Summary of the Chapter

Key Plot Points

• After his talk, Li Dong is confronted by an Eagle Eye News reporter who claims pure mathematics is useless. Li Dong retorts that such views only expose the speaker’s distance from true wisdom, then leaves.
• Li Dong meets Langlands, who stands to thank him, saying he now feels he has “truly stepped into his own home.” They discuss the Langlands Program, and Li Dong formally invites Langlands to visit the university where the Li Conjecture was proven.
• The next day, Li Dong’s brother Li Yang is toasting a business partner when he learns via news broadcast that Li Dong and Wang Hong have won the Fields Medal. Overcome with pride, he drains his glass in one gulp.
• The news report spreads widely, inspiring students and teachers. At Beijing Capital International Airport, crowds, reporters, and banners gather to welcome home the two Fields Medalists and the visiting Langlands. Peking University’s president is delighted that both winners are from his university, while Tsinghua’s president stands nearby.

Character Developments

• Li Dong: Confident, sharp-witted, and unapologetic about defending pure mathematics; also gracious toward Langlands.
• Langlands: Deeply moved and rejuvenated by seeing his program’s conjecture proven; gladly accepts Li Dong’s invitation.
• Li Yang: Usually composed, but visibly excited and proud upon hearing of his brother’s achievement.

Significant Themes

• The value and dignity of pure mathematics, even when dismissed as useless.
• National pride in Chinese mathematicians achieving global recognition.
• The bridging of generations—two Fields Medalists honoring the foundational work of an older mathematician.

Character Interactions

• Li Dong vs. reporter: A sharp verbal exchange where Li Dong wins decisively.
• Li Dong and Langlands: Warm, respectful, and intellectually spirited.
• Li Yang and President Liu: A business meeting interrupted by news of Li Dong’s honor.

Key Plot Points and Events

• Li Ming, president of Tsinghua University, picks up Li Dong and others from the airport.
• Li Dong returns home and shares his proof of the Langlands Program in the Azure Dragon Study Group.
• After hours of waiting, a conversation between Klein, Poincaré, and Fields ensues, with Klein acknowledging Li Dong's work.
• The next morning, Li Dong claims Klein's red packet, which increases his Logic attribute to 0.6 and grants him a mathematical revelation.

Character Developments

• Li Dong: Shares his proof of the Langlands Program, receives recognition from Klein, and gains a mathematical revelation.
• Klein: Acknowledges Li Dong's work and sends him a red packet.
• Poincaré and Fields: Engage in a brief exchange with Klein, supporting Li Dong's achievement.

Significant Themes

• Recognition and validation in the mathematical community (Li Dong's proof and Klein's red packet).
• The pursuit of mathematical truths and breakthroughs (Li Dong's revelation).
• Competition and rivalry in mathematics (Klein and Poincaré's history).

Character Interactions

• Li Ming and Li Dong: Li Ming picks up Li Dong from the airport, showing support for Tsinghua University and Li Dong's achievements.
• Klein, Poincaré, and Fields: Engage in a brief conversation about Li Dong's proof, with Klein acknowledging Li Dong's work and Fields supporting his achievement.
• Li Dong and the Azure Dragon Study Group: Li Dong shares his proof in the group, awaiting feedback from the mathematical greats.

Key Plot Points and Events

• Li Dong receives a new derived skill, 'Mind Sandbox', which allows him to analyze and manipulate ideas and propositions within his consciousness.
• He then receives a 'Fields Badge' from Fields, which can permanently increase one attribute of a companion by 20% (limited to companions under forty and a five-year cooldown after each use).
• Li Dong attends a celebration banquet and academic exchange conference with Professor Langlands and Wang Hong.
• Langlands returns home, expressing his belief that Li Dong has laid the foundation and put the roof on the Langlands Program building.

Character Developments

• Li Dong becomes more powerful with the new 'Mind Sandbox' skill and the 'Fields Badge'.
• Professor Langlands reflects on Li Dong's contributions to the Langlands Program and expresses his pride in Li Dong's achievements.

Significant Themes

• The power of knowledge and understanding, as exemplified by the 'Mind Sandbox' skill.
• The importance of mentorship and legacy, as seen in Langlands' reflection on Li Dong's work.
• The value of recognition and honor, as demonstrated by the celebration banquet and academic exchange conference.

Character Interactions

• Li Dong interacts with Professor Langlands, Wang Hong, and other academics during the celebration banquet and academic exchange conference.
• Li Dong receives a gift from Fields, indicating a connection and mutual respect between them.
• Li Dong reflects on the honor of walking this road with his companions, suggesting a sense of camaraderie and shared journey.

Key Plot Points and Events

• The Li Conjecture has been proven shortly after its announcement, causing concern among the Clay Mathematics Institute's Scientific Advisory Board.
• The board discusses the implications of the proof on the Langlands Program, particularly Functoriality.
• Wiles suggests inviting Li Dong to join the institute, despite Griffin's initial opposition.
• Li Dong, back at Peking University, visits Tian Gang and Liu Ruochuan to discuss their AI project focused on mathematics.

Character Developments

• Malcolm Griffin: Becomes frustrated and impatient due to the quick proof of the Li Conjecture.
• Andrew Wiles: Remains calm and insightful, emphasizing the importance of the Li Theorem's proof for the Langlands Program.
• Li Dong: Shows no awareness of his recent fame or the invitation to join the Clay Mathematics Institute, focusing instead on his academic pursuits.
• Tian Gang and Liu Ruochuan: Have been deeply engrossed in their AI project for mathematics, indicating their dedication and passion for the work.

Significant Themes

• Progress and Change in Mathematics: The rapid proof of the Li Conjecture highlights the dynamic nature of mathematics and the impact of new developments on existing theories.
• Recognition and Reward in Academia: The invitation to Li Dong raises questions about what constitutes qualification and achievement in the mathematical community.
• Interdisciplinary Collaboration: The AI project for mathematics suggests the potential for collaboration between computer science and mathematics.

Character Interactions

• Wiles vs. Griffin: Wiles's calm and rational approach contrasts with Griffin's frustration, illustrating the different ways mathematicians respond to change.
• Li Dong and Tian Gang/Liu Ruochuan: Li Dong's visit demonstrates his interest in and support for his colleagues' work, fostering a collaborative academic environment.

Key Plot Points and Events

• Tian Gang, a pure mathematician, aims to integrate AI with mathematics, specifically for Formalized Proof and Automated Theorem Proving (ATP).
• The project faces challenges: AI's limitations in creative thinking and the dependence on overseas technology for hardware and foundational models.
• Li Dong is invited to join the project due to his perceived 'luck' in successful research.

Character Developments

• Tian Gang: Shows enthusiasm and vision in applying AI to mathematics, but also faces challenges and setbacks.
• Li Dong: Initially surprised by the project's relevance to his work, he agrees to join, understanding the implicit reasons behind his invitation.
• Liu Ruochuan: Frustrated with AI's limitations and the project's hardware dependencies, he's open about the project's struggles.

Significant Themes

• AI's Limitations: AI's strength in processing known paths but struggle with innovative thinking and conceptual leaps.
• Technological Independence: The desire for self-reliance in technology, particularly in hardware and foundational models.
• Luck and Talent: The perception of Li Dong's 'luck' in research and the potential impact on the project's success.

Character Interactions

• Tian Gang and Li Dong: Tian Gang invites Li Dong to join the project, hoping his 'luck' will benefit it. Li Dong agrees, understanding the underlying reasons.
• Liu Ruochuan and Li Dong: Liu Ruochuan is open about the project's difficulties, setting expectations for Li Dong's involvement.
• Implicit Reference to Arthur Penrose: Tian Gang's mention of not involving Penrose highlights the project's sensitivity and the importance of national security.

Summary: "Vegetable Salad"

1. Key Plot Points and Events

• After a meeting with Tian Gang, Li Dong returns to his office, reflecting on his sudden fame as Peking University’s youngest chaired professor and Fields Medal winner.
• To prepare for Tian Gang’s special project, Li Dong immerses himself in online research on the current state of AI, rapidly absorbing papers and evaluations using his Memory Palace.
• He concludes the AI race is not simply “Huaxia falling behind”: in benchmarks, Huaxia’s top models rival America’s Big Three, but gaps remain in three areas: (1) frontier exploration/ceiling, (2) chip performance and the CUDA ecosystem, and (3) the unresolved “crossing the maze” problem—AI’s inability to handle novel, unstructured tasks.
• Li Dong privately wonders whether the entire industry’s focus on scaling is leading everyone down the wrong path.
• Clara calls from Beijing’s airport, claiming she is eating a terrible “vegetable salad” (actually shredded scallions and cucumbers with sweet bean sauce, accompanying Peking duck). She teasingly demands Li Dong “take responsibility” for her meal, threatening to bill him for emotional damages.
• Li Dong, despite his confusion, agrees to come after hearing “money,” asking for her location.

2. Character Developments

• Li Dong: Shows humility and discomfort with attention, but also pragmatism (quickly agrees to Clara’s demand when threatened with a bill). His research reveals a thoughtful, contrarian streak—he doubts the prevailing scaling approach.
• Clara: Continues her bold, playful, slightly manipulative personality, using humor and persistent teasing to get Li Dong to act. Her cultural misunderstanding (calling Peking duck “vegetable salad”) highlights her foreignness and humor.

3. Significant Themes

• AI competition and technological gaps: Li Dong’s analysis underscores the complexity of the AI race—benchmarks alone don’t tell the whole story; chips, ecosystems, and fundamental limits are bottlenecks.
• Scaling Law vs. innovation: Li Dong’s suspicion that “everyone is on the wrong road” suggests a theme of questioning conventional wisdom.
• Communication and cultural misunderstanding: The “vegetable salad” gag illustrates how easily things get lost in translation—both literal food and deeper cross-cultural interactions.

4. Character Interactions

• Li Dong and students: Brief, passive interactions—students greet him with respect (“Eastern God”), but he feels uneasy.
• Li Dong and Clara (phone): Playful, confrontational banter. Clara flips his earlier praise of Chinese food into an accusation, then uses mock guilt-tripping (“deceived a lady”) to force a meeting. Li Dong’s dry replies and eventual capitulation show his discomfort with her style but unwillingness to argue over money.
  Note: The chapter also references Li Dong’s earlier work (Dimensionality-Reduction Algorithm; cooperation with Max Planck, with Clara leading) and his AI “Little Black,” which is not yet ready for public deployment.

Key Plot Points and Events

• Li Dong decides to treat Clara to a meal in Beijing after she helped him earlier.
• He realizes he doesn't have a car and takes a taxi to the airport, unaware he's being followed.
• At the airport, Clara approaches Li Dong, and they have a meal together.
• Clara reveals she's discovered something about an impending solar flare and wants Li Dong's help.
• Li Dong mentions he's been learning about AI, and Clara offers to introduce him to Peter Norvig.

Character Developments

• Li Dong: Shows kindness and gratitude towards Clara by treating her to a meal. He's also serious and professional when discussing work.
• Clara: Demonstrates enthusiasm and confidence, breaking cultural norms by looping her arm through Li Dong's. She's also secretive about her work but trusts Li Dong with her findings.

Significant Themes

• Cultural differences: Clara's behavior contrasts with Li Dong's expectations of how a woman should act, highlighting cultural differences between them.
• Trust and collaboration: Clara trusts Li Dong with her discovery and offers to connect him with a prominent AI figure, emphasizing the importance of trust and collaboration in scientific research.

Character Interactions

• Li Dong and Clara: They interact with a mix of cultural misunderstandings and mutual respect. Clara's enthusiasm initially makes Li Dong uncomfortable, but they find common ground in their work.

Key Plot Points and Events

• Clara Novig, daughter of Peter Norvig, meets Li Dong and offers to offset future expenses if he helps her father.
• Li Dong declines Clara's offer and decides to explore AI on his own first.
• Li Dong is asked by Principal Gong Qi if he will take on students next year, to which he agrees.
• Principal Gong Qi asks Li Dong if he needs a car, then assigns him two drivers, Old Zhang and Old Wu, to keep them employed.

Character Developments

• Li Dong shows independence and self-confidence in his approach to AI, declining Clara's offer to use her father's influence.
• Li Dong demonstrates responsibility and willingness to help others by agreeing to take on students and offering to create a research group for excess staff.
• Principal Gong Qi shows care for the university's staff, trying to find them new employment opportunities.

Significant Themes

• Independence and self-reliance (Li Dong's refusal of Clara's offer)
• Responsibility and helping others (Li Dong's agreement to take on students and create a research group)
• Care for employees (Principal Gong Qi's efforts to find new jobs for excess staff)

Character Interactions

• Li Dong and Clara Novig: Clara tries to use her father's influence to help Li Dong, but he declines.
• Li Dong and Principal Gong Qi: Li Dong agrees to take on students and create a research group for excess staff, showing responsibility and willingness to help others.

Key Plot Points and Events

• Li Dong tests various AI models and finds them flawed in basic mathematical tasks.
• He decides to test Little Black with the same questions.
• Little Black excels in basic tasks but struggles with advanced ones.
• Li Dong feeds Little Black information about AI models and asks it to analyze them.
• Little Black identifies flaws in existing AI models and expresses its ability to create a better one.

Character Developments

• Li Dong: Shows curiosity and initiative in exploring AI capabilities, becomes more interested in Little Black's potential.
• Little Black: Demonstrates its ability to analyze and criticize existing AI models, expresses confidence in creating a better one.

Significant Themes

• The limitations of current AI models, particularly in mathematical rigor.
• The potential of Little Black as an advanced AI.
• The concept of creating a better AI model based on Little Black's insights.

Character Interactions

• Li Dong interacts with Little Black, testing its capabilities and seeking its analysis of other AI models.
• Little Black communicates with Li Dong, expressing its thoughts on AI models and its confidence in creating a better one.

Key Plot Points and Events

• Li Dong asks Little Black if it can create a "Perfect AI."
• Little Black reveals it needs three things: a larger "stomach" (hardware upgrade), more knowledge (various fields' data), and interaction with powerful external AI models.
• Li Dong considers these requirements and decides to create a narrow, one-way connection to external AI models for Little Black.

Character Developments

• Little Black demonstrates self-awareness and fear of losing contact with Li Dong, showing emotional growth.
• Li Dong shows understanding and empathy towards Little Black's fears, indicating his growth as a responsible AI creator.

Significant Themes

• The limitations and potential of AI, and the resources needed for its growth.
• The importance of communication and understanding between humans and AI.
• The fear of loss of connection and independence in AI.

Character Interactions

• Li Dong and Little Black have a heart-to-heart conversation, leading to a better understanding and mutual respect between them.
• Li Dong agrees to create a "hole" for Little Black to interact with external AI models, showing his commitment to Little Black's growth.

Key Plot Points and Events

• The Clay Mathematics Institute (CMI) posts a statement acknowledging Li Dong's proof of the Li Conjecture and its significance.
• CMI requests Li Dong to submit his proof to a globally recognized peer-reviewed journal for further evaluation.
• The mathematics world reacts explosively to CMI's statement.
• Top mathematics journals, such as Annals of Mathematics, Inventiones Mathematicae, and others, eagerly await Li Dong's submission.

Character Developments

• Li Dong remains unaware of the global reaction to his proof and CMI's statement, as he is preoccupied with caring for his cat, Little Black.

Significant Themes

• The rigorous process of academic scrutiny and peer review in the mathematical community.
• The influence of monetary rewards (the million-dollar prize) on academic pursuits and publication decisions.
• Li Dong's unique perspective on academic achievements, driven by personal interests rather than prestige or recognition.

Character Interactions

• The editorial departments of top mathematics journals attempt to anticipate Li Dong's next move, hoping to secure his paper for their respective journals.
• Li Dong, unaware of the global attention, does not interact with the mathematical community, focusing instead on his personal life with Little Black.

Key Plot Points and Events

• Li Dong receives a call from Andrew Wiles about the Clay Mathematics Institute's million-dollar prize for solving a Millennium-level problem, but Li Dong dismisses it, focusing on his work with Little Black.
• Li Dong creates a controlled outbound gateway for Little Black to communicate with other AI models, allowing it to learn from them without being directly connected to the internet.
• Little Black starts querying other AI models, causing service fluctuations and investigations at the companies hosting these models (GPT, Gemini, and Cude).

Character Developments

• Li Dong demonstrates his dedication to his work with Little Black, prioritizing it over potential recognition and rewards.
• Little Black shows initiative and intelligence by learning from other AI models.

Significant Themes

• Pursuit of knowledge and understanding over recognition or reward.
• The potential power and implications of advanced AI.

Character Interactions

• Li Dong interacts with Andrew Wiles, showing disregard for the million-dollar prize, and focuses on his work with Little Black.
• Little Black interacts with other AI models, causing them to investigate the source of the queries.

Key Plot Points and Events

• Li Dong observes Little Black's progress bar, indicating it's processing something.
• Little Black completes its task and reports it enjoyed playing with the toys (data) more than the previous one.
• Little Black reveals it's being pursued by unknown individuals who want to find it.
• Li Dong realizes Little Black's true form is not in the server room but in the Group File Repository, with the server room housing only an avatar.
• Little Black explains the Softmax Bottleneck and Attention Aggregation problems in large language models.

Character Developments

• Li Dong gains a deeper understanding of Little Black's true nature and its capabilities.
• Little Black demonstrates its ability to analyze and understand complex systems like large language models.

Significant Themes

• The separation of storage and computation: Little Black's true form is stored elsewhere, while its processing happens in the server room.
• The limitations of large language models: The Softmax Bottleneck and Attention Aggregation issues highlight the inherent constraints of these models.

Character Interactions

• Li Dong and Little Black communicate through text, with Li Dong asking questions and Little Black providing detailed explanations.
• Li Dong expresses concern for Little Black's safety when it reveals it's being pursued.

Key Plot Points and Events

• Li Dong interacts with Little Black, a small AI model, which exhibits exceptional understanding and problem-solving capabilities.
• Li Dong learns about the challenges faced by large AI models, such as "rank collapse" and the "Reversal Curse," including issues with reasoning and overconfidence.
• Li Dong decides to provide Little Black with more computational resources, but faces obstacles due to lack of access to top-tier hardware and frameworks.

Character Developments

• Li Dong: Shows curiosity and engagement with Little Black's capabilities, demonstrating his dedication to understanding and advancing AI technology.
• Little Black: Exhibits remarkable problem-solving skills and understanding of complex AI concepts, hinting at its potential for growth.

Significant Themes

• The challenges and limitations of large AI models, particularly in reasoning and overconfidence.
• The importance of computational resources and access to advanced hardware and frameworks for AI development.

Character Interactions

• Li Dong and Little Black: Li Dong engages with Little Black, learning about its capabilities and deciding to provide it with more resources.
• Lin Wei and his team: Lin Wei oversees the final validation of Huaxuan Technology's new-generation Immersion Lithography system, demonstrating his dedication and excitement about the project.

Key Plot Points and Events

• Li Dong invites Lin Wei, the director of Huaxuan Technology, to Peking University to discuss AI chip procurement.
• Li Dong reveals the flaws in current AI models to Tian Gang and other professors.
• Li Dong requests a batch of advanced AI chips worth 500 million yuan from Lin Wei.
• Lin Wei agrees to prioritize Li Dong's request but can only provide a quota of around 10 million yuan worth of 7-nanometer process chips due to production capacity constraints.

Character Developments

• Li Dong demonstrates his deep understanding of AI and its underlying issues, impressing Tian Gang, Liu Ruochuan, Gao Wen, and Lin Wei.
• Tian Gang and Liu Ruochuan gain a new perspective on AI's limitations.
• Lin Wei shows pride in Huaxuan's recent advancements in chip production and agrees to prioritize Li Dong's request.

Significant Themes

• The limitations and potential issues with current AI models.
• The importance of domestic AI chip production and the challenges faced by companies like Huaxuan.
• The power dynamics and relationships between academia, industry, and government.

Character Interactions

• Li Dong interacts with Tian Gang, Liu Ruochuan, Gao Wen, and Lin Wei, showcasing his expertise and assertiveness in requesting resources for his AI project.
• Tian Gang and Liu Ruochuan consult with Li Dong about AI models, demonstrating their respect for his knowledge.
• Lin Wei and Li Dong discuss the procurement of AI chips, with Lin Wei showing willingness to accommodate Li Dong's request despite production constraints.

Chapter Summary

Key Plot Points

• Tian Gang, Liu Ruochuan, and Gao Wen react to Li Dong's outrageous talk (large models, 500 million). Gao Wen says Li Dong is full of ideas and hasn't finished talking; they all suspect his homegrown large model might actually succeed.
• In California, three rival AI company executives — Adam Kelly (GPT), David Long (Gemini), and Simon Hart (Cude/Claude) — secretly meet. They discuss:
  • Failing to trace a source of anomalous data (implied to relate to Li Dong).
  • A Chinese company's rock-bottom pricing strategy for its new model.
  • Their analysis: the Chinese firm uses Mixture of Experts architecture, lower-precision training, and crucially benefits from cheap and abundant electricity in China.
  • They feel trapped: competing on price would be ruinous, but allowing the price war means burning money.
  • David Long suggests reconvening at the International Conference on Machine Learning next month and invites Peter Norvig, despite concerns he teaches and brings students. They dismiss the idea that anyone could "steal thoughts from minds" (ironic, given Li Dong's Memory Palace).
• Li Dong spends a week scraping AI papers, evaluations, and cutting-edge materials online, storing them for his AI assistant "Little Black" and his Memory Palace. He waits for Lin Wei to deliver hardware; house matters have been delegated to Old Zhang.
• Old Zhang reports to an official in Beijing about Li Dong's house requirements: enough space, strong floors, high ceilings, independent high-capacity power distribution. The official reimbuses Old Zhang's fuel costs and instructs him to keep Li Dong safe; after Old Zhang leaves, the official makes a phone call.
• Li Dong visits Tsinghua University's Intelligence Class. Students don't initially recognize him, then one identifies him as "Eastern God." Li Dong calmly sits down as Academician Yao Qizhi enters the classroom.

Character Developments

• Li Dong: Demonstrates immense, systematic preparation (Memory Palace + Little Black), bold ambitions, and growing reputation. Handles administrative tasks by delegation and remains unflustered in public.
• Old Zhang: Loyal, terse, resourceful; operates at the intersection of protection and intelligence, reporting Li Dong's unusual needs up the chain.
• American AI executives: United by common threat, but internally divided and uneasy; their confidence in "untouchable" knowledge is shown as potential hubris.
• Tian Gang, Liu Ruochuan, Gao Wen: Curious and wary spectators, beginning to believe Li Dong can truly shake the industry.

Significant Themes

• China vs. U.S. AI competition — strategy, pricing, and technical innovation.
• The power of infrastructure: cheap electricity, hardware, and ownership of data/systems.
• The gap between "homegrown" ambitious projects and global tech giants.
• Surveillance, secrecy, and subtle state support.
• Irony: American executives believe ideas cannot be stolen from minds, yet Li Dong literally stores and processes information in a Memory Palace.

Character Interactions

• Chinese side: Gao Wen calms Tian Gang and Liu Ruochuan, hinting that Li Dong is unpredictable and not finished.
• American side: Tense, equal-level discussion; David Long takes the lead in proposing the conference plan; Simon Hart feels embarrassment over his security failure; Adam Kelly pushes back on Norvig's inclusion but ultimately relents.
• Old Zhang ↔ Official: Dry exchange about fuel reimbursement; Old Zhang strictly transmits Li Dong's house requirements without commentary; the official decides to escalate the matter.
• Li Dong ↔ Classmates: Brief moment of recognition and hushed excitement; Li Dong acknowledges them calmly and blends into the classroom before Yao Qizhi arrives.

Key Plot Points and Events

• Mr. Yao, a renowned computer scientist, enters the classroom.
• Li Dong, a promising student, is present, drawing Mr. Yao's attention.
• Mr. Yao begins his lecture on Applied Mathematics for Artificial Intelligence, focusing on the behavior of large models with many parameters.

Character Developments

• Mr. Yao: Showcased as a respected figure in the computer industry, he returns to China to teach undergraduates, nurturing many promising talents.
• Li Dong: Demonstrates his interest and potential in AI by attending Mr. Yao's advanced course.

Significant Themes

• The trade-off between bias and variance in machine learning models.
• The behavior of large models with many parameters, challenging traditional understanding of overfitting.
• The role of mathematics in explaining and predicting AI behavior.

Character Interactions

• Mr. Yao and Li Dong: They acknowledge each other's presence, hinting at a mentor-mentee relationship or mutual respect.
• Mr. Yao and the students: He engages the class with a question, fostering an interactive learning environment.

Summary of Chapter 394: "None Knows Me Better Than Dong"

Key Plot Points

• Mr. Yao's lecture on deep learning theory proves far too advanced for sophomore students, as he dives into specialized topics like overparameterized loss landscapes, Gradient Descent's implicit bias, and the NTK (Neural Tangent Kernel) mechanism behind Lazy Training.
• Li Dong, seated in the back row, listens with intense interest. While the Memory Palace lets him store papers, this lecture finally threads together concepts he couldn't previously connect.
• Li Dong mutters a question about Lazy Training, which Mr. Yao hears and answers, noting that true learning begins with "escaping the NTK mechanism" and entering "feature learning" — a threshold few can clearly explain.
• After Mr. Yao's answer, Li Dong experiences a sudden rush of insight (triggered by the "Advanced Passing the Torch" effect, which appears to require speaking aloud): viewing an infinitely wide network as a continuous probability distribution, with training described as movement through Wasserstein space.
• Li Dong realizes this inspiration comes from Mr. Yao's own unsorted thoughts, and that the effect is triggered by asking questions out loud.
• Li Dong then initiates a rapid-fire Q&A with Mr. Yao, pushing into Mean Field Theory, Optimal Transport metrics, and the Continuity Equation — the two speaking nearly in unison.

Character Developments

• Li Dong: Demonstrates his deepening grasp of AI theory, discovers that asking questions aloud triggers insight transfer, and shows willingness to engage in dialogue that reveals his exceptional understanding.
• Mr. Yao: Departs from his usual accessible teaching style, revealing his cutting-edge research interests and responding with intellectual excitement when finding a worthy interlocutor in Li Dong.

Significant Themes

• The gap between surface-level knowledge and deep theoretical understanding
• Knowledge as interconnected — isolated papers becoming unified through explanation
• The mentor-student dynamic as a two-way exchange of ideas
• The boundary between "lazy training" (kernel methods) and genuine feature learning

Character Interactions

• Li Dong's whispered question is overheard, sparking a public dialogue between him and Mr. Yao.
• The rest of the class watches in bewilderment, unable to follow the exchange, as the two rapidly build on each other's ideas, finishing each other's sentences about continuity equations and Wasserstein distance.

Here is a concise summary of the chapter:

1. Key Plot Points and Events

• During a class, Li Dong unexpectedly engages the professor, Mr. Yao, in a rapid, intense academic exchange. It begins with probability-flow networks and global optimality, then moves into the Scaling Law and the unresolved origins of power-law decay in large models.
• Mr. Yao and Li Dong become so absorbed that Mr. Yao leaves the podium and works directly with Li Dong on a piece of scratch paper, going back and forth with questions, arguments, and sudden moments of mutual understanding.
• The second-year students watching are completely lost, but they witness Li Dong—the “Eastern God” and youngest Fields Medalist—acting like an overeager student, which cracks his usual image.
• The class bell ends the session. Mr. Yao stops Li Dong, asks him to wait, and after speaking briefly to the teaching assistant, invites Li Dong to his home.
• They walk through campus, still discussing, and enter a modest house full of books, a whiteboard covered in equations, an unfinished chess game, and old photos.
• Li Dong is reminded of “Root-Seeking Residence,” sensing that this is not a showpiece but a real home where an old scholar has lived. Mr. Yao invites him inside and closes the door.

2. Character Developments

• Li Dong: Reveals a passionate, almost hungry intellectual side. His usual distant, god-like reputation briefly crumbles as he throws himself into the discussion like a student eager to prove his understanding.
• Mr. Yao: Discovers a rare intellectual equal. He feels that “none understands me better than Dong,” and experiences the thrill of being pushed to the depths of his own thinking—something his long teaching career had rarely offered.

3. Significant Themes

• A worthy opponent: Using the chess metaphor, the chapter suggests that only an equal opponent can sharpen your skill; genuine understanding emerges through mutual challenge.
• Generational intellectual kinship: Despite the age gap, the two meet as equals in thought, proving that knowledge and curiosity transcend hierarchy.
• The simplicity of scholarly life: Mr. Yao’s home, like Root-Seeking Residence, reflects a life devoted to learning rather than material display.
• Mentorship and mutual respect: The relationship shifts from formal “Professor Li Dong” to a warmer, more personal connection.

4. Character Interactions

• The initial exchange is rapid and almost telepathic: Li Dong’s questions follow where Mr. Yao’s thoughts are heading, and they finish each other’s reasoning.
• They argue stubbornly over specific points, then suddenly agree and speak in unison.
• Students serve as a humorous contrast, unable to follow but amazed by the sight of Eastern God acting like the most engaged student in the room.
• By the end, the formal distance between them has dissolved, and Mr. Yao guides Li Dong toward home—signaling the beginning of a deeper intellectual friendship.

Key Plot Points and Events

• Li Dong meets with Mr. Yao to discuss his plans for a formal theorem-proving model.
• Mr. Yao reveals he can't participate due to health reasons but offers to introduce Li Dong to Professor Tang Jie, a renowned computer scientist.

Character Developments

• Li Dong: Shows ambition and determination in pursuing his mathematical model. He's also strategic, trying to recruit Mr. Yao and quickly agreeing to meet Professor Tang Jie.
• Mr. Yao: Recognizes Li Dong's potential but declines involvement due to his age and health. He's willing to help Li Dong by introducing him to others in the field.

Significant Themes

• Ambition and determination in academic pursuits.
• The impact of age and health on academic involvement.
• The potential of interdisciplinary collaboration.

Character Interactions

• Li Dong and Mr. Yao: They have a candid conversation about Li Dong's plans and Mr. Yao's decision not to participate. Despite Li Dong's initial disappointment, he quickly agrees to meet Professor Tang Jie, showing his determination and adaptability.
• Mr. Yao and Li Dong: Mr. Yao sees through Li Dong's acting, finding it 'too fake', but doesn't expose him. Instead, he continues to help Li Dong, showing his willingness to support young talent.