
• Luo Yu and Li Dong: Luo Yu's secret decision to act against Li Dong sets up potential conflict between them.

Here is a concise summary of the chapter:

Emerging from Nowhere – Summary

1. Key Plot Points & Events

• The Clay Mathematics Institute holds a meeting and decides to offer a one-million-dollar prize for the Li Conjecture, treating it with the same weight as the Millennium Problems. Malcolm Griffin, previously opposed, now supports it after praising Elias Weber's recent paper.
• After the meeting, Griffin secretly calls Weber, saying "Five years will do" — revealing a scheme: if the Li Conjecture is proved within five years, the prize will be discredited as a joke.
• The announcement shocks the mathematical community. Weber's paper is widely celebrated, and he is viewed as a leading candidate to prove the conjecture. Some note his results seem to contradict Li Dong's earlier warnings.
• Meanwhile, at Peking University, Li Dong and Penrose finish a monumental proof: they establish that Pairing Correspondence holds if and only if an exact Functoriality Transfer exists between the relevant Automorphic Representations — effectively capping the Langlands program.
• Professor Wang Zhigang interrupts with bad news: three journals have demanded supplementary proofs from Wang, Chen Yan, and Zhou Yun for already-published papers, threatening retraction if not provided. Li Dong sees this as orchestrated bullying by someone pulling strings.
• Instead of backing down, Li Dong proposes to Penrose that they "turn this muddy pool completely upside down." Penrose agrees.
• The next day, a paper appears on arXiv: "Proof of the Langlands Functoriality Conjecture" by Li Dong and Penrose.

2. Character Developments

• Li Dong: Transitions from quiet achievement to decisive action. After completing the proof, he refuses to tolerate the behind-the-scenes manipulation and chooses to publicly confront the conspiracy.
• Penrose: Shows intense emotional investment in the proof, embracing Li Dong in joy. He willingly joins Li Dong's plan to expose the corruption.
• Malcolm Griffin: Revealed as a schemer. He uses the prize announcement as a trap, secretly coordinating with Weber to undermine the credibility of the Li Conjecture.
• Elias Weber: Implied to be Griffin's ally, positioned as a rival whose results conflict with Li Dong's.

3. Significant Themes

• Academic politics and manipulation: The chapter highlights how journals and institutions can be weaponized to suppress or discredit researchers.
• Truth vs. power: Li Dong chooses to fight back against unjust practices rather than suffer quietly.
• Mathematical rivalry and legacy: The competition over the Li Conjecture and the Langlands program reflects larger stakes of prestige and influence.
• Collaboration: Li Dong and Penrose work as a team, with their joint proof symbolizing unity against external pressure.

4. Character Interactions

• Griffin & Weber: A clandestine conversation reveals their coordinated plan to make the Li Conjecture prize look foolish if proved too soon.
• Li Dong & Penrose: An emotional, intimate moment of triumph when their proof succeeds; Penrose hugs Li Dong. Later, Li Dong proposes a bold plan and Penrose immediately agrees.
• Wang Zhigang & Li Dong: Wang delivers the troubling news about journal retractions; his expression reflects concern and perhaps suspicion about what he just witnessed.
• The mathematical community: Reacts to the prize announcement, debating Weber's merits and whether Li Dong will be sidelined from the Fields Medal.

This chapter sets up a direct confrontation between the independent proof by Li Dong and Penrose and the scheming of Griffin/Weber, promising escalating conflict in the mathematical world.

Summary: "Philadelphia Is Too Far Away (Free, Sorry)"

1. Key Plot Points and Events

• At Princeton, Professor Clark is in high spirits, believing that if Li Dong skips the International Congress of Mathematicians (ICM) in Philadelphia, Weber will win the Fields Medal. He praises Weber's GL(3) paper.
• A panicked teaching assistant rushes in with news that the Li Conjecture has been proven by Li Dong and Arthur Penrose.
• Weber and Clark read the arXiv paper titled "Proof of the Langlands Functoriality Conjecture"—a complete proof framework. Weber initially looks for flaws but instead finds the exact step he had failed to solve, then admits he cannot understand part of it.
• The paper explodes across the mathematical world: Andrew Sutherland (MIT), Matthew Emerton (University of Chicago), and countless others complain that Li Dong has skipped too many steps, making the proof nearly impossible to follow.
• Terence Tao publicly retracts his earlier claim that Li Dong's lighthouse would shine for 20–30 years, stating Li Dong has sailed beneath it. He also admits even he doesn't understand parts of the paper.
• Diana Shelstad fields phone calls about Langlands's reaction; Langlands simply laughs in his study.
• Peking University issues a statement: Li Dong's workload makes him unable to leave Beijing for an extended period, implying he may not attend the Philadelphia ICM.
• The real implication is revealed: the 2030 ICM is scheduled for Hong Kong, which is much closer to Beijing. The chapter title ("Philadelphia Is Too Far Away") frames this as a political/circumstantial push toward relocating the venue.

2. Character Developments

• Weber (Elias): A proud, reserved mathematician who silently endures Clark's chatter. The core development is his moment of humility—confronted with Li Dong's proof, he admits he cannot understand it, which is a painful truth for such a proud man. He also uncharacteristically snaps "Shut up" at Clark.
• Clark: Starts the chapter smug and dismissive of Li Dong, but his confidence visibly drains as he watches Weber's reactions. He ends the chapter cold and shaken.
• Terence Tao: Undergoes a public reversal, conceding the magnitude of Li Dong's achievement and revising his own earlier assessment.
• Li Dong: Off-screen protagonist, now proven to be on another level entirely; his absence from the ICM becomes a leverage point. His habit of "skipping steps" in papers frustrates the entire field but is treated as a mark of his exceptional depth.

3. Significant Themes

• Irreducible genius: Even the world's top mathematicians (Weber, Tao) cannot fully follow Li Dong's reasoning—his work exceeds even elite comprehension.
• Academic hierarchy and pride: The tension between established reputation (Princeton, Weber) and transformative outside genius (Li Dong, Peking University).
• The "skipping steps" motif: Represents the impossibility of transferring profound insight into readable, pedagogical form; readers must reconstruct the logic themselves.
• Geopolitics of mathematics: Institutional statements are used as political leverage—attendance at ICM is weaponized to pressure the venue toward Hong Kong.
• Lighthouse metaphor: Old landmarks of achievement (Tao's lighthouse) are obsolete once a genius sails past them.

4. Character Interactions

• Clark and Weber: One-sided banter shifting into discomfort; Weber directs Clark to "shut up," and Clark reads the paper's weight through Weber's increasingly grim expressions.
• Weber and the paper: A near-silent, intense reading session where Weber's confidence erodes page by page.
• Terence Tao and the online mathematical community: Tao posts a two-line retraction, then receives a flood of questions he declines to answer, instead directing them to Li Dong and admitting his own limits.
• Shelstad and callers: Sher repeatedly deflects inquiries about Langlands, ending in the image of Langlands's laughter.
• Correspondence reactions (Sutherland, Emerton): Function as a chorus of distressed experts, illustrating and humorously emphasizing the paper's difficulty.

Key Plot Points and Events

• International Mathematical Union (IMU) President Nakajima Kei visits Professor Yau in Beijing to discuss the venue change for the 30th International Congress of Mathematicians (ICM 2026) from Philadelphia to Hong Kong.
• After a week, the IMU officially announces the venue change due to "special circumstances," widely understood to be Li Dong's suspected proof of the Li Conjecture and his refusal to attend the conference in Philadelphia.

Character Developments

• Professor Yau: Maintains his calm and collected demeanor, subtly influences Nakajima Kei's decision by reminding him of the past and the current political climate.
• Nakajima Kei: Initially reluctant to change the venue, he ultimately accepts the inevitable after his conversation with Yau and the growing pressure from the mathematics community.

Significant Themes

• The influence of politics and power dynamics on academic events, particularly the ICM.
• The impact of Li Dong's suspected proof of the Li Conjecture on the mathematics community and the ICM.
• The tension between academic freedom and the expectations of the international mathematics community.

Character Interactions

• Yau and Nakajima Kei: Their conversation reveals the underlying reasons for the venue change and the delicate balance of power between them.
• The mathematics community (online discussions): Netizens from different countries react to the venue change, highlighting the global impact of Li Dong's actions and the ICM.

Key Plot Points and Events

• Li Dong holds his first public lecture at Tsinghua University, focusing on study methods and experiences rather than the Li Conjecture.
• The lecture hall is packed with over three hundred students, despite being intended for two hundred.
• Li Dong shares study methods inspired by Feynman, Grothendieck, and Hamming.

Character Developments

• Li Dong demonstrates humility and self-awareness by acknowledging that his methods may not suit everyone.
• Students begin to reevaluate their study methods and approaches to learning.

Significant Themes

• The importance of understanding one's own limitations and not fooling oneself.
• The power of compounding knowledge and the benefits of a broader perspective.
• The value of learning from great minds and adapting their methods to one's own needs.

Character Interactions

• Li Dong engages with the audience, acknowledging their thoughts and feelings, and encouraging them to reflect on their own learning processes.
• Students interact with each other, discussing their expectations and takeaways from the lecture.

Key Plot Points and Events

• Li Dong's open lecture at Tsinghua University is recorded and forwarded to Luo Yu and Clark.
• Luo Yu and Clark misinterpret Li Dong's statement about not having figured out the explanation for his paper, assuming it means he hasn't understood his own work.
• Luo Yu shares his findings with a contact, expressing his intention to expose Li Dong's paper at the upcoming ICM.
• Clark shows Weber the video, trying to convince him to help find flaws in Li Dong's paper, but Weber remains unconvinced.
• Langlands continues to study Li Dong's paper, struggling with certain sections, and decides to attend the ICM in Hong Kong.

Character Developments

• Li Dong: Stated that he hadn't figured out how to explain his paper clearly, leading to misinterpretations by Luo Yu and Clark.
• Luo Yu: Becomes more determined to expose Li Dong's paper, believing it lacks substance.
• Clark: Grows more desperate to discredit Li Dong's work, trying to rally support from others.
• Weber: Remains skeptical of Li Dong's paper but hasn't found any flaws, and is still trying to understand it fully.
• Langlands: Continues to study Li Dong's paper, making progress but still struggling with certain parts.

Significant Themes

• Misinterpretation and Assumption: Luo Yu and Clark misinterpret Li Dong's words, leading to wrong assumptions about his work.
• Perseverance and Patience: Langlands continues to study Li Dong's paper, showing determination and patience in understanding complex mathematical concepts.
• Hubris and Arrogance: Luo Yu and Clark display overconfidence in their abilities and underestimate Li Dong's work.

Character Interactions

• Luo Yu and Li Dong: Indirect interaction through the open lecture video, with Luo Yu misinterpreting Li Dong's words.
• Clark and Weber: Clark tries to convince Weber to help find flaws in Li Dong's paper, but Weber remains unconvinced.
• Langlands and Diana: Langlands asks Diana to book a flight to Hong Kong for the ICM, showing their close working relationship.

Key Plot Points and Events

• Li Dong travels to Hong Kong for the International Congress of Mathematicians, accompanied by his life teachers, Old Zhang and Old Wu.
• Upon arrival, he is greeted by Director Zhang Ming from Hong Kong University, who invites him for an academic exchange, but Li Dong declines due to his preparation for the conference.
• Li Dong stays at the Grand Hyatt Hotel, where he continues working on his presentation, feeling it's too wordy and not up to his usual standards.
• The International Congress of Mathematicians begins, with mathematicians from around the world gathering, discussing, and debating various topics. The Li Conjecture is the main attraction of this year's conference.

Character Developments

• Li Dong: He is focused on perfecting his presentation for the conference, showing his dedication and meticulousness. He also displays humility and politeness in declining Director Zhang's invitation.
• Old Zhang and Old Wu: They demonstrate their loyalty and protective nature towards Li Dong, as seen in their immediate response to block Director Zhang when he approaches Li Dong too quickly.

Significant Themes

• The power of mathematics to bring people together from all corners of the world.
• The anticipation and significance of the Li Conjecture, which has the potential to greatly advance number theory and the Langlands Program.
• The humility and dedication of mathematicians, who are eager to share and learn from each other despite their individual achievements.

Character Interactions

• Li Dong and Director Zhang Ming: Their brief interaction highlights Li Dong's politeness and Director Zhang's understanding and tactfulness in not pressing Li Dong for a commitment.
• Li Dong and Old Zhang/Old Wu: Their dynamic shows the close, protective relationship between Li Dong and his life teachers, who are always ready to defend him.

Key Plot Points and Events

• Li Dong and Penrose encounter each other at the hotel, with Sarah present in Penrose's room, leading to a misunderstanding.
• Li Dong faces reporters questioning his Li Conjecture, to which he confidently responds.
• The International Congress of Mathematicians begins, and the awards ceremony starts with the Abacus Prize and Chern Prize.
• Li Dong is announced as the first recipient of the Fields Medal.

Character Developments

• Li Dong maintains his composure and confidence amidst reporters' questioning, showing maturity.
• Penrose is flustered due to the misunderstanding and tries to explain but is dismissed by Li Dong.
• Sarah is excited about her breakthrough but remains respectful and considerate of her mentor's situation.

Significant Themes

• Mathematical Excellence: The congress highlights the achievements of mathematicians, emphasizing the value of their contributions to the field.
• Recognition and Rewards: The awards ceremony underscores the importance of recognition and rewards in academia, driving scholars to strive for excellence.
• Misunderstandings and Trust: The encounter between Li Dong, Penrose, and Sarah highlights the potential for misunderstandings to arise and the importance of trust in relationships.

Character Interactions

• Li Dong and Penrose have a tense encounter due to a misunderstanding, with Penrose trying to explain and Li Dong dismissing it.
• Li Dong interacts with reporters, maintaining his composure and confidence.
• Li Dong reconnects with his professors, Liu Ruochuan and Tian Gang, showing respect and camaraderie.
• Li Dong is acknowledged by other mathematicians, such as Yang Shengguo, who express their anticipation for his potential Fields Medal win.

Key Plot Points and Events

• Li Dong, a Huaxia mathematician, wins the Fields Medal, the first from his country.
• The award is announced at a conference in Hong Kong, sparking national pride and excitement.
• The medal, awarded every four years to mathematicians under 40, is considered the highest honor in mathematics.

Character Developments

• Li Dong: Becomes the first Huaxia mathematician to win the Fields Medal, fulfilling a long-standing national aspiration.
• Tian Gang: Li Dong's teacher, who had been close to winning the medal in 2002 but missed out. He is deeply moved by Li Dong's achievement.
• Chen Ke: A physics teacher who is happy but also jealous that Li Dong won the Fields Medal instead of a Nobel Prize in Physics.

Significant Themes

• National Pride: Li Dong's achievement is seen as a source of national pride and a symbol of Huaxia's rise.
• Regret and Fulfillment: Tian Gang's regret over not winning the medal in 2002 is fulfilled through Li Dong's victory.
• Ambition and Achievement: The Fields Medal represents the highest ambition in mathematics, and Li Dong's win signifies his exceptional achievement.

Character Interactions

• Tian Gang and Liu Ruochuan: Tian Gang's student, Liu Ruochuan, consoles him and helps him see Li Dong's win as a reflection of his own work.
• Chen Ke and his student: Chen Ke expresses his happiness and jealousy to his student, who is impressed by Li Dong's achievement.
• Online Community: The online community reacts with excitement, pride, and some skepticism to Li Dong's win.

Chapter Summary

1. Key Plot Points & Events

• The IMU ceremony continues after the first Fields Medal announcement. Nakajima Kei announces the second recipient: Wang Hong (Huaxia), for solving the Three-Dimensional Kakeya Conjecture with collaborators.
• The third Fields Medal goes to John Pardon (Princeton) for symplectic topology and low-dimensional geometry breakthroughs.
• Razivil (Chicago) is not selected—this was his last chance before the age limit, and he silently watches.
• Li Dong later talks with Wang Hong, then is introduced by Diana to Robert Langlands, the founder of the Langlands Program. Langlands praises Li Dong’s proof of functoriality, while joking that Li Dong “locked the door too well.”
• Over the next days, Li Dong attends lectures (including Terence Tao’s), stores interesting ideas in his Memory Palace, and meets with Tian Gang and Liu Ruochuan, who hint at discussing their AI-related work back at the university.

2. Character Developments

• Li Dong: Confident yet humble; he promises to “open the door” to the Langlands program for Langlands. He also remains curious and collaborative, wanting to learn about AI.
• Wang Hong: Friendly and slightly playful; she congratulates Li Dong and teases him about asking hard questions later.
• Robert Langlands: Reflective and emotional; seeing his life’s vision realized by a young mathematician stirs memories, but he responds with warmth and approval.
• Gu Chengzhi (elderly Huaxia mathematician): Moved to tears, remembering his teacher Shiing-Shen Chern’s dream of China becoming a mathematical powerhouse—now fulfilled by the younger generation.

3. Significant Themes

• Generational legacy and national pride: Ninety years without a homegrown Huaxia Fields Medalist, then two in one year—symbolizing the fruition of past mathematicians’ struggles.
• Passing the torch: Langlands passing his vision to Li Dong; older generation’s hopes realized by the young.
• Collaboration across fields: Wang Hong’s geometry and Li Dong’s number theory both honored; mutual respect and friendship.
• The grandeur of the Langlands Program: Referenced as the “Grand Unified Theory of Mathematics” and a door that Li Dong has unlocked for others.

4. Character Interactions

• Li Dong & Wang Hong: They congratulate each other, exchange friendly banter about future questions, and represent a new generation of Huaxia mathematicians.
• Li Dong & Langlands: A meaningful meeting—Langlands is impressed, slightly envious, but ultimately delighted; Li Dong promises to assist him in understanding the proof.
• Gu Chengzhi & his fellow elderly scholars: Silent, tearful pride as they watch the young recipients on stage.
• Li Dong & Tian Gang/Liu Ruochuan: A brief but important setup for future collaboration on AI research.

Key Plot Points and Events

• Li Dong's Fields Medal lecture, scheduled on the final day of the conference, draws an unprecedented crowd due to his proof of the Li Conjecture, a core part of the Langlands Program.
• Security is taken over by a special department due to the overwhelming crowd and unauthorized attendees.
• Li Dong's lecture begins, and he presents a simplified version of his original paper, walking the audience through it line by line.

Character Developments

• Li Dong demonstrates his expertise and thoroughness in explaining his work, filling in skipped steps and simplifying complex concepts for the audience.
• Old Zhang, a professor in the audience, overcomes a long-standing issue in his understanding of Li Dong's work during the lecture.

Significant Themes

• The Langlands Program and Automorphic Representations: Li Dong's lecture revolves around these central themes in number theory.
• The connection between zeros of L-functions, Satake Parameters, primes, and random matrix theory.
• The use of the Rankin–Selberg convolution to determine whether two representations are the same.

Character Interactions

• Li Dong interacts with the audience through his lecture, addressing their unspoken questions and providing clarifications.
• Old Zhang silently interacts with Li Dong's lecture, finally understanding a concept that had eluded him for over half a month.

Summary

1. Key Plot Points & Events

• Li Dong gives a highly detailed lecture at the International Congress of Mathematicians, explaining his proof step-by-step — including ramification index conditions, his zero criterion for functoriality, and local-global compatibility.
• He reaches a critical step involving pair correlation functions: he argues that second-order statistics (pair correlation) alone cannot reverse-engineer the exact arrangement of zeroes; multiple candidates can share the same averaged statistics.
• He uses local-global compatibility to constrain candidates, then uses a Rankin-Selberg pole at s=1 to finalize the verification.
• To make the point clearer, he presents a counterexample: two cuspidal representations with identical pair correlation functions that are nonetheless not isomorphic. He calls this the “Functorial Degeneration Locus” — invisible to second-order statistics.
• This counterexample directly dismantles Weber's famous paper “Rigidity of Zero Pair Correlations — A Complete Invariant for GL(n) Cuspidal Automorphic Representations”, which claimed pair correlation uniquely determines the representation.
• Li Dong concludes with the cutting remark: “The second order is too low. It simply cannot see everything.”

2. Character Developments

• Li Dong: Shows both technical mastery and tactical ruthlessness. He deliberately explains his own proof so clearly that everyone can understand his counterexample — making Weber’s humiliation unavoidable and public. He is calculating, calm, and quietly devastating.
• Weber: Begins confident, proud of his own Inversion Lemma. As Li Dong diverges from his approach, Weber becomes unsettled; when the counterexample lands, he realizes his own paper’s core argument is flawed. He sits visibly humiliated, his expression darkening.
• Liu Ruochuan: Initially confused by Li Dong’s unusually patient manner, then realizes Li Dong’s real motivation — to ensure everyone understands enough to see Weber’s paper destroyed.
• Wiles, Langlands, Tian Gang, Yau, and other senior mathematicians: Among the first to grasp what is about to happen, and silently watch the debacle unfold.

3. Significant Themes

• Mathematical rigor vs. false completeness: Li Dong demonstrates that a “beautiful” argument can collapse if it oversimplifies — here, second-order statistics can miss structural twists.
• Academic rivalry and public demolition: The lecture is not just a proof, but a carefully staged refutation of a rival’s work.
• The phrase “too low” functions as a double insult: mathematically insufficient and personally belittling.

4. Character Interactions

• Li Dong addresses the audience but pointedly looks at Weber when introducing the counterexample — making it a direct, public attack.
• The audience’s silence and gazes shift between Li Dong and Weber, marking Weber as the clear loser.
• Weber says nothing throughout; his realization dawns silently while others record Li Dong’s explanation.
• The veteran mathematicians exchange knowing looks, having anticipated the outcome before everyone else.

Key Plot Points and Events

• Li Dong, undeterred by the audience's reactions, continues his presentation to defend his group members' work.
• He refutes Weber's paper and supports three previously criticized papers from his research group.
• Li Dong proves the Li Conjecture, causing a stir in the audience and online viewers.
• Weber raises his hand to ask a question after Li Dong's presentation.

Character Developments

• Li Dong: Shows unwavering support for his group members and proves the Li Conjecture, solidifying his reputation as a mathematical genius.
• Weber: Initially discredited, he remains composed and decides to ask a question after Li Dong's presentation, hinting at a potential change in his stance.

Significant Themes

• Support and loyalty: Li Dong stands up for his group members, highlighting the importance of unity and mutual support in academic pursuits.
• Truth and recognition: The refutation of Weber's paper and the acceptance of Li Dong's proof emphasize the pursuit of truth and the importance of recognition in the academic community.

Character Interactions

• Li Dong vs. Weber: Li Dong publicly refutes Weber's paper, leading to a tense interaction between the two mathematicians.
• Li Dong and the audience: Li Dong's calm and confident demeanor captivates the audience, earning their respect and admiration.
• Online viewers: The livestream audience engages in lively discussions, expressing their excitement and awe at Li Dong's accomplishment.

Chapter Summary

1. Key Plot Points & Events

• Weber, a humiliated Princeton professor, publicly acknowledges Li Dong's dismantling of his paper. He then attempts to ask a question about whether Li Dong's Complete Invariant method could identify "objects" that have no number field or automorphic representation but whose spectra obey the Higher-Order Pairing Correspondence.
• A mysterious suited man interrupts, and Weber becomes visibly terrified. He apologizes and follows the man out. Old Zhang quietly follows them.
• Inside the Memory Palace, Li Dong retrieves Weber's incomplete "inspiration" (a document) via his Passing the Torch ability. The idea: use higher-order correlations as "fingerprints" to recognize that two seemingly unrelated objects are calculating the same thing. Li Dong senses it could be a "key" for an unknown, potentially larger application.
• Post-lecture, Li Dong is swarmed by media. He clarifies that he and Wang Hong are co-first recipients, and predicts more Chinese mathematicians coming. He rebuffs Eagle Eye News.
• A reporter mutters that pure math "can't be turned into productivity"; Li Dong stops walking, hinting at an impending, potentially intense response.

2. Character Developments

• Li Dong: Shows confidence and composure, both in handling academics and media. He is highly introspective via the Memory Palace, and intuitively senses that Weber's half-baked idea might be significant beyond what it seems. He sets aside the "key" but appears poised to respond to provocation.
• Weber: Maintains academic dignity after defeat, using it to sharpen Li Dong's critique. However, his demeanor shifts drastically when the suited man appears—he is drenched in cold sweat, realizes he has "signed" something consequential, and immediately yields; his fear turns a professional matter into a personal one.
• Old Zhang / Old Wu: Their nonverbal exchange reveals they are operating as silent observers with a shared, unspoken agenda, prompting Old Zhang to follow the mysterious man and Weber.

3. Significant Themes

• Academic prestige vs. hidden dangers: Math is not just abstract theory; it is entangled with something mysterious, and certain ideas carry severe, personal consequences.
• The "uselessness" of pure mathematics: Contrasts the foreign reporter's dismissal (pure math cannot produce productivity) with the suggestion that such mathematics may actually unlock unknown, powerful doors (Weber's idea, the key).
• National pride and rivalry: Li Dong's claim that Huaxia mathematicians will become the norm signals shifting global academic power, and his clash with Eagle Eye News highlights tension between foreign media and Chinese achievement.

4. Character Interactions

• Weber ↔ Li Dong: Weber publicly sharpens Li Dong's argument rather than defending himself, framing himself as a worthy adversary and posing a potentially deep challenge.
• Weber ↔ Mysterious Man: The man's presence silences Weber; Weber obeys immediately—establishing a power dynamic beyond academia.
• Old Zhang ↔ Old Wu: A brief glance is enough for them to coordinate surveillance, showing they are long-time collaborators.
• Li Dong ↔ Media: Li Dong is polite but firm with domestic media, deflects provocation from Eagle Eye News, and deliberately stops at the "mutter" to provoke the reporter into pursuing a scandal he seems willing to engage with.