Chapter Summaries

Key Plot Points and Events

• Shen Qi, Gong Changwei, and Faltings receive the 'Breakthrough Prize in Mathematics' for their significant contributions to elliptic and parabolic PDEs, Number Theory, and the proof of the Wash Conjecture, respectively.
• Shen Qi, at 22, becomes the youngest recipient of the prize.
• After the ceremony, Shen Qi is interviewed and expresses his ambition for future awards like the Fields Medal.

Character Developments

• Shen Qi's academic achievements and confidence grow, leading him to believe he will sweep major awards in the coming years.
• Gong Changwei and Faltings recognize Shen Qi's academic standing, treating him as an equal despite his lack of a PhD.

Significant Themes

• The value of academic achievements and the respect they command in the academic community.
• The impact of age and youth on perception and opportunities in academia.

Character Interactions

• Shen Qi, Gong Changwei, and Faltings bond over their shared academic pursuits and awards, discussing their plans and car preferences.
• Shen Qi and Ou Ye go on a drive together, with Ou Ye expressing her desire to visit Shen Qi's dorm at Princeton.

Key Plot Points and Events

• Shen Qi drops Ou Ye off at Columbia University and discusses academic matters with Gong Changwei.
• Shen Qi reviews his academic achievements at Princeton, including publishing five papers, solving three major problems, and receiving prestigious awards like the Chern Prize, Ford Prize, and Breakthrough Prize.
• Shen Qi calculates potential future awards to aim for, such as the Fields Medal, Ramanujan Prize, Cole Prize, and Steele Prize.
• Shen Qi adjusts his Riemann Hypothesis paper into a standard journal format.
• An IMU representative, Mr. Andre Weiser, visits Shen Qi and invites him to speak at the International Congress of Mathematicians.
• Weiser, also a Senior Manager at Springer Publishing Group, offers to cooperate with Shen Qi for publishing his academic works globally.

Character Developments

• Shen Qi demonstrates ambition and strategic thinking by considering future awards and potential publishing opportunities.
• Weiser shows his business acumen and understanding of the academic publishing industry.

Significant Themes

• The pursuit of academic fame and recognition.
• The importance of publishing in prestigious journals and with established publishing houses for global influence.
• The intersection of academia and industry, with Weiser's dual role as an IMU representative and a publishing group manager.

Character Interactions

• Shen Qi and Gong Changwei discuss academic matters, showing their shared passion and understanding of mathematics.
• Shen Qi and Weiser discuss potential cooperation, with Weiser offering Springer's global publishing services and Shen Qi considering the benefits for his academic career.

Key Plot Points and Events

• Shen Qi discusses publishing options for his Riemann Hypothesis proof with Weiser.
• The paper is submitted to the Journal of Mathematics for review by a grand panel of 11 number theory experts.
• Shen Qi's team struggles with deriving the third expression for ζ(s) in the latter half of the proof.
• Shen Qi is informed that the grand review panel will visit the U.S. to question him directly.

Character Developments

• Shen Qi shows humility regarding record-breaking publications and focuses on his work.
• Jonas takes a break from the project due to exhaustion.
• Ou Ye joins Shen Qi's team, strengthening the collaboration.

Significant Themes

• The rigorous review process for groundbreaking mathematical proofs.
• The international collaboration and recognition in the mathematics community.
• The challenges and perseverance in solving complex mathematical problems.

Character Interactions

• Shen Qi discusses publishing options with Weiser, revealing his preference for journals over conference proceedings.
• Shen Qi's team members, including Mary, Jonas, and Ou Ye, collaborate on the latter half of the Riemann Hypothesis proof.
• Shen Qi anticipates facing questions from the grand review panel, indicating his readiness for the international defense.

Key Plot Points and Events

• Shen Qi hosts an academic exchange on his "Riemann Hypothesis Proof Based on the Twin Matching Method" at Princeton University.
• An eleven-member Grand Review Committee, comprising top Number Theory experts from around the world, attends the event.
• The review begins, with Maynard questioning Shen Qi's first expression, arguing it contradicts the Hardy system.

Character Developments

• Shen Qi demonstrates confidence and preparedness, ready to defend his work against the esteemed reviewers.
• Maynard shows his opposition to Shen Qi's approach, targeting his first expression.
• Chairman Kabrovsky and Brazilian mathematician Rodriguez express disagreement with Maynard, potentially supporting Shen Qi's system theory.

Significant Themes

• The global recognition and validation of Shen Qi's work, which could significantly advance his career.
• The clash of mathematical systems and theories, with Shen Qi asserting the Hardy system is outdated for the Riemann Hypothesis.
• The international collaboration and competition in the mathematical community.

Character Interactions

• Shen Qi greets and interacts with the reviewers, acknowledging their reputations and the gravity of the event.
• Maynard challenges Shen Qi's work, setting the stage for a debate.
• Kabrovsky and Rodriguez hint at their support for Shen Qi, potentially creating a divide among the reviewers.

Key Plot Points and Events

• Shen Qi presents his 'twin matching method' and defends it against criticism.
• Nakamura Kenji supports Shen Qi's method, verifying its logical soundness.
• The review committee asks Shen Qi a series of questions over three days, with Shen Qi answering them satisfactorily.
• On the fourth day, Kabrovsky asks the final question, which Shen Qi answers brilliantly, winning over the remaining neutral mathematicians.
• Shen Qi presents a new formula, further solidifying his proof's validity.

Character Developments

• Shen Qi demonstrates his genius and passion for mathematics, winning over the review committee with his innovative method and flawless answers.
• Maynard, initially critical, becomes increasingly frustrated as Shen Qi's proof gains support.
• Nakamura Kenji shows fairness and professionalism by supporting Shen Qi's method.
• Sabhasin, initially opposed, is won over by Shen Qi's final proof, describing it as "genius-like imagination, devil-like deductive logic."

Significant Themes

• The pursuit of mathematical truth and the acceptance of new methods.
• The clash between established theories (Hardy system) and innovative approaches (Shen Qi's 'twin matching method').
• The importance of fairness and professional ethics in academic review.

Character Interactions

• Shen Qi interacts with the review committee, defending his method and answering their questions.
• Maynard, initially hostile, becomes increasingly isolated as Shen Qi gains support.
• Nakamura Kenji and Sabhasin interact with Shen Qi, supporting his method and acknowledging its validity.
• The review committee members interact with each other, expressing their opinions and voting on Shen Qi's proof.

Key Plot Points and Events

• Shen Qi successfully defends his Ph.D. thesis, proving the Riemann Hypothesis.
• The review committee, impressed by Shen Qi's work, congratulates him and flies back to Europe to submit their report.
• The Journal of Mathematics publishes a special issue containing Shen Qi's proof, with four authors: Shen Qi, Mary Schultz-Schmidt, Jonas Karl, and Allen Muller.
• The International Mathematical Union (IMU) officially announces that Shen Qi has proven the Riemann Hypothesis.
• The news spreads rapidly, gaining significant public attention.

Character Developments

• Shen Qi gains confidence in his abilities and achieves international recognition.
• Other mathematicians, such as Kabrovsky, Rodrigues, Carrick, and Sabhasin, express their admiration and respect for Shen Qi's work.

Significant Themes

• Genius and talent: Shen Qi's exceptional mathematical abilities are highlighted.
• Recognition and fame: The chapter explores the impact of Shen Qi's achievement on his reputation and the mathematical community.
• Mathematical breakthroughs: The proof of the Riemann Hypothesis is presented as a significant milestone in the field of mathematics.

Character Interactions

• Shen Qi interacts with the review committee members, who acknowledge his genius and the quality of his work.
• The international mathematical community reacts to Shen Qi's achievement, with mathematicians from different countries expressing their admiration and anticipation for future developments.
• The public, both in China and internationally, responds to the news, with some understanding the significance of the Riemann Hypothesis and others simply admiring Shen Qi's accomplishment.

Key Plot Points and Events

• Shen Qi and his team (Muller, Mary, Jonas) celebrate proving the Riemann Hypothesis.
• Muller is nominated for the Leibniz Prize, Mary becomes a Princeton researcher, and Jonas is forcibly graduated with a PhD.
• Shen Qi is to defend his thesis within a month and will become a lecturer in the Princeton Mathematics Department.
• Shen Qi gives a lecture to the entire Princeton faculty and student body, discussing the Millennium Prize Problems and inviting students to join his team.

Character Developments

• Shen Qi is excited about his upcoming role as a lecturer and principal investigator of the "RT Third Expression" project.
• Muller feels a sense of loss as his students (Shen Qi, Mary, Jonas) will leave him but is comforted by Shen Qi's assurance that they will continue to work together on the "Third Expression" project.
• Jonas finds his purpose after graduating, deciding to continue working with Shen Qi.
• Zhou Yu'an expresses his admiration for Shen Qi's lecture and offers to join his team if given a suitable project.

Significant Themes

• Transition and Change: The chapter explores the psychological transition period for Shen Qi and his team as they move from students to teachers and researchers, and the changes in their roles and responsibilities.
• Mathematical Pursuits: The love for mathematics and the pursuit of solving complex problems, like the Millennium Prize Problems, drive the characters.
• Mentorship and Collaboration: The relationships between Muller and his students, and between Shen Qi and his team, highlight the importance of mentorship and collaboration in academic pursuits.

Character Interactions

• Shen Qi interacts with Muller, Mary, and Jonas, expressing his gratitude and excitement about their joint work and future collaborations.
• Shen Qi interacts with Zhou Yu'an, inviting him to join his team and expressing his need for help in teaching.
• Muller expresses his sadness at the departure of his students but finds comfort in their continued collaboration on the "Third Expression" project.

Key Plot Points and Events

• Shen Qi's team proves the Riemann Hypothesis, qualifying him for the $1 million Millennium Prize.
• Shen Qi receives the award and the Clay Research Award at the Clay Mathematics Institute in Massachusetts.
• He attends his PhD defense at Princeton University, receiving his doctorate title earlier due to his recent accomplishments.
• Shen Qi is interviewed by a Discovery Channel reporter after receiving his awards.

Character Developments

• Shen Qi maintains his humility despite his extraordinary achievements, refusing to compare himself to the reclusive Russian mathematician Perelman.
• He demonstrates his independence and self-assurance by declining to return to China immediately, prioritizing his commitments in the US.

Significant Themes

• Humility and Modesty: Shen Qi's refusal to boast about his accomplishments and his respect for Perelman's modesty highlight his humility.
• Responsibility and Commitment: Shen Qi's decision to fulfill his commitments in the US before returning to China showcases his sense of responsibility.

Character Interactions

• Shen Qi and Sun Erxiong: Shen Qi's conversation with Sun Erxiong reveals his respect and affection for his former professor and alma mater, Yanjing University.
• Shen Qi and the Clay Mathematics Institute: Shen Qi's interaction with the Clay Mathematics Institute demonstrates his professionalism and cooperation in receiving his awards.

Key Plot Points and Events

• Shen Qi, after a successful keynote speech at MIT, gives lectures across the US, gaining significant attention.
• The Chinese Mathematical Society awards him "Senior Honorary Member" status to encourage his return to China.
• Shen Qi returns to China for a visit, with a packed schedule including keynote speeches, academic forums, media interviews, and a grassroots outreach activity.

Character Developments

• Shen Qi: Shows pride in his accomplishments but feels a lack of belonging in the US. He's eager to return to China and share his success.
• Wang Minxing (President of Chinese Mathematical Society & Dean of Yanjing University): Shows eagerness to welcome Shen Qi back, representing both the society and the university.

Significant Themes

• National Pride and Belonging: Shen Qi's feelings of pride in his achievements and his eagerness to return to China highlight the theme of national pride and belonging.
• Recognition and Reward: The Chinese Mathematical Society's actions emphasize the theme of recognition and reward for outstanding contributions to the field.

Character Interactions

• Shen Qi interacts with Wang Minxing, who extends an invitation on behalf of the Chinese Mathematical Society and Yanjing University.
• Shen Qi communicates with his team members (Little Yezi, Mary, Jonas, and Zhou Yu'an) to arrange his work during his return to China.
• Shen Qi meets with the task force members in the Capital to discuss his itinerary during his stay in China.

Key Plot Points and Events

• Shen Qi, a renowned mathematician, returns to Yanjing University, his alma mater, for a visit.
• He tours the campus with the current Principal, Lu, who praises Shen Qi's achievements and the university's inclusive philosophy.
• Shen Qi visits his old dormitory, finding it unchanged and his desk filled with pens as a tribute from fellow students.
• He reunites with his former roommate, Luo Ji, and learns about the legends and tributes left in his honor by fellow students.
• Shen Qi treats his former classmates to a graduation dinner, expressing his happiness for their futures.

Character Developments

• Shen Qi: Maintains his humility despite his achievements, values his university years, and cares for his former classmates' well-being.
• Luo Ji: Remains dedicated to his studies, shows excitement upon seeing Shen Qi, and provides insights into the campus culture.
• Principal Lu: Demonstrates pride in Shen Qi's accomplishments, embodies the university's inclusive spirit, and shares amusing anecdotes about the Goldbach Conjecture.
• Other former classmates: Pursue various paths after graduation, showing dedication to their chosen fields and contributing to society.

Significant Themes

• The power of education and intellectual pursuits in shaping individuals and society.
• Nostalgia and the importance of preserving and honoring one's past.
• The influence of legends and role models on younger generations.
• The value of camaraderie and shared experiences among peers.

Character Interactions

• Shen Qi and Principal Lu: Engage in a friendly and respectful conversation, with Principal Lu expressing admiration for Shen Qi's accomplishments.
• Shen Qi and Luo Ji: Reunite warmly, reminisce about their university years, and discuss their respective academic paths.
• Shen Qi and former classmates: Catch up, express happiness for each other's futures, and share a graduation dinner together.

Key Plot Points and Events

• Shen Qi returns to Yanjing University for his graduation dinner.
• Nine of his male classmates bring their girlfriends, indicating a high partner-finding rate among math majors.
• Shen Qi gives a speech at Yanjing University, discussing the Riemann Hypothesis and its implications.

Character Developments

• Shen Qi: Reveals his mischievous idea of wanting to overturn the Riemann Hypothesis for fame, but ultimately proves it true.
• Luo Ji's girlfriend, Lingling: Shows boldness and admiration for talented men, toasts Shen Qi.
• Other classmates: Display camaraderie, cry together at the dinner, and support Shen Qi's speech.

Significant Themes

• Friendship and camaraderie among classmates.
• The importance of mathematics and its impact on human civilization.
• The tension between theoretical research and practical application.

Character Interactions

• Shen Qi interacts with his classmates, their partners, and the audience at his speech.
• Luo Ji and Lingling have a playful interaction regarding Shen Qi's safety.
• The audience at Shen Qi's speech engages with his ideas and responds enthusiastically.

Key Plot Points and Events

• Shen Qi, a prodigy mathematician, is invited back to Yanjing University by Dean Wang and other professors.
• Shen Qi is offered a direct professorship and recognition as an 'Outstanding Youth' if he returns to China through the 'Thousand Talents Program.'
• A special seminar is held to discuss Shen Qi's proof of the Riemann Hypothesis and the RT Third Expression.
• Academician Lin presents a potential solution to the RT Third Expression, but it's later dismissed by Shen Qi.

Character Developments

• Shen Qi: Confirms his intention to return to China but not immediately. He remains humble and eager to learn from more experienced mathematicians.
• Professor Nian Ruiming: Recognizes Shen Qi as a peer and acknowledges his impressive achievements.
• Dean Wang: Eager to have Shen Qi return to Yanjing University, offers him a direct professorship and generous treatment.
• Academician Lin: Shows affection towards Shen Qi, shares his insights on the RT Third Expression, and encourages Shen Qi's spirit of doubt.

Significant Themes

• The importance of returning to one's roots and contributing to one's home country (China).
• The value of humility and continuous learning in the academic world.
• The collaborative nature of mathematical research and the importance of sharing ideas.

Character Interactions

• Shen Qi interacts with Dean Wang, Professor Nian, Professor Sun, Professor Lu, and several academicians, discussing his potential return to China and the RT Third Expression.
• Dean Wang and Academician Lin have a friendly argument about Academician Lin's chess habits and mathematical insights.
• Academician Lin shares his personal opinion on the RT Third Expression with Shen Qi, encouraging him to continue exploring the problem.

Key Plot Points and Events

• Shen Qi gains insights from Yanjing University's mathematicians.
• The Chinese Mathematical Society hosts an event with award ceremonies, lectures, and academic discussions.
• Shen Qi wins the "Zhong Jiaqing Mathematics Prize Gold Medal" due to his exceptional achievements, including proving the Riemann Hypothesis.
• Shen Qi is nominated for the Fields Medal, with a presentation slot secured at the International Congress of Mathematicians.
• Various mathematical organizations award Shen Qi to capitalize on his potential Fields Medal win.

Character Developments

• Shen Qi's reputation and achievements grow, making him a strong contender for the Fields Medal.
• Shen Qi remains humble and dedicated to his work, expressing a desire to conduct interviews in his native language.

Significant Themes

• The pursuit of excellence in mathematics and the recognition it brings.
• The global nature of mathematical achievements and the international community's interest in Shen Qi's work.
• The strategic mobilization of resources to support young mathematicians in their quest for prestigious awards.

Character Interactions

• Shen Qi interacts with the Chinese Mathematical Society, receiving awards and recognition.
• Shen Qi is interviewed by international media, including CCTV Radio's English channel and mainstream Western media like CNN and the Discovery Channel.
• Shen Qi is mentioned alongside three other Chinese mathematicians (Gong Changwei, Yun Wei, and Xu Yang) as potential Fields Medal contenders, highlighting the competition among them.

Upcoming Events

• The International Congress of Mathematicians in October, where Shen Qi will present and potentially win the Fields Medal.
• The possibility of Shen Qi winning the Ramanujan Prize, further boosting his chances for the Fields Medal.

Key Plot Points and Events

• Shen Qi learns he's a candidate for the Ramanujan Prize, an A-class award in the real world.
• He meets with old high school friends Xu Rui and Chen Xiaoting for dinner.
• Shen Qi learns about Xu Rui's injury and weight gain, and Chen Xiaoting's single status.
• Shen Qi gives a lecture at Shuimu University, where he's welcomed as a renowned international mathematician.

Character Developments

• Shen Qi: Confident about his potential to win the Ramanujan Prize, maintains a positive attitude.
• Xu Rui: Struggles with weight gain after retiring from competitive sports, accepts his new role as a coach, and is about to get married.
• Chen Xiaoting: Beautiful and successful in her career, remains single with high standards for a partner.

Significant Themes

• The pressure and expectations of competition, both in academics and sports.
• The importance of alliances and cooperation in achieving common goals.
• The changes in one's life and body, and accepting them.

Character Interactions

• Shen Qi, Xu Rui, and Chen Xiaoting reminisce about old times, joke around, and catch up on each other's lives.
• Shen Qi and Xu Rui discuss the latter's weight gain and future plans.
• Shen Qi, Xu Rui, and Chen Xiaoting discuss their relationship status and make a pact to bring their significant others to their next gathering.
• Shen Qi gives a lecture at Shuimu University, highlighting his status as a renowned mathematician.

Key Plot Points and Events

• Shen Qi, a 22-year-old mathematician who proved the Riemann Hypothesis, gives a lecture at Shuimu University.
• He emphasizes the importance of cooperation and hints at a potential alliance between Shuimu and Yanjing universities.
• Shen Qi's lecture is well-received, and he gains fans among the students.
• After the lecture, a student named Hu Congming seeks Shen Qi's autograph and engages in a brief mathematical discussion with him.
• Shen Qi then leaves for the U.S., bringing snacks for Ou Ye, but the pretzel twists are confiscated by customs.
• In the U.S., Shen Qi and Ou Ye discuss their ongoing research on the RT Third Expression.

Character Developments

• Shen Qi: He demonstrates maturity and humility by not boasting about Yanjing University during his lecture at Shuimu. He shows kindness and sentimentality by wanting to help Shuimu, his alma mater.
• Hu Congming: A graduate student from Shuimu's School of Mathematics, he shows initiative and mathematical insight by engaging Shen Qi in a brief discussion.
• Ou Ye: She has made progress in her research on the RT Third Expression, deriving a corollary concerning the Function log Zeta(s). She shows enthusiasm and dedication to her work.

Significant Themes

• Cooperation: Shen Qi emphasizes the importance of cooperation in his lecture, hinting at a potential alliance between universities.
• Repaying Kindness: Shen Qi wants to help Shuimu, his alma mater, as a way of repaying the kindness he received there.
• Academic Responsibility: Shen Qi fulfills his social and academic responsibilities by participating in seminars and teaching mathematics at a middle school.

Character Interactions

• Shen Qi and the Shuimu Students: Shen Qi interacts positively with the Shuimu students, showing respect and kindness towards them.
• Shen Qi and Hu Congming: They have a brief mathematical discussion, with Hu Congming showing insight and Shen Qi expressing pleasure in their interaction.
• Shen Qi and Ou Ye: They discuss their ongoing research, with Shen Qi providing guidance and Ou Ye showing enthusiasm and dedication.

Key Plot Points and Events

• The International Congress of Mathematicians (ICM) is approaching, with the Fields Medal winners to be announced on the ninth day.
• Professor Faltings presents a mathematical analysis predicting the winners of the Fields Medal, favoring Simon Blundell (65.76%) and Joseph Ayub (57.35%) as almost certain winners.
• Shen Qi asks for the third-ranked mathematician, revealed to be Jordi Williamson with a 48.03% chance.

Character Developments

• Shen Qi: Returns to Princeton, remains silent about his own chances, and shows curiosity about the third-ranked mathematician.
• Professor Faltings: Presents a mathematical analysis of the Fields Medal winners, showing his expertise and influence in the mathematical community.

Significant Themes

• Seniority and Recognition: Faltings' prediction system favors older, more senior mathematicians, raising questions about fairness and opportunity for younger mathematicians.
• Mathematical Excellence: The chapter highlights the exceptional achievements of the mathematicians under consideration for the Fields Medal.

Character Interactions

• Faltings and Shen Qi: Faltings presents his analysis, while Shen Qi listens and asks about the third-ranked mathematician, showing interest but not revealing his own thoughts.
• Faltings and Feierman: Faltings presents his analysis, and Feierman questions and challenges Faltings' methods, showing a different perspective on the prediction system.
• The Princeton Mathematics Department: The coffee hour discussion reveals the department's insider knowledge, opinions, and predictions about the Fields Medal winners.

Key Plot Points and Events

• Professor Faltings reveals his top four predictions for the Fields Medal, including Sophia Morel, a Frenchwoman specializing in Algebraic Geometry.
• He predicts Peter Schultz, a German mathematician, as the fifth, despite widespread belief he should be in the top four.
• Faltings predicts Shen Qi, the 'China Key', as sixth, with a 34.24% chance of winning.
• The department believes Shen Qi's chances are higher than Faltings' due to his unique research field and achievements.
• The competitive landscape is complex, with European schools divided and strong national rivalries.
• Shen Qi and Director Feierman decide to release the basic framework of the RT Third Expression to build momentum.
• Shen Qi is expected to win the Ramanujan Prize and potentially the Steele Prize before the International Congress of Mathematicians.

Character Developments

• Shen Qi shows curiosity and confidence in his abilities, asking for his rank and probability of winning.
• Professor Faltings demonstrates objectivity and fairness in his predictions, considering academic aspects, seniority, and schools of thought.
• Director Feierman shows support for Shen Qi, offering to handle momentum building while Shen Qi focuses on academics.

Significant Themes

• Competition and rivalry in the mathematical community, both within and between countries.
• The importance of momentum building and public relations in the academic world.
• The influence of national identity and expectations on a mathematician's career.

Character Interactions

• Shen Qi interacts with Professor Faltings, seeking clarification on his prediction ranking.
• Shen Qi and Director Feierman discuss strategy, deciding to release the RT Third Expression's basic framework.
• Shen Qi convenes a meeting with his team to plan their next steps, highlighting their urgency and heavy task.

Key Plot Points and Events

• Shen Qi leads the "RT Third Expression Project" with Professor Muller as his deputy.
• Mary makes significant progress in her research, surpassing Ou Ye.
• Mary reveals she's legally still married to Pete Schultz, her former husband and a rival mathematician.
• Pete Schultz wins the Keith Prize and makes significant strides in proving the Hodge conjecture, gaining widespread recognition and support for the Fields Medal.
• Shen Qi's team studies Schultz's latest work, acknowledging its potential to prove the Hodge conjecture within three years.

Character Developments

• Shen Qi: Shows concern for his team members' personal lives while maintaining a competitive spirit against Schultz.
• Mary: Reveals her determination to defeat her former husband, Pete Schultz, in the mathematical field.
• Pete Schultz: Gains recognition and support for the Fields Medal after winning the Keith Prize and making progress on the Hodge conjecture.

Significant Themes

• Competition and rivalry in the mathematical community.
• The pursuit of the Fields Medal and other prestigious awards.
• The exploration of the Millennium Prize Problems.

Character Interactions

• Shen Qi and Mary discuss her divorce and her desire to defeat Schultz.
• Shen Qi's team studies Schultz's work, acknowledging its significance.
• The mathematical community reacts to Schultz's achievements, building momentum for the Fields Medal announcement.

Key Plot Points and Events

• Shen Qi, Muller, and Faltings discuss Schultz's genius and divorce.
• Shen Qi picks up Ou Ye and buys her a Bentley SUV.
• Shen Qi leads a team meeting to discuss the RT Third Expression project, assigning tasks to each member.

Character Developments

• Shen Qi shows maturity and leadership in managing the team and project.
• Ou Ye demonstrates her independence by wanting to buy and drive her own car.
• Mary shows concern about Ou Ye's ability to handle her assigned path.

Significant Themes

• The pressure and challenges of leading a high-end Math team.
• The importance of teamwork and resource integration in academic research.
• The personal lives and relationships of the characters intertwining with their academic pursuits.

Character Interactions

• Shen Qi and Ou Ye's relationship deepens, with Shen Qi showing affection and care for Ou Ye.
• Shen Qi, Muller, and Faltings share insights about Schultz's character and divorce.
• Mary and Ou Ye observe each other, with Mary showing some doubt about Ou Ye's capabilities.

Key Plot Points and Events

• Ou Ye spends the night at Shen Qi's apartment and returns to New York with him the next day.
• Shen Qi reveals that Mary's husband, Peter Schultz, is abusive and they're going through a divorce.
• Shen Qi and Ou Ye purchase a Bentley SUV together.
• Shen Qi travels to Trieste, Italy, for the Ramanujan Prize award ceremony and academic conference.
• Shen Qi wins the Ramanujan Prize, becoming the youngest recipient ever.
• Andrew Wiles, who presented Shen Qi with the IMO gold medal five years ago, presents him with the Ramanujan Prize.

Character Developments

• Shen Qi: Confirmed as a devoted and trustworthy boyfriend, he wins the Ramanujan Prize, further cementing his status as a mathematical prodigy.
• Ou Ye: Shows concern for Mary's situation and trust in Shen Qi's character.
• Andrew Wiles: Aged and impressed by Shen Qi's achievements, he looks forward to Shen Qi's keynote presentation on the Riemann Theorem.

Significant Themes

• Trust and faithfulness in relationships (Ou Ye's concern for Mary and her trust in Shen Qi).
• Mathematical prowess and recognition (Shen Qi's win of the Ramanujan Prize).
• Aging and the passage of time (Wiles's aging and Shen Qi's growth over five years).

Character Interactions

• Shen Qi and Ou Ye: Discuss Mary's situation, purchase a car together, and share a moment of connection.
• Shen Qi and Andrew Wiles: Reunite after five years, with Wiles presenting Shen Qi with the Ramanujan Prize and expressing excitement for Shen Qi's keynote presentation.