Chapter Summaries

Key Plot Points and Events

• Li Dong returns to class after a 20-day absence and attends Liu Ruochuan's advanced mathematics lecture.
• Liu Ruochuan discusses the Montgomery Pair Correlation Conjecture, and Li Dong reveals he's made progress on it.
• Li Dong learns about the upcoming ICCM conference in Shanghai and plans to attend.

Character Developments

• Li Dong: Shows maturity and confidence in his academic pursuits, particularly in tackling the Montgomery Pair Correlation Conjecture. He also demonstrates a pragmatic approach to his unusual group chat situation.
• Liu Ruochuan: Shows concern for Li Dong's academic progress and offers guidance without tainting Li Dong's first-authorship attribution.

Significant Themes

• Academic Pursuit and Integrity: Both Li Dong and Liu Ruochuan value academic integrity and the pursuit of knowledge.
• Mentorship: Liu Ruochuan serves as a mentor figure to Li Dong, guiding him without interfering with his progress.
• Progress and Perseverance: Li Dong's struggle with the Montgomery Pair Correlation Conjecture highlights the importance of steady progress and perseverance in academic pursuits.

Character Interactions

• Li Dong and Liu Ruochuan: Their interaction showcases a mentor-mentee relationship, with Liu Ruochuan offering guidance and Li Dong updating Liu on his progress.
• Li Dong and Qi Yu: Their brief interaction highlights Li Dong's guilt over neglecting Qi Yu's feelings and his struggle to maintain his academic pursuits while dealing with personal matters.

Chapter Summary: “Old Yao Really ‘Understood’”

Key Plot Points and Events

• Li Dong returns to his normal routine of attending classes, returning to the dormitory, and researching the Montgomery Pair Correlation Conjecture.
• While working on error bounds, he realizes that further progress requires refining his Fourier Optimization Framework and using his massive dataset of Riemann zeta-function nontrivial zeros.
• Wang Hao returns to the dormitory in a distressed state and asks whether Li Dong really failed mathematics in high school and whether he is secretly a rich second-generation heir.
• Wang Hao shows Li Dong a video by the overseas science blogger “Old Yao and Xiao Wei.” The video praises Li Dong’s achievements while implying that his success comes from his wealthy and influential family background.
• The blogger falsely claims that Li Dong’s uncle owns a factory producing core components for Huaxuan Technology. In reality, the factory only manufactures peripheral items such as nuts, washers, and stamped parts.
• Li Dong is disappointed that his uncle has not become as successful as the video suggests, but he is also angered by the blogger’s misleading claims.
• In response, Li Dong uploads a short paper to arXiv releasing a dataset of verified nontrivial zeros of the Riemann zeta function extending to the (10^{23}) scale.
• He deliberately withholds his core Dimensionality-Reduction Algorithm 2.0, protecting the method he needs for his own research.
• After submitting the paper, Li Dong casually calls his uncle and then goes to sleep, leaving the academic world to react to his challenge.

Character Developments

• Li Dong remains highly confident in his mathematical abilities and protective of his intellectual work. He refuses to reveal his core algorithm and treats the blogger’s claims as scientifically ignorant.
• His pride in his achievements is contrasted with his old history of failing high-school mathematics, which Wang Hao uses to provoke him.
• Li Dong also shows a somewhat playful and retaliatory side: rather than publicly arguing with the blogger, he responds by releasing data that directly tests the claim that “old algorithms” could achieve comparable results.
• Wang Hao becomes increasingly insecure and frustrated. He is disturbed that Li Dong, whom he believes surpassed him despite failing high-school math, may be even more extraordinary than he realized.
• Old Yao and Xiao Wei are portrayed as superficial commentators who use selective praise and insinuation rather than genuine understanding. Their attempt to explain Li Dong’s achievements is based on rumors and class-based assumptions.

Significant Themes

• Genuine expertise versus superficial commentary: The bloggers speak confidently about advanced mathematics without understanding the significance of Li Dong’s work.
• Merit and family background: The video tries to attribute Li Dong’s achievements to family privilege, while Li Dong insists that he earned his success through his own abilities.
• Scientific proof through action: Instead of debating the bloggers, Li Dong releases an unprecedented dataset that forces others to test their claims themselves.
• Protecting intellectual secrets: Li Dong distinguishes between sharing results and revealing the algorithm behind them, emphasizing the strategic value of his research.
• Misrepresentation and reputation: The chapter shows how online figures can distort facts about both Li Dong’s mathematics and his family for attention.

Character Interactions

• Wang Hao questions Li Dong about his past and family background, irritating Li Dong and revealing Wang Hao’s own feelings of inferiority.
• The video’s hosts indirectly provoke Li Dong by praising him while spreading false information about his family.
• Li Dong’s reaction to the video leads him to challenge their claims through his arXiv submission rather than through direct confrontation.
• His brief call with his uncle, Li Yang, reinforces the contrast between the exaggerated online rumors and the modest reality of the family business.

Chapter Summary: “First Signs of Brilliance”

Key Plot Points and Events

• At Princeton’s Institute for Advanced Study, Professor Arthur Penrose continues studying Li Dong’s groundbreaking dimensional-reduction algorithm, which combines techniques from several mathematical fields with unusual elegance.
• Penrose believes the algorithm could transform high-dimensional matrix computation and modern cryptography, rather than merely calculating nontrivial zeros of the Riemann zeta function. He is angered that media outlets distorted his comments into claiming Li’s work had no practical value.
• Penrose discovers Li’s new arXiv preprint, containing verified nontrivial zeta zeros at the enormous scale of (10^{23}). He independently checks several values with Mathematica and confirms their accuracy.
• Realizing that current hardware could not reach this scale using Li’s published method, Penrose concludes that Li has developed a further, undisclosed improvement. Impressed and excited, he decides to travel to Huaxia to meet Li personally.
• In Kyoto, researcher Zhou Shenzhi struggles to extend his own group’s computations beyond the (10^{17}) scale. His mentor, Jiang Yubai, suspects Li concealed an additional optimization in the published algorithm. Zhou is determined to uncover it to support Jiang’s unified Langlands Program research.
• The next morning, Li receives a call from his teacher, Liu Ruochuan, who informs him that the international mathematical community has been shaken by his new results.
• Liu tells Li that Penrose wants to visit Peking University. Li respectfully declines for now because his priority is proving progress on the Montgomery Pair Correlation Conjecture, which would also increase his research permissions.
• Liu also reports that Huaxuan Technology wants to reopen discussions about Li’s algorithm. The company believes Li’s improved method could significantly accelerate thermal-fluid simulations and the deployment of its lithography systems.
• Li agrees to meet Huaxuan representatives in Shanghai during the upcoming ICCM conference, but postpones any engineering collaboration until he has more time.
• The chapter ends with Li returning to work on the Montgomery Pair Correlation Conjecture.

Character Developments

• Arthur Penrose shifts from admiration to outright awe. His verification of Li’s data confirms that Li is not merely talented but capable of breakthroughs beyond the expectations of established experts. Penrose becomes personally eager to meet him.
• Li Dong remains focused and self-directed despite receiving international attention. He displays a sharper, more defiant side when discussing critics, but remains practical and modest about his limits, acknowledging that hardware—not mathematics—is currently restricting his computations.
• Zhou Shenzhi is shown as exhausted but deeply committed. His desperation reflects both respect for Li’s work and his desire to help his mentor’s larger mathematical project.
• Liu Ruochuan acts as Li’s supportive teacher and intermediary. He is amused and impressed by Li’s confidence, while helping manage the attention from foreign scholars and industry.
• Sarah, Penrose’s doctoral student, serves as the messenger who brings the decisive preprint to him.
• Li’s wife shows concern for Zhou’s deteriorating health, highlighting the personal cost of his obsessive research.

Significant Themes

• Genius and originality: Li’s work is presented as a rare synthesis of previously separate mathematical methods, suggesting an almost unprecedented level of insight.
• Limits of existing technology: The computational barrier at (10^{23}) demonstrates that Li’s mathematics has advanced faster than available hardware.
• Recognition versus focus: International acclaim, prestigious scholars, and corporate interest surround Li, but he prioritizes his own research agenda over publicity.
• Misrepresentation and reputation: Penrose’s comments being distorted by online media emphasizes the conflict between serious scholarship and sensationalized reporting.
• Academic ambition and pressure: Zhou’s sleepless efforts reveal how major mathematical projects can create intense personal and professional burdens.
• The practical value of pure mathematics: Li’s theoretical algorithm attracts interest from cryptography, semiconductor manufacturing, and engineering, reinforcing the idea that abstract breakthroughs may have far-reaching applications.

Character Interactions

• Penrose and Sarah interact when she urgently brings him Li’s new preprint, triggering his discovery and decision to travel to Huaxia.
• Zhou and his wife interact briefly, with her urging him to rest while he remains consumed by his research.
• Liu and Li discuss Li’s sudden global impact, Penrose’s proposed visit, and Huaxuan Technology’s renewed interest. Liu offers guidance, while Li calmly sets his own priorities.
• Li’s exchange with Liu also reveals a more combative attitude toward critics, as he challenges them to reproduce his results using the older algorithm.
• Although Penrose and Li do not meet in the chapter, Penrose’s desire to meet him and Li’s decision to postpone the encounter establish an important future relationship between the two mathematicians.

Key Plot Points and Events

• Li Yang's factory in Chengdu receives a mysterious order to visit Huaxuan Technology's headquarters in Shanghai.
• Li Dong completes his proof of the Montgomery Pair Correlation Conjecture and submits it to the Annals of Mathematics.
• Li Dong's Azure Dragon Study Group stabilizes, and Riemann joins the group. Li Dong discovers the 'Data Transfer' function, which can transmit knowledge across dimensions and adapt it to the recipient's cognitive framework.

Character Developments

• Li Yang: Grows from a small workshop owner to a legitimate entrepreneur, and senses Liu Chengfu's hidden agenda.
• Li Qin: Shows concern for Li Yang's well-being and mentions Li Dong's upcoming trip to Shanghai.
• Li Dong: Completes a groundbreaking mathematical proof and discovers the 'Data Transfer' function in the Azure Dragon Study Group.

Significant Themes

• Ambition and growth (Li Yang's business expansion, Li Dong's academic achievements)
• Hidden agendas and ulterior motives (Liu Chengfu's true purpose)
• Interdimensional communication and knowledge transfer (Azure Dragon Study Group's 'Data Transfer' function)

Character Interactions

• Li Yang and Li Qin: Siblings discussing business and Li Dong's academic pursuits.
• Li Yang and Liu Chengfu: Business partners with hidden agendas.
• Li Dong and Azure Dragon Study Group members: Interdimensional communication and collaboration.

Chapter Summary: “Claude E. S What?”

Key Plot Points and Events

• Li Dong, now officially the group owner after a permission upgrade, revisits two pending membership requests.
• One request remains unreadable, while the other partially reveals the name “Claude E. S.”* Li Dong speculates about which famous historical scientist might be behind it but cannot identify the person.
• Although he still cannot accept the requests, Li Dong is satisfied with his newly unlocked data-transfer function, which allows two-way communication with scientific figures from across history.
• The next day, while traveling from Kyoto to Shanghai for the ICCM Congress, Li Dong sees an online controversy involving science bloggers Old Yao and Xiao Wei.
• The bloggers had deliberately or carelessly taken Princeton professor Arthur Penrose’s comments about Li Dong’s Dimensionality-Reduction Algorithm out of context. After learning what happened, Penrose publicly denounces them and praises the algorithm as a major breakthrough.
• The bloggers apologize and delete their videos, but their apology fuels conspiracy theories among online commenters, who claim they were pressured or that Li Dong’s supporters bought Penrose’s endorsement.
• Li Dong is frustrated by the public’s ignorance and tendency to believe imagined conspiracies, but he chooses not to dwell on the controversy.
• Meanwhile, the international mathematical community is stunned by Li Dong’s arXiv paper, which presents the first (10^{23}) nontrivial zeros of the Riemann zeta function. Multiple supercomputing centers independently verify the data, confirming that the zeros lie on the critical line.
• As a result, the ICCM Congress unexpectedly attracts many world-famous mathematicians and computer scientists, including Peter Sarnak, Zhang Yitang, Terence Tao, and Enrico Bombieri. They all want to attend Li Dong’s forty-five-minute invited lecture.
• Li Dong arrives in Shanghai, checks into the conference hotel, and prepares to organize his presentation. Just as he is about to shower, a tall blonde foreign woman knocks on his door.

Character Developments

• Li Dong demonstrates increasing confidence and composure. He recognizes the extraordinary value of his upgraded group abilities while remaining realistic about their current limitations.
• He also shows maturity by refusing to become emotionally consumed by online criticism, even though he finds the conspiracy theories absurd.
• His academic reputation has grown dramatically: he is no longer merely a talented young researcher but the central attraction of an internationally significant mathematical conference.
• Arthur Penrose emerges as a forceful defender of scientific rigor. He personally confronts the bloggers and openly endorses Li Dong’s work.
• Old Yao and Xiao Wei lose credibility after their misleading commentary is exposed and are forced to apologize.
• Liu Ruochuan is shown to be overwhelmed by the expanded scale of the conference and unable to personally accompany Li Dong.

Significant Themes

• Scientific truth versus public misinformation: The chapter contrasts rigorous verification by experts with sensationalized online commentary.
• The gap between expertise and popular understanding: Many netizens dismiss the algorithm because they cannot understand its implications, making them vulnerable to conspiracy theories.
• Recognition and reputation: Li Dong’s work rapidly earns worldwide academic attention once its results are independently confirmed.
• The power and limitations of technology: The mysterious group’s data-transfer ability promises unprecedented communication across time, but Li Dong still lacks enough authority to use it fully.
• Academic achievement amid media chaos: Genuine scientific progress unfolds while online discourse reduces complex breakthroughs to scandal and speculation.

Character Interactions

• Li Dong interacts indirectly with the mysterious applicants through the group interface, attempting unsuccessfully to accept them.
• Penrose confronts Old Yao and Xiao Wei through a public video, defending Li Dong’s algorithm and condemning their distortion of his words.
• Online commenters reinterpret the apology as evidence of a conspiracy, highlighting the disconnect between Li Dong’s work and public perception.
• Liu Ruochuan remains involved in the conference organization but communicates with Li Dong only through an electronic invitation because of his responsibilities.
• The chapter ends with Li Dong opening his hotel room door to an unidentified blonde foreign woman, creating a new mystery and cliffhanger.

Chapter Summary: University Research

Key Plot Points and Events

• Sarah, a foreign researcher and assistant to Princeton mathematics professor Arthur Penrose, visits Li Dong at his hotel room.
• Penrose wants to meet Li Dong, likely because of Li Dong’s groundbreaking work in computational mathematics and his algorithm related to the Montgomery Pair Correlation Conjecture.
• Li Dong declines the immediate meeting, claiming he needs to prepare his presentation for the upcoming International Congress of Chinese Mathematicians (ICCM). In reality, he is already fully prepared and remains suspicious of Penrose’s motives.
• Li Dong decides that, after the conference, he will meet Penrose with Dean Liu Ruochuan present to help manage the discussion.
• Li Dong checks the Azure Dragon Study Group and discovers that Bernhard Riemann has finally spoken, thanking him.
• The group mysteriously changes Li Dong’s username from “Currently Grinding Senior-Year Problems” to “University Research,” demonstrating that it can adapt its members’ identities automatically.
• Li Dong speculates that Riemann may understand the connection between Li Dong’s computational assistance, the recovered manuscript, and the strange parallel-universe circumstances surrounding Riemann’s survival.
• The next morning, the World Chinese Mathematicians Congress begins at the Shanghai International Conference Center.
• Li Dong explores the poster exhibition, critically evaluating research on deep-learning methods for high-dimensional partial differential equations and rational-point counting on elliptic curves.
• Despite being a freshman, Li Dong unconsciously behaves like an experienced professor reviewing junior researchers’ work.
• The chapter ends when Li Dong notices a familiar person standing beside a poster.

Character Developments

• Li Dong: Becomes increasingly cautious and politically aware. Rather than immediately accepting Penrose’s invitation, he suspects the professor has a deeper purpose. His confidence in his own mathematical abilities is clear, as he knows he does not need to prepare extensively for his presentation. At the conference, he displays remarkable expertise and adopts the mindset of a senior academic despite his youth.
• Sarah: Is introduced as polite, professional, and understanding. She accepts Li Dong’s refusal without offense and recognizes the pressure associated with giving a major conference presentation.
• Professor Arthur Penrose: Though he never appears directly, his eagerness to meet Li Dong establishes him as a powerful international figure with a potentially significant interest in Li Dong’s work.
• Bernhard Riemann: His first message in the group suggests that he understands more about Li Dong’s role and the mysterious connection between mathematics, computation, and the parallel universe than previously revealed.
• Dean Liu Ruochuan: Although absent from the immediate events, he remains Li Dong’s trusted institutional support and potential protection during the future meeting with Penrose.

Significant Themes

• Youth versus expertise: Li Dong is technically a freshman, yet his knowledge and judgment surpass those of many established researchers.
• Academic recognition and power: The conference hierarchy, hotel arrangements, and poster sessions show how prestige and personal connections shape the mathematical world.
• Mystery and hidden knowledge: Riemann’s brief thank-you and Penrose’s urgent request imply that Li Dong is involved in secrets extending beyond ordinary academic research.
• Caution amid success: Li Dong does not allow his international fame to make him careless; he remains alert to others’ intentions.
• The changing nature of mathematics: The posters highlight modern intersections between mathematics, deep learning, numerical computation, and advanced theoretical fields.

Character Interactions

• Sarah approaches Li Dong on Penrose’s behalf, but Li Dong politely postpones the meeting.
• Li Dong internally evaluates Sarah’s explanation while concealing his suspicion about Penrose’s motives.
• His interaction with Riemann occurs through the Azure Dragon Study Group, where Riemann’s cryptic gratitude creates new questions.
• At the conference, Li Dong observes and mentally critiques the work of younger researchers, though he has not yet directly engaged with them.
• The final sighting of an acquaintance foreshadows Li Dong’s next significant interaction.

Chapter Summary: “Which Big Shot Was This?”

1. Key Plot Points and Events

• At ICCM’s poster presentation, Qin Fei and his classmates present their project on efficiently computing nontrivial zeros of Dirichlet (L)-functions under quadratic characters.
• An elderly Fudan professor criticizes their work for having a crude algorithmic structure, outdated truncation-error handling, and overly rigid incomplete Gamma function approximations, especially for large conductor modulus (q).
• Qin Fei reflects that their original project—multithreaded optimization of an algorithm for Riemann zeta zeros—was rendered obsolete after Li Dong published a much faster method using Nonlinear FFT Grid Expansion and Chebyshev interpolation.
• Forced to switch topics shortly before the conference, Qin’s team produced their current project in only one or two months, explaining its roughness.
• Li Dong happens to pass by and identifies the main flaw in their method. He recommends using the Fast Mellin Transform and Poisson summation formula to convert the computation into a global frequency-domain convolution, improving both complexity and error control.
• Qin Fei and his classmates immediately understand the solution and realize that the helpful “passing expert” is actually Li Dong, the young mathematical prodigy whose earlier work displaced their original project.
• After the poster session, the formal ICCM conference begins. Peking University mathematics dean Liu Ruochuan delivers a lecture on local geometry in (p)-adic Hodge theory and Shimura varieties, focusing on local-global compatibility within the Langlands Program.
• Liu answers several difficult questions from international experts flawlessly.
• Afterward, Liu introduces Li Dong to renowned mathematicians including Peter Sarnak, Yitang Zhang, and Terence Tao.
• Liu also reveals that Enrico Bombieri has come to the conference largely because of Li Dong, and warns that the next day’s Q&A session may be particularly challenging.

2. Character Developments

• Qin Fei: Experiences embarrassment and frustration over his team’s outdated project, but also demonstrates humility and admiration toward Li Dong. His reaction shifts from awkwardness to recognition of Li’s extraordinary ability.
• Qin Fei’s classmates: Initially demoralized by the professor’s criticism, they quickly become excited when Li Dong provides a practical solution. Their awe grows once they discover his identity.
• Li Dong: Continues to display exceptional mathematical insight despite his youth. He casually diagnoses a difficult technical issue and proposes an advanced method that impresses senior students and faculty alike. He remains modest and friendly rather than boastful.
• Liu Ruochuan: Appears confident, accomplished, and supportive of Li Dong. His successful lecture establishes his authority, while his introductions show that he is actively helping Li enter the international mathematical community.
• International mathematicians: Their presence emphasizes Li Dong’s growing reputation and the importance of his upcoming interactions with leading scholars.

3. Significant Themes

• Youthful genius and academic hierarchy: Li Dong’s ability surpasses that of experienced researchers, highlighting the disruptive impact of exceptional talent.
• The rapid evolution of mathematics: Qin Fei’s carefully developed project becomes obsolete almost immediately after Li Dong introduces a superior algorithm, showing how quickly research advances.
• Humility versus reputation: Li Dong’s understated behavior contrasts with the enormous attention surrounding him.
• Failure as a consequence of progress: Qin Fei’s team is not incompetent; their work is simply overtaken by a breakthrough, reflecting the competitive and unstable nature of mathematical research.
• Recognition and pressure: Li Dong’s growing fame brings him into contact with legendary mathematicians, but also creates expectations and foreshadows a demanding public examination.

4. Character Interactions

• The elderly professor critiques Qin Fei’s poster, exposing its methodological weaknesses.
• Li Dong offers Qin Fei’s team a more sophisticated approach, turning an embarrassing encounter into a valuable learning experience.
• Qin Fei awkwardly recognizes Li Dong as the person whose earlier publication forced their project change, creating an amusing mix of admiration and resentment.
• Liu Ruochuan warmly checks whether Li Dong understood his advanced lecture, then introduces him to several famous mathematicians.
• Liu informs Li Dong that Bombieri has specifically come because of him, increasing the tension surrounding the upcoming Q&A session.

Key Plot Points and Events

• The International Conference on Complex Mathematics (ICCM) in Shanghai features cutting-edge research presentations.
• Li Dong, a Peking University undergraduate, is invited to give a talk on the second day, drawing significant attention.
• Li Dong presents his approach to the Riemann-Siegel formula, using complex analysis and topological deformation to reduce time complexity.

Character Developments

• Li Dong: Shows remarkable composure and confidence while presenting to an audience of renowned scholars. His mathematical thinking is described as akin to that of a god.
• Qin Fei: Feels a significant disparity between his academic level and Li Dong's, leading to self-reflection and admiration.
• Zhou Shenzhi: Struggles to understand Li Dong's algorithm and asks a crucial question about the advanced version used for the 10^23 scale zero dataset.

Significant Themes

• The clash of immortals: The conference features academic titans unveiling cutting-edge research, creating a sense of awe and competition.
• Mathematical thinking: The chapter explores the depth and uniqueness of Li Dong's mathematical thinking, likening it to that of a god.
• The power of complex analysis and topology: Li Dong's approach demonstrates the potential of these fields in solving computational number theory problems.

Character Interactions

• Li Dong interacts with the audience, trying to gauge their reaction to his presentation. He receives no immediate response, creating an awkward moment.
• Zhou Shenzhi asks Li Dong a question about his advanced algorithm, representing the curiosity and eagerness of the scholarly community to understand his work better.
• Qin Fei observes Li Dong's presentation, feeling a sense of disparity between their academic levels and expressing admiration for Li Dong's achievements.

Key Plot Points and Events

• Zhou Shenzhi from Beijing Normal University asks Li Dong to share the core algorithm of his latest dataset, arguing that academic achievements should belong to all humanity.
• Li Dong refuses, stating "No," causing an uproar in the hall.
• Wang Zhiqiang from Beijing Normal University argues that the algorithm's usefulness would be maximized through public sharing, but Li Dong counters that he hasn't seen any significant optimization from the academic community on his first-generation algorithm.
• Liu Ruochuan, dean of Peking University's School of Mathematics, supports Li Dong, arguing for intellectual property rights.
• A heated debate ensues between those supporting Li Dong and those advocating for academic sharing.
• Bombieri receives a phone call about a paper submitted to the Annals of Mathematics, titled "A Proof of the Montgomery Pair Correlation Conjecture on the Interval |a| ∈ [0,4]," authored by Li Dong.

Character Developments

• Li Dong demonstrates assertiveness and confidence in his academic stance, refusing to bow to pressure.
• Zhou Shenzhi and Wang Zhiqiang are portrayed as representing the academic establishment, pushing for sharing while potentially harboring self-interest.
• Liu Ruochuan shows support for Li Dong and intellectual property rights.
• Bombieri is initially dismissive of a paper but becomes intrigued when he learns it's by Li Dong.

Significant Themes

• The tension between academic sharing and intellectual property rights.
• The potential self-interest behind calls for academic sharing.
• The role of academic journals and peer review in recognizing and validating academic achievements.

Character Interactions

• Li Dong vs. Zhou Shenzhi and Wang Zhiqiang: Li Dong stands his ground against their pressure to share his algorithm.
• Liu Ruochuan vs. Zhou Shenzhi and Wang Zhiqiang: Liu Ruochuan supports Li Dong and criticizes their approach.
• Bombieri vs. the Annals of Mathematics editor: Bombieri initially dismisses a paper but changes his mind upon learning it's by Li Dong.

Chapter Summary: “Professor Bombieri, Please Go Ahead”

Key Plot Points and Events

• Enrico Bombieri initially assumes Li Dong’s paper is fraudulent because it claims to extend Montgomery’s Pair Correlation result from (|a|<1) to (|a|\in[0,4]), an astonishing advance in analytic number theory.
• After watching Li Dong’s rigorous lecture, Bombieri agrees to review the paper sent to his email.
• The lecture hall remains divided: Wang Zhiqiang, Beijing Normal University representatives, and Jiang Yubai’s students criticize Li Dong for withholding his computational algorithm, while Liu Ruochuan and other professors defend him.
• Bombieri studies the paper, which relies on:
  • The Riemann Explicit Formula
  • Precise Prime Number Theorem estimates
  • A verified dataset of the first (10^{23}) nontrivial zeta zeros
  • A Fourier Optimization Framework to control high-power prime remainder terms
• Although Bombieri cannot immediately follow every technical scaling argument, he recognizes that the paper’s overall logic is coherent and apparently free of contradictions.
• He realizes the result could have major consequences beyond the Montgomery conjecture, particularly for automorphic (L)-functions, local ramification indices, and the Langlands Program.
• The magnitude of the discovery overwhelms Bombieri, causing him to suffer a brief heart-related episode. His assistant gives him medication and helps him recover.
• Bombieri then confronts the central problem: Li Dong’s enormous numerical dataset was generated using a secret dimensionality-reduction algorithm. Because the data cannot currently be reproduced, top journals such as Annals of Mathematics may reject the paper, even if its theoretical framework is correct.
• Unable to verify the crucial details without Li Dong’s explanation, Bombieri decides to ask him directly about the Montgomery Pair Correlation Conjecture.
• The hall falls silent as Bombieri rises and addresses Li Dong. Li Dong, realizing Bombieri has likely read the submitted paper, confidently invites him to continue.

Character Developments

• Enrico Bombieri: Moves from skepticism and instinctive rejection to profound admiration and concern for the mathematical implications of Li Dong’s work. His willingness to stand and question Li Dong demonstrates humility and respect for genuine mathematical achievement. He also struggles between protecting academic standards and ensuring that a potentially revolutionary result is not lost.
• Li Dong: Remains confident, composed, and protective of his secret algorithm. His earlier refusal to disclose it becomes more understandable as Bombieri recognizes that the paper’s theoretical value may depend on inaccessible computational evidence. Li Dong’s final response shows that he is prepared to defend his work before the world’s leading mathematicians.
• Wang Zhiqiang and Jiang Yubai’s group: Continue pressuring Li Dong to disclose his algorithm, representing the hostile or opportunistic side of academic politics.
• Liu Ruochuan and allied professors: Defend Li Dong through reasoned arguments, contrasting with the moral accusations of his opponents.
• Bombieri’s assistant: Provides practical support when Bombieri’s excitement causes a medical scare, highlighting Bombieri’s physical vulnerability despite his intellectual authority.

Significant Themes

• Genius versus academic skepticism: Extraordinary claims naturally provoke disbelief, but rigorous reasoning can overcome even deep suspicion.
• The conflict between openness and intellectual ownership: The chapter questions whether researchers must immediately reveal every tool and dataset, especially when disclosure risks losing credit for a groundbreaking discovery.
• Reproducibility versus mathematical insight: The paper may be logically sound, yet its reliance on unverifiable black-box computation threatens its acceptance by the academic community.
• The transformative power of mathematics: A technical improvement in pair-correlation estimates could affect analytic number theory, random matrix theory, quantum chaos, automorphic representations, and the Langlands Program.
• Respect for knowledge: Bombieri’s decision to stand while questioning Li Dong symbolizes reverence for mathematics and recognition of a younger scholar’s achievement.
• Academic politics and integrity: The arguments surrounding Li Dong’s algorithm reveal the tension between legitimate demands for transparency and attempts to appropriate another scholar’s work.

Important Character Interactions

• Bombieri and the academic editor: The editor initially seeks Bombieri’s judgment, and Bombieri agrees to review the paper after witnessing Li Dong’s lecture.
• Bombieri and Li Dong: Their interaction forms the chapter’s climax. Bombieri’s question reflects both professional responsibility and deep respect, while Li Dong responds with calm confidence.
• Wang Zhiqiang’s faction and Liu Ruochuan’s group: Their opposing arguments create the background conflict over whether Li Dong is obligated to reveal his algorithm.
• Bombieri and his assistant: The assistant’s concern during Bombieri’s health scare contrasts with Bombieri’s intense focus on the mathematical discovery.

Chapter Summary: “Reject My Paper”

Key Plot Points and Events

• During a lecture, renowned mathematician Enrico Bombieri publicly asks Li Dong to let the Annals of Mathematics reject his paper.
• The audience realizes that Li Dong submitted a paper addressing the Montgomery Pair Correlation Conjecture, a major unsolved problem in analytic number theory.
• Bombieri explains that the paper relies on data involving (10^{23}) nontrivial zeros. Since Li Dong’s unpublished iterative algorithm is required to reproduce that data, the journal may reject the paper under its reproducibility rules.
• Many scholars, especially Zhou Shenzhi and his supporters, assume this requirement will force Li Dong to reveal his secret algorithm. They view the situation as evidence that his paper cannot be accepted without compromising his research.
• Li Dong initially appears surprised, but Zhou’s explanation makes him recognize that the enormous zero dataset is not essential to the proof itself.
• Li Dong realizes that the data merely helped him discover the mathematical pattern and locate a possible route through the problem. The final paper instead presents a rigorous, self-contained derivation using mathematical logic, Functional Analysis, and the Fourier Optimization Framework.
• Because the proof can theoretically be checked without reproducing the (10^{23}) zeros, the reproducibility objection does not undermine the paper.
• Li Dong sincerely thanks Zhou for clarifying the issue, then calmly tells Bombieri to ask the Annals of Mathematics to reject the paper.

Character Development

• Li Dong demonstrates confidence, intellectual clarity, and independence. Rather than fearing rejection from the world’s most prestigious mathematical journal, he prioritizes protecting his algorithm and recognizes that his proof stands on its own.
• Enrico Bombieri is portrayed as conflicted and ethically uneasy. He respects Li Dong’s work but feels obligated to enforce the journal’s reproducibility standards, even though doing so may bury a historically important result.
• Terence Tao becomes increasingly convinced that Li Dong may have overcome the long-standing barrier in the Montgomery Conjecture. His reaction shows both professional admiration and genuine shock.
• Zhou Shenzhi tries to use academic rules to corner Li Dong, believing the requirement to reproduce the data will force him to disclose his methods. Instead, his intervention unintentionally helps Li Dong understand the strength of his own argument.
• Liu Ruochuan recognizes the seriousness of the journal’s policy and supports Li Dong’s response, though he is visibly troubled by the situation.

Significant Themes

• Independence from academic prestige: Li Dong refuses to sacrifice his discoveries merely to gain publication in the Annals of Mathematics.
• Discovery versus proof: The chapter distinguishes between the tools used to discover a theorem and the rigorous argument needed to prove it. The massive dataset helped Li Dong find the route, but the proof itself does not depend on it.
• Academic rules and their limitations: Reproducibility standards are presented as important for rigor, yet potentially inadequate when groundbreaking work depends on unprecedented computational methods.
• Intellectual confidence: Li Dong’s calm willingness to accept rejection signals that he values mathematical truth more than institutional approval.
• Unexpected reversal: Zhou’s apparent attack becomes an advantage, while Bombieri’s attempt to warn Li Dong ultimately highlights the paper’s strength.

Character Interactions

• Bombieri publicly confronts Li Dong about the paper while carefully avoiding direct disclosure of confidential review information.
• Tao and Arthur Penrose silently recognize the significance of Bombieri’s question and infer that Li Dong may have broken through a fifty-year mathematical barrier.
• Zhou Shenzhi presents the journal’s reproducibility rule as a seemingly reasonable academic objection, hoping it will undermine Li Dong.
• Li Dong thanks Zhou instead, revealing that the objection has helped him clarify why the paper remains valid without the original data.
• Li Dong and Bombieri end the chapter in a dramatic exchange: Bombieri warns that the paper may be rejected, and Li Dong confidently accepts—and even requests—that rejection.

Key Plot Points and Events

• Li Dong presents his paper on the Montgomery Pair Correlation Conjecture at the International Congress of Mathematicians (ICCM).
• Professor Enrico Bombieri, a Fields Medal winner, is impressed by the paper's perfection but is concerned about Li Dong's refusal to publish in Annals of Mathematics.
• Bombieri recommends the paper for expedited external peer review, unaware that the data Li Dong used is not crucial to the proof.
• After the talk, international luminaries like Terence Tao and Yitang Zhang want to meet Li Dong, but Liu Ruochuan intervenes and takes Li Dong away.
• In the car, Li Dong reveals to Liu Ruochuan that the vast data he cited in his paper is not necessary for the proof, making Annals of Mathematics' rejection potentially problematic.

Character Developments

• Li Dong demonstrates maturity and confidence in his academic decisions, prioritizing his Azure Dragon Study Group's advancement over personal recognition.
• Professor Bombieri shows concern for the mathematical community's progress and is willing to support Li Dong's work.
• Liu Ruochuan becomes increasingly impressed by Li Dong's capabilities and starts to see the potential consequences of Annals of Mathematics' rejection.

Significant Themes

• The pursuit of academic excellence versus personal recognition and institutional prestige.
• The responsibility of mathematicians to advance their field and the potential consequences of their decisions.
• The power dynamics and politics within the academic community.

Character Interactions

• Li Dong and Professor Bombieri: Li Dong's refusal to publish in Annals of Mathematics concerns Bombieri, who tries to persuade Li Dong to reconsider.
• Li Dong and Liu Ruochuan: Liu Ruochuan becomes more aware of Li Dong's capabilities and the potential implications of his actions, leading to a shift in their dynamic.
• Li Dong and international luminaries: Li Dong's talk sparks interest from renowned mathematicians, but Liu Ruochuan prevents immediate interactions.

Key Plot Points and Events

• Li Dong meets Sarah, Arthur Penrose's student, who invites him to meet Penrose.
• Penrose, fascinated by Li Dong's algorithm, invites him to discuss it.
• Li Dong hints at future collaboration with Peking University professors on the algorithm.
• Li Dong publishes his paper on arXiv.

Character Developments

• Li Dong demonstrates maturity and strategic thinking in handling Penrose's interest in his algorithm.
• Penrose shows his obsession with mathematical research and lack of social etiquette.
• Liu Ruochuan shows concern for Li Dong's academic decisions and Huaxia's interests.

Significant Themes

• The pursuit of mathematical truth and its personal cost (Penrose's single-minded focus).
• The potential impact of Li Dong's algorithm on Huaxia's technological advancement.
• The strategic use of information and promises (Li Dong's hint at future collaboration).

Character Interactions

• Li Dong and Penrose engage in a deep mathematical discussion, with Penrose treating Li Dong as an equal.
• Li Dong and Liu Ruochuan discuss Li Dong's plans for the algorithm and his decision to publish the paper.
• Li Dong's wink to Liu Ruochuan hints at their shared understanding and agreement on future actions.

Key Plot Points and Events

• Nicholas Katz, a prominent mathematician at Princeton University, is intrigued by Li Dong's work on the Riemann Zeta Function and watches his ICCM talk live.
• Li Dong, during the Q&A, tells Katz to reject his paper on the Montgomery Pair Correlation Conjecture, which he had submitted to the Annals of Mathematics.
• Katz, piqued by Li Dong's arrogance and the paper's content, decides to review it himself.
• Li Dong uploads his paper on the Montgomery Conjecture to arXiv, sparking widespread interest and debate among mathematicians.
• Li Yang, Li Dong's uncle, meets with Huaxuan Technology's director, Lin Wei, who offers to include his factory in Huaxuan's core supply chain training program.
• Li Dong and Li Yang have a conversation about Huaxuan's offer and Li Dong's academic conference.

Character Developments

• Nicholas Katz: Initially intrigued by Li Dong's work, Katz becomes annoyed by Li Dong's arrogance but is drawn into reviewing his paper due to its content.
• Li Dong: Confident in his abilities, Li Dong publicly expresses his disinterest in having his paper published in the Annals of Mathematics and uploads it to arXiv, drawing significant attention.
• Li Yang: Initially hesitant to accept Huaxuan Technology's offer for his factory, Li Yang ultimately agrees after discussing it with Li Dong.

Significant Themes

• Arrogance vs. Confidence: Li Dong's public statement about his paper raises questions about the line between confidence and arrogance in academic circles.
• Recognition and Opportunity: Li Dong's work garners significant attention, opening doors for both him and his uncle's business.
• Mentorship and Support: Li Yang's conversation with Li Dong highlights the importance of their relationship and Li Dong's influence on his uncle's decisions.

Character Interactions

• Nicholas Katz and Li Dong: Katz's interest in Li Dong's work leads him to review Li Dong's paper, setting up a potential mentor-mentee relationship.
• Li Dong and Li Yang: Their conversation demonstrates their close relationship and Li Dong's influence on his uncle's decisions regarding business opportunities.

Key Plot Points and Events

• Li Dong receives calls from prominent mathematicians representing top journals (New Advances in Mathematics, Acta Mathematica Sinica) offering to publish his paper and expedite the review process.
• Li Dong is surprised by the direct and competitive nature of these foreign journals.
• Li Dong receives a call from Henryk Iwaniec of Acta Mathematica, offering a special symposium for his paper if accepted.

Character Developments

• Li Dong: Becomes more confident in his work and is flattered by the attention from top journals. He remains cautious and considers the offers carefully.
• Peter Sarnak: Shows eagerness to publish Li Dong's paper in New Advances in Mathematics, taking a jab at Annals of Mathematics.
• Henryk Iwaniec: Represents Acta Mathematica Sinica, offering an expedited review and a special symposium for Li Dong's paper.

Significant Themes

• Competition among top academic journals.
• The value of academic papers and the importance of peer review.
• The influence of age and experience on academic understanding and decision-making.

Character Interactions

• Li Dong and Peter Sarnak: Sarnak tries to poach Li Dong's paper, criticizing Annals of Mathematics and praising Invent. Math.
• Li Dong and Henryk Iwaniec: Iwaniec offers Li Dong's paper expedited review and a special symposium, showing Acta Mathematica's high regard for the work.
• Li Dong and Li Yang: Li Yang, Li Dong's uncle, notices the importance of the calls and is proud of Li Dong's achievements. He decides to share the good news with Li Dong's mother later.

Key Plot Points and Events

• Li Dong returns to his hotel and finds Terence Tao, a Fields Medal winner, waiting outside his door.
• Tao is reviewing Li Dong's paper for Annals of Mathematics and has questions about certain proofs.
• Tao reveals that Nicholas Katz, a key figure on Annals' editorial board, wants Li Dong to reconsider publishing with them.

Character Developments

• Li Dong: Shows exceptional mathematical prowess and confidence in his work, but remains humble and respectful to Tao.
• Terence Tao: Initially surprised by Li Dong's approach, he comes to admire Li Dong's work and sees similarities with nineteenth-century masters.

Significant Themes

• The clash between classical and modern mathematical approaches.
• The pursuit of academic reputation and honor over financial rewards.

Character Interactions

• Li Dong and Tao discuss Li Dong's paper, with Tao seeking clarification on certain proofs. Li Dong explains his methods clearly and confidently.
• Tao conveys Katz's message to Li Dong, hoping to persuade him to publish with Annals of Mathematics.

Key Plot Points and Events

• Riemann breaks his silence in the Azure Dragon Study Group chat.
• Li Dong realizes he hasn't reported his findings from Riemann's manuscript to Riemann.
• Li Dong tries to send the data but fails due to the group's cognitive boundary.
• He uses a data transfer function to send the file to Riemann.
• Riemann responds with a red packet, acknowledging Li Dong's work.

Character Developments

• Li Dong demonstrates humility and eagerness to learn from Riemann.
• Riemann shows appreciation for Li Dong's work, indicating he's paying attention to the group's activities.

Significant Themes

• The power of mathematical legacy and the importance of sharing findings.
• The challenge of communicating complex mathematical ideas and data across dimensions.

Character Interactions

• Li Dong and Riemann interact through the group chat, with Li Dong showing respect and Riemann responding with acknowledgment and guidance.
• Li Dong's interaction with Jiang Yubai is implied, as he thinks about a paper co-authored by Jiang.

Key Plot Points and Events

• Li Dong receives a call from Liu Ruochuan, who informs him that his paper has gained significant attention in the academic community.
• Liu Ruochuan visits Li Dong and discusses the implications of his paper, emphasizing the importance of publishing in a top international journal.
• They decide that Li Dong should choose between Annals and Invent.Math. for submitting his paper.
• Liu Ruochuan mentions that Huaxuan Technology has invited them for a discussion the next day.

Character Developments

• Li Dong shows maturity and calmness in handling the attention his paper has received.
• Liu Ruochuan demonstrates his mentorship and concern for Li Dong's academic career, guiding him on publishing and negotiating with Huaxuan Technology.

Significant Themes

• The importance of publishing in top international journals for academic recognition and influence.
• The responsibility of a mentor to guide their student's career.
• The negotiation process between Li Dong and Huaxuan Technology, highlighting the balance between contribution and fair compensation.

Character Interactions

• Li Dong and Liu Ruochuan discuss the implications of Li Dong's paper and the best course of action for publishing it.
• Liu Ruochuan expresses his willingness to accompany Li Dong to the meeting with Huaxuan Technology, showing his support and commitment to ensuring fair terms for Li Dong.

Key Plot Points and Events

• Professor Arthur Penrose returns to Princeton for a faculty meeting, where the department's funding is discussed.
• Penrose's Analytic Number Theory group's budget remains unchanged, while Algebraic Geometry receives a 15% increase.
• Penrose argues with Marvin Clark, a professor in Algebraic Geometry, about the funding decision.
• Penrose considers applying for a dual appointment at the Institute for Advanced Study but worries about Clark's influence.

Character Developments

• Penrose shows frustration with the political aspects of academia and the lack of recognition for his group's achievements.
• Clark is portrayed as politically savvy and well-connected, unlike Penrose.
• Sarah, a doctoral student in Penrose's group, is shown to be struggling with student debt, highlighting the financial pressures on young academics.

Significant Themes

• The political nature of academia and the influence of connections on funding decisions.
• The contrast between the academic environments in the US and Huaxia (China), with Huaxia portrayed as more supportive of young academics.
• The tension between academic purity and practical considerations, such as funding and career prospects.

Character Interactions

• Penrose and Clark's tense exchange in the faculty meeting highlights their differing views on academic priorities and funding decisions.
• Penrose's conversation with Sarah reveals her financial struggles and his consideration of visiting a Huaxia university.

Key Plot Points and Events

• Li Dong and Liu Ruochuan visit Huaxuan Technology, where they meet Lu Zhengming, the executive vice president of Guowei Equipment Group.
• Lu Zhengming offers Li Dong a ten-million annual salary and a five-hundred-million remuneration for his algorithm, to be paid in installments upon achieving specific milestones.
• Liu Ruochuan negotiates for Li Dong's access to Guowei's experimental facilities for future research.

Character Developments

• Li Dong remains calm and composed throughout the negotiations, showing maturity beyond his years.
• Lu Zhengming demonstrates his shrewdness and understanding of strategic value, offering a fair deal to Li Dong.
• Liu Ruochuan proves to be an effective mentor and negotiator, securing access to experimental facilities for Li Dong.

Significant Themes

• The value of core technologies and the importance of investing in them.
• The distinction between shrewdness and pettiness in business.
• The role of mentors in guiding young talent.

Character Interactions

• Li Dong and Liu Ruochuan work together to negotiate with Lu Zhengming, with Liu Ruochuan driving the negotiations and Li Dong maintaining a calm demeanor.
• Lu Zhengming and Li Dong engage in a direct and candid conversation about the terms of their potential collaboration.
• Liu Ruochuan secures a valuable resource (access to experimental facilities) for Li Dong, demonstrating his commitment to Li Dong's future success.