Chapter Summaries

Key Plot Points and Events

• Li Dong is appointed as Tian Gang's teaching assistant for a graduate class.
• Tian Gang begins lecturing on the long-time existence problem of the Kähler-Ricci Flow.
• Li Dong actively assists Tian Gang during the lecture, anticipating and writing down key steps and references.

Character Developments

• Li Dong demonstrates his exceptional learning ability and intuitive judgment, keeping pace with Tian Gang's rapid lecture.
• Tian Gang recognizes Li Dong's extraordinary potential and decides he needs a mentor across multiple cutting-edge fields.

Significant Themes

• The struggle to keep up with advanced mathematical concepts and the exhilaration of understanding them.
• The value of having a strong foundation in mathematics to grasp complex ideas.
• The importance of mentorship for exceptional students.

Character Interactions

• Li Dong and Tian Gang collaborate during the lecture, with Li Dong anticipating and supporting Tian Gang's teaching.
• Other graduate students struggle to keep up with the lecture, highlighting Li Dong's exceptional abilities.
• Tian Gang recognizes Li Dong's potential and considers becoming his mentor.

Chapter Summary

1. Key Plot Points

• Tian Gang asks Li Dong for help, which surprises Li Dong because Tian Gang is an academician.
• Tian Gang explains that Li Dong’s paper on the Montgomery Pair Correlation Conjecture has become a foundational tool in number theory and the Langlands Program, not just a solved problem.
• Tian Gang’s doctoral student, Song Zheyuan, is stuck on a project about zero spacing in Dirichlet L-functions and needs Li Dong’s guidance.
• Li Dong agrees and diagnoses the problem: Song Zheyuan was applying the full interval uniformly instead of stratifying characters by conductor and matching intervals.
• Li Dong’s proposed “layered matching” method unblocks the research and opens further possibilities.
• Tian Gang notices something unusual: Song Zheyuan’s questions are unusually precise and on-target, making Tian Gang suspect Li Dong is somehow guiding him.

2. Character Developments

• Li Dong: Shows generosity, sharp mathematical insight, and exceptional teaching clarity. He understands how foundational research works and accepts the role of being a tool-builder for others.
• Tian Gang: Strategic and institutionally proud. He sees Li Dong’s work not just as a personal achievement but as a resource that Peking University should harness. He also becomes wary when Song Zheyuan behaves abnormally well.
• Song Zheyuan: Initially nervous, but quickly becomes inspired and sees his research path clearly after Li Dong’s explanation. His rapid comprehension surprises even his own advisor.

3. Significant Themes

• Foundational mathematics: A truly great paper is judged by how much later work it enables.
• Academic influence and citation: Being cited and extended is how a mathematician’s legacy grows.
• Mentorship and collaboration: Even top researchers need guidance from the right person.
• Institutional ambition: Universities and advisors want their own scholars to be the ones who build on new breakthroughs.
• Mathematical clarity: Li Dong’s ability to explain cutting-edge ideas in an understandable way is itself remarkable.

4. Character Interactions

• Tian Gang ↔ Li Dong: Tian Gang carefully flatters and persuades Li Dong into helping, revealing his larger plan for Peking University. Li Dong agrees readily.
• Li Dong ↔ Song Zheyuan: Li Dong directly addresses the technical problem, writes formulas on the board, and gives a clear solution. Song Zheyuan’s mindset shifts from being stuck to seeing the full path forward.
• Audience ↔ Li Dong: Graduate students and listeners can follow the advanced discussion surprisingly well, showing Li Dong’s unusual pedagogical gift.
• Tian Gang internal observation: Tian Gang becomes suspicious that Song Zheyuan’s perfect questions are too good to be natural, hinting that Li Dong may be influencing events in a way not fully explained.

Key Plot Points and Events

• Jiang Yubai, a renowned mathematician, reminisces about a past incident involving a student who discovered a crucial p-adic integration path-deformation scheme, which Jiang Yubai later published without proper credit.
• Zhou Shenzhi, Jiang Yubai's current student, struggles to extend the same method to a new case (e_v=3) due to lack of understanding of the underlying logic.
• Li Dong, a 19-year-old freshman at Peking University, publishes a groundbreaking paper on the Montgomery Pair Correlation Conjecture, offering a new line of attack for the Langlands Program.

Character Developments

• Jiang Yubai: Reflects on his past actions, showing regret and admiration for Li Dong's work.
• Zhou Shenzhi: Struggles with his research, facing a crisis of confidence and inspiration, and feels his teacher's disappointment.
• Li Dong: Demonstrates exceptional mathematical prowess and understanding, attracting the attention and admiration of senior mathematicians.

Significant Themes

• Academic Integrity: The chapter explores the consequences of academic dishonesty and the importance of giving credit where it's due.
• Mentorship and Legacy: It delves into the complex dynamics between mentors and students, and the impact of a mentor's actions on their students' academic trajectories.
• Inspiration and Understanding: The struggle to extend a mathematical method highlights the importance of understanding the underlying logic for true progress.

Character Interactions

• Jiang Yubai and Zhou Shenzhi: Their dynamic shows the tension between a mentor's expectations and a student's struggles, with Jiang Yubai's disappointment in Zhou Shenzhi's progress.
• Li Dong and Tian Gang: Their interaction demonstrates Li Dong's eagerness to learn and grow, and Tian Gang's pride in his student's achievements.
• Li Dong and the doctoral students: Their interaction showcases Li Dong's ability to engage with and explain complex mathematical concepts to his peers.

Key Plot Points and Events

• Li Dong approaches Professor Tian Gang with a research topic that aims to extend local-global compatibility from GL2 to GL(n), shocking everyone present.
• Tian Gang expresses doubts about Li Dong's high school teacher's capability to contribute to such a complex project.
• Li Dong requests help from Tian Gang to secure a position for his high school teacher as an externally appointed researcher or visiting scholar at Peking University.
• Tian Gang suggests Li Dong apply to establish a research group himself and then secure the position for his teacher through the university's formal procedures.

Character Developments

• Li Dong: Shows initiative and ambition by proposing a highly complex research topic and seeking help to involve his high school teacher.
• Tian Gang: Demonstrates his expertise and experience by understanding the magnitude of Li Dong's proposed research topic and offering guidance on how to proceed.

Significant Themes

• Ambition and Initiative: Li Dong's eagerness to tackle a challenging research topic and involve his high school teacher highlights his ambition and initiative.
• Mentorship and Guidance: Tian Gang's willingness to provide guidance to Li Dong, despite his initial reservations, underscores the importance of mentorship in academic pursuits.

Character Interactions

• Li Dong and Tian Gang: Their interaction reveals Li Dong's audacious research plans and Tian Gang's willingness to guide and challenge Li Dong.
• Li Dong and Li Qin: Li Qin's call to inform Li Dong about their mother's potential visit to Kyoto shows their close sibling relationship.

Key Plot Points and Events

• Li Qin, Li Dong's mother, unexpectedly decides to visit him in Kyoto.
• Li Dong learns that Yang Shengguo (his former teacher) and his family will also visit Kyoto during winter break.
• Professor Arthur Penrose secretly travels to Kyoto to meet Li Dong, without informing his university.

Character Developments

• Li Dong shows concern for his mother's unexpected visit and is eager to help Yang Shengguo achieve recognition.
• Professor Penrose is driven by his passion for mathematics and Li Dong's work, leading him to secretly travel to Kyoto.

Significant Themes

• Family and personal relationships (Li Dong's concern for his mother and Yang Shengguo).
• Academic passion and pursuit of knowledge (Professor Penrose's obsession with Li Dong's paper).

Character Interactions

• Li Dong and Li Qin: Li Dong is suspicious about his mother's sudden decision to visit, while Li Qin tries to keep the reason secret.
• Li Dong and Yang Shengguo: Li Dong is excited to help his former teacher and is eager to welcome him to Kyoto.
• Professor Penrose and Sarah: Penrose is determined to visit Li Dong, while Sarah worries about the potential academic and administrative implications.

Key Plot Points and Events

• Zhou Shenzhi attempts to arrange a meeting with Li Dong to discuss the Zero Criterion but is blocked by Peking University.
• Zhou Shenzhi decides to post a Comment on ArXiv challenging Li Dong's paper to force him to respond publicly.
• Li Dong requests leave from his counselor to meet his mother in Kyoto.

Character Developments

• Zhou Shenzhi: Becomes more determined to challenge Li Dong's paper to advance his own research and honor his teacher.
• Li Dong: Maintains his independence and confidence, requesting leave without hesitation.

Significant Themes

• Academic rivalry and the pursuit of knowledge.
• The tension between protecting a student's privacy (Peking University's refusal to allow a meeting) and the open exchange of ideas in academia (Zhou Shenzhi's Comment).
• The pressure and expectations placed on exceptional individuals (Li Dong).

Character Interactions

• Zhou Shenzhi's internal struggle and determination to challenge Li Dong's paper.
• Li Dong's casual interaction with his counselor, highlighting his independence and confidence.
• The implicit tension between Zhou Shenzhi and Li Dong, with Zhou Shenzhi feeling pressured by Li Dong's achievements.

Key Plot Points and Events

• Li Dong awaits Li Qin and Old Yang's arrival in Beijing while pondering Riemann's hint about automorphic functions and zero-point pairing correspondence.
• Li Dong struggles to determine the convergence interval for the pair-correlation function F_π(a) of zeros of automorphic L-functions.
• He remembers a paper by Jiang Yubai and Zhou Shenzhi that might provide a special case for comparison.
• Li Dong deciphers the omitted steps in the paper and understands the brilliance of Old Yang's construction.

Character Developments

• Li Dong demonstrates his exceptional mathematical intuition and ability to piece together complex ideas.
• Old Yang (Jiang Yubai) is revealed to have significant mathematical prowess, with a logical attribute of at least 0.1.

Significant Themes

• The struggle to prove local-global compatibility in the Langlands Program, and the potential of using statistical properties of zeros to bypass algebraic methods.
• The importance of understanding the underlying logic and intuition behind mathematical constructions.

Character Interactions

• Li Dong's thoughts about Old Yang's potential and their future collaboration.
• Li Dong's silent interaction with Riemann's hint, driving his exploration and understanding of the mathematical problem.

Key Plot Points and Events

• Li Dong is engrossed in mathematical enlightenment, ignoring his surroundings.
• Wang Hao, Liu Qiang, and Chen Nan go to the cafeteria, discussing the upcoming winter break and the National Undergraduate Mathematical Contest in Modeling (CUMCM).
• Li Dong receives a call from Zhang Wenping, a renowned academician, who invites him to serve as an innovative achievement review expert for the upcoming CUMCM.

Character Developments

• Li Dong: Shows exceptional mathematical prowess and is recognized by an esteemed academician, indicating his potential and growth.
• Wang Hao: Demonstrates leadership and ambition by organizing a team for the CUMCM, but feels overshadowed by Li Dong's invitation to be a review expert.
• Liu Qiang and Chen Nan: Struggle with their academic project and feel the gap between their mathematical abilities and Wang Hao's.

Significant Themes

• Genius and Prodigy: Li Dong's exceptional abilities are highlighted, contrasting with his peers' more average academic performances.
• Competition and Rivalry: Wang Hao's ambition to excel in the CUMCM is tempered by Li Dong's invitation, creating a subtle rivalry.
• Mentorship and Recognition: Zhang Wenping's invitation to Li Dong underscores the importance of recognition and mentorship in academic growth.

Character Interactions

• Wang Hao, Liu Qiang, and Chen Nan interact as roommates, discussing their plans for winter break and the CUMCM. Their dynamic shifts when Li Dong is invited to be a review expert.
• Li Dong interacts with Zhang Wenping, showcasing his expertise and thoughtfulness in his responses to the academician's questions.

Chapter Summary

1. Key Plot Points and Events

• Winter break begins at Peking University; Li Dong prepares to pick up his mother, Li Qin, at Beijing Capital International Airport (flight lands around noon).
• Before leaving, he promises his roommates (Wang Hao, Liu Qiang, and another) a dinner that night, warning them not to say anything foolish.
• Li Dong runs into Professor Arthur Penrose (a visiting American mathematician from Princeton) on campus. Penrose had arrived days earlier but had been unable to meet Li Dong directly due to procedural restrictions tied to Li Dong’s involvement in sensitive tech (Dimensionality-Reduction Algorithm 2.1, lithography, semiconductor strategy).
• Penrose has been wandering campus, attending undergraduate lectures, and observing differences between Peking University and Princeton education.
• Li Dong is in a hurry but promises Penrose he will show him something “especially fun” in a few days—hinting at a new joint project (extension of local-global compatibility from GL₂ to GL(n) automorphic representations) proposed by Liu Ruochuan to keep Penrose engaged without involving classified work.
• Meanwhile, Tian Gang (a professor at the School of Mathematical Sciences) reads a harsh critical commentary by Zhou Shenzhi about omitted steps in Li Dong’s proof of the Montgomery Pair Correlation Conjecture and its applicability to GL(n). Tian Gang dismisses the criticism as “academic bullying,” saying he has already dealt with that tactic before.

2. Character Developments

• Li Dong: Shows a mix of personal warmth (worry about his mother) and strategic thinking (quickly improvising a “fun” promise to manage Penrose). He remains confident, proactive, and aware of institutional constraints.
• Arthur Penrose: Characterized as a genuinely enthusiastic, patient academic. He adapts to the waiting period by exploring the university, showing open-mindedness and appreciation for differing educational systems. His faith in Li Dong’s integrity grows—he does not see the promise as a brush-off.
• Tian Gang: Portrayed as experienced and shrewd, immediately recognizing the critical commentary as an attempt at academic bullying. His reaction suggests a history of navigating such attacks, implying determination and resilience.

3. Significant Themes

• Academic Bullying and Rivalry: The chapter’s title and Tian Gang’s inner monologue frame the core theme—intellectual attacks disguised as criticism. Zhou Shenzhi’s commentary is presented as a calculated attempt to undermine Li Dong’s work.
• International Academic Relations & Security: The friction between pure academic curiosity and national/technological sensitivities. Penrose’s visit is delayed due to Li Dong’s connection to classified projects; the solution is to redirect Penrose to a safe but prestigious mathematical problem.
• Contrast of Educational Philosophies: Penrose’s reflections highlight differences between the Chinese and American systems—strong fundamentals and specialized training vs. broader interdisciplinary exposure; also the emotional weight of student debt in the U.S. versus hope among Peking University students.
• Personal/Family Concern: Li Dong’s worry about his mother’s sudden visit adds an undercurrent of personal mystery and emotional stakes.

4. Character Interactions

• Li Dong and Roommates: Brief, comedic exchange—roommates tease him about possibly having a girlfriend; he warns them to behave around his mother.
• Li Dong and Penrose: Chance encounter on campus. Penrose is excited and eager; Li Dong is polite but pressed for time. Their exchange ends with Li Dong making a tantalizing promise, which Penrose takes seriously (contrasting with Sarah’s skepticism).
• Penrose and Sarah: Sarah shows mild cynicism, suggesting Li Dong was brushing them off; Penrose trusts Li Dong’s credibility.
• Tian Gang (with the commentary): Solo interaction with a document, but marked by a defiant, confrontational internal response to the author, Zhou Shenzhi.

Key Plot Points and Events

• Zhou Shenzhi's Comment on Li Dong's paper triggers a storm in the mathematical community.
• Li Dong's mother, Li Qin, visits him in Beijing.
• A special seminar is announced to address the academic questions raised about Li Dong's paper, with prominent mathematicians including Terence Tao, Arthur Penrose, and Shing-Tung Yau confirmed to attend.

Character Developments

• Li Dong remains calm and confident in the face of academic scrutiny.
• Li Qin shows concern for Li Dong's well-being and is determined to support him.
• Zhou Shenzhi's Comment garners respect due to his academic standing and the influence of his mentor, Jiang Yubai.
• Tian Gang demonstrates his influence and connections by organizing a high-profile seminar and inviting prominent mathematicians, including his long-time rival, Yau.

Significant Themes

• Academic integrity and self-awareness in the mathematical community.
• The power dynamics and rivalries within the academic world.
• The importance of family support and presence.

Character Interactions

• Li Dong and Li Qin's mother-son dynamic is shown, with Li Qin expressing concern for Li Dong's health and Li Dong trying to understand his mother's true intentions for visiting.
• Tian Gang and Li Dong's mentor-mentee relationship is strengthened as Tian Gang supports Li Dong and organizes the seminar to address the academic questions raised about his paper.
• The relationship between Tian Gang and Yau is highlighted, with their long-standing feud put aside for the sake of attending the seminar focused on Li Dong's work.

Key Plot Points and Events

• A symposium on Li Dong's complete analytic proof of the Montgomery Pair Correlation Conjecture is held at Peking University's Sunshine Hall.
• The event is organized by Tian Gang, head of BICMR, in just three days, attracting scholars from across China and internationally.
• The symposium aims to publicly address and refute the thirteen objections raised against Li Dong's paper.

Character Developments

• Tian Gang: Shows his influence and network in China's mathematical community by organizing the symposium in record time.
• Li Dong: Prepares to present his proof publicly, demonstrating confidence and resilience in the face of academic bullying.
• Penrose: Anticipates Li Dong's presentation with excitement and eagerness, viewing him as a prodigy.
• Marvin Clark: Arrives at the symposium with the intention to challenge Li Dong's work, revealing his political maneuvering and jealousy of Li Dong's achievements.

Significant Themes

• Academic Integrity vs. Bullying: The symposium highlights the tension between academic integrity and bullying, with Tian Gang and Li Dong standing up against the latter.
• International Collaboration: The event showcases international cooperation and mutual respect among mathematicians, transcending geographical boundaries.
• Mentorship and Recognition: Penrose's eagerness to witness Li Dong's presentation underscores the importance of mentorship and recognition in academia.

Character Interactions

• Tian Gang and Li Dong: Tian Gang supports Li Dong by organizing the symposium, demonstrating his faith in Li Dong's work and his commitment to protecting young mathematicians from bullying.
• Penrose and Marvin Clark: Their interaction reveals the underlying tension and competition between them, with Clark attempting to undermine Li Dong's work and Penrose's support for him.
• Li Dong and the Mathematical Community: Li Dong's presentation brings together the global mathematical community, fostering dialogue, debate, and mutual learning.

Key Plot Points and Events

• Li Dong is about to begin his seminar at Peking University, titled "The Montgomery Pair Correlation Conjecture for |α| ∈ [0, 4]: A Complete Proof."
• He expresses surprise that so many renowned mathematicians are attending, including Terence Tao, Zhang Yitang, Clark, and others.
• Li Dong plans to give a brief overview of his 47-page paper in just half an hour.

Character Developments

• Li Dong shows confidence and nonchalance, stating he'll summarize his complex proof in a short time.
• Yang Shengguo, Li Dong's former teacher, attends the seminar but chooses to sit in the back, avoiding the front row where his former student, Zhou Shenzhi, is seated.

Significant Themes

• The theme of mathematical prowess and the challenge of proving complex theorems is prominent.
• The dynamics of academic rivalry and respect among mathematicians are explored.

Character Interactions

• Li Dong interacts with the audience, expressing surprise at their attendance and his intention to summarize his proof quickly.
• Yang Shengguo interacts with his family, showing hesitation about attending the seminar due to his past with Zhou Shenzhi.
• Mathematicians in the audience react to Li Dong's claim, with some expressing skepticism or amusement (e.g., Tao, Clark, Zhou Shenzhi).

Key Plot Points and Events

• Li Dong presents his proof of the Montgomery Pair Correlation Conjecture at a seminar.
• He addresses and clarifies thirteen points of criticism from his paper's comments on ArXiv.
• The audience, including renowned mathematicians, is impressed by Li Dong's explanation and understanding of the subject.

Character Developments

• Li Dong demonstrates exceptional mathematical prowess, clarity, and confidence in his presentation.
• Mathematicians like Terence Tao, Zhang Yitang, and Roger Penrose are awestruck by Li Dong's understanding and ability.
• Clark, a skeptic, is left with no choice but to applaud Li Dong's presentation.

Significant Themes

• Genius and Creativity: Li Dong's unique approach to mathematics is presented as a form of genius, inspiring and humbling other mathematicians.
• Understanding vs. Following: The audience realizes they had merely followed Li Dong's paper's conclusions without truly understanding his logic.
• The Beauty of Mathematics: The intellectual thread of Li Dong's proof is described as beautiful, inspiring mathematicians to appreciate the subject's inherent beauty.

Character Interactions

• Li Dong interacts with the audience, clarifying his proof and addressing their doubts.
• Mathematicians like Tao, Zhang, and Penrose react with awe and recognition to Li Dong's presentation.
• Clark, initially skeptical, is forced to acknowledge Li Dong's abilities.
• Yau and Tian Gang, despite their past conflict, acknowledge Li Dong's talent with a silent nod.

Key Plot Points and Events

• Li Dong, the presenter, addresses the audience, ready to answer questions about his paper.
• He calls on each person who posted a Comment on ArXiv, remembering every name and question, putting each questioner on the spot.
• Li Dong answers questions, clarifies misunderstandings, and even offers a detailed explanation of a complex question posed by Zhou Shenzhi.

Character Developments

• Li Dong: Shows exceptional memory, quick thinking, and confidence in handling complex mathematical concepts and questions. He demonstrates maturity and politeness in addressing the audience and questioners.
• Zhou Shenzhi: Remains calm and composed under Li Dong's gaze, showing confidence in his own abilities. He is open to Li Dong's detailed explanation of his complex question.

Significant Themes

• Mathematical Prowess: Li Dong's mastery of his subject matter is evident in his ability to recall and answer complex questions.
• Confidence and Composure: Both Li Dong and Zhou Shenzhi exhibit confidence and composure under pressure.
• Respect and Politeness: Li Dong shows respect and politeness in his interactions with the audience and questioners, even when correcting their misunderstandings.

Character Interactions

• Li Dong interacts with each questioner, clarifying their doubts and addressing their concerns. He shows respect and patience throughout.
• Zhou Shenzhi maintains a calm demeanor when Li Dong singles him out, showing respect for Li Dong's abilities and openness to learning from him.
• The audience watches these interactions with a mix of awe, amusement, and tension.

Key Plot Points and Events

• Li Dong decides to explain Zhou Shenzhi's fourth question in detail, surprising Tian Gang and Jiang Yubai.
• Li Dong reveals that his Zero Criterion might not be the best tool for extending local-global compatibility to General Linear Group GL(n).
• He points out that Zhou Shenzhi's own work on p-adic integration path-deformation provides a better approach.

Character Developments

• Li Dong demonstrates his deep understanding of complex mathematical concepts and his ability to identify core issues quickly.
• Zhou Shenzhi is caught off guard by Li Dong's insights and remains silent, indicating his discomfort with the situation.
• Jiang Yubai shows no visible reaction, suggesting he is not easily ruffled or surprised.

Significant Themes

• The importance of understanding the underlying logic of mathematical tools and methods.
• The potential for new insights to come from unexpected sources.
• The tension between academic collaboration and competition.

Character Interactions

• Li Dong challenges Zhou Shenzhi's understanding of his own work, putting him on the spot.
• Tian Gang and Jiang Yubai both show concern about Li Dong's actions, suggesting they understand the potential consequences.
• Li Dong indirectly involves Jiang Yubai by asking Professor Yang to explain the path-deformation scheme, hinting at a potential confrontation.

Key Plot Points and Events

• Li Dong invites Yang Shengguo, his high school mathematics teacher, onto the stage at an academic seminar.
• Yang Shengguo, a former mathematical prodigy who disappeared from the academic scene, agrees to collaborate with Li Dong to push a significant mathematical proof onstage.
• They aim to extend the local-global compatibility of automorphic representations to the case of ramification index e_v=3, a major breakthrough in the field.

Character Developments

• Li Dong: Shows exceptional confidence and ambition, inviting his former teacher to collaborate on a high-stakes proof.
• Yang Shengguo: Initially hesitant, Yang Shengguo regains his fighting spirit and agrees to work with Li Dong, demonstrating his expertise and determination.
• Zhou Shenzhi: Reacts with shock and silence when Yang Shengguo is revealed as the collaborator.
• Jiang Yubai: Shows anger and frustration when Li Dong and Yang Shengguo announce their intention to push the mathematical boundary he has been pursuing for over a decade.

Significant Themes

• Redemption and Second Chances: Yang Shengguo's return to the academic stage suggests a chance at redemption and a second act in his career.
• Mentorship and Legacy: The relationship between Li Dong and Yang Shengguo highlights the impact of a teacher on a student's life and career.
• Ambition and Rivalry: The intense academic competition and rivalry are evident in the characters' reactions and goals.

Character Interactions

• Li Dong and Yang Shengguo: Their interaction shows mutual respect and trust, with Li Dong encouraging Yang Shengguo and Yang Shengguo initially doubting Li Dong's sanity but ultimately agreeing to collaborate.
• Yang Shengguo and Jiang Yubai: Their silent exchange reveals tension and history between them, likely stemming from Yang Shengguo's past disappearance from the academic scene.
• Zhou Shenzhi and Yang Shengguo: Zhou Shenzhi's shock and silence suggest a connection between him and Yang Shengguo, possibly as a former student or colleague.

Yang Shengguo presented a layer-by-layer recursive method for solving the p-adic integration problem, with Li Dong helping him through several technical obstacles. The lecture threatened to complete Jiang Yubai’s long-running research project before Li Dong finally told his teacher to stop.

• Yang Shengguo began explaining his recursive filtered embedding method and wrote down a recurrence relation that addressed the problem Zhou Shenzhi had struggled with for years.
• Jiang Yubai recognized the potential of Yang Shengguo’s lifting operator and saw how it could unlock his own research.
• When Yang Shengguo got stuck on the second-layer lifting operator, Li Dong supplied the equivariant version of Faltings’s p-adic comparison theorem, and Yang continued.
• Li Dong later helped Yang resolve issues involving Berger’s equivalence theorem and the final convergence estimates as the lecture continued for hours.
• Zhou Shenzhi became overwhelmed by the derivation, while Jiang Yubai realized Yang and Li were close to completing the project he had pursued for over a decade.
• Li Dong told the absorbed Yang Shengguo, “That’s enough, Mr. Yang.”

Key Plot Points and Events

• Li Dong stops Yang Shengguo from completing the proof of GL? to GL? onstage, despite being close to completion.
• Li Dong reveals that he and Yang Shengguo have limited abilities and leave the rest of the proof to the audience.
• Jiang Yubai accuses Li Dong and Yang Shengguo of not using his Zero Criterion from the Montgomery Conjecture in their proof.

Character Developments

• Li Dong demonstrates his selflessness and generosity by giving away a nearly completed proof to the mathematical community.
• Jiang Yubai shows his possessiveness and narrow-mindedness regarding his decade-long work on the GL? to GL? problem.

Significant Themes

• The selflessness and generosity of mathematics as a field, as embodied by Li Dong's actions.
• The possessiveness and narrow-mindedness that can arise from long-term investment in a single research topic, as seen in Jiang Yubai.

Character Interactions

• Li Dong and Yang Shengguo: Li Dong respects Yang Shengguo's work and gives him credit for the core framework of the proof.
• Li Dong and Jiang Yubai: Li Dong remains calm and composed in the face of Jiang Yubai's accusations, showing his maturity and confidence.
• Tian Gang and Yau: Tian Gang understands Li Dong's true intentions and criticizes Yau for underestimating Li Dong.

Key Plot Points and Events

• Li Dong's seminar challenges the academic integrity of Jiang Yubai, a renowned mathematician.
• Li Dong reproduces a complex mathematical derivation and extends a key conjecture, demonstrating his exceptional abilities.
• Li Dong exposes Jiang Yubai's academic misconduct, revealing that his most celebrated work was based on a student's (Yang Shengguo) ideas.

Character Developments

• Li Dong: Proves himself as a mathematical prodigy, challenging established norms and exposing academic misconduct.
• Jiang Yubai: Loses academic credibility after Li Dong's revelations; faces potential consequences for his past actions.

Significant Themes

• Academic Integrity: The chapter explores the consequences of academic misconduct and the importance of integrity in academic circles.
• Genius and Recognition: Li Dong's extraordinary abilities challenge the traditional norms of academic recognition and age-based hierarchy.
• Ambition and Hubris: Jiang Yubai's overconfidence in his own abilities and disregard for others' contributions lead to his downfall.

Character Interactions

• Li Dong vs. Jiang Yubai: Li Dong's public challenge to Jiang Yubai's academic integrity leads to a dramatic shift in their power dynamics.
• Yang Shengguo vs. Jiang Yubai: Yang Shengguo's ideas, which Jiang Yubai had claimed as his own, are exposed, leading to Jiang Yubai's fall from grace.
• Tian Gang: As Li Dong's teacher, Tian Gang remains silent but likely supports Li Dong's actions, indicating a shift in academic power dynamics.

Key Plot Points and Events

• The seminar is over, and attendees are leaving.
• Professor Penrose is excited about Li Dong's seminar and expresses interest in his previous idea.
• Terence Tao, Academician Yuan Yaxiang, and Zhang Wenping praise Li Dong's seminar.
• Academician Yau invites Li Dong and his teacher to Tsinghua University.
• Li Qin meets Li Dong's teachers.
• Li Dong receives a group message from the Azure Dragon Study Group about Gauss's unusual activity.
• A red packet from Gauss appears in the group chat.

Character Developments

• Li Dong gains recognition and respect from renowned mathematicians.
• Professor Penrose shows interest in Li Dong's ideas.
• Academician Yau attempts to invite Li Dong to Tsinghua University.
• Li Qin meets Li Dong's teachers and expresses pride in her son's achievements.
• Gauss struggles to communicate due to dimensional barriers.

Significant Themes

• Recognition and respect in the academic community.
• Interdimensional communication challenges and security.
• The power of mathematical genius and its impact on others.

Character Interactions

• Li Dong interacts with various professors, including Penrose, Tao, Yuan Yaxiang, Zhang Wenping, and Yau.
• Li Qin meets Li Dong's teachers and expresses her gratitude for their support.
• Li Dong interacts with Gauss through the Azure Dragon Study Group's red packet.