Chapter Summaries

Key Plot Points and Events

• Shen Qi returns to Hong Kong after winning the Chern Prize in Mathematics.
• He attends a banquet with Ou Ye, hosted by his father, Shen Zhishan.
• Shen Zhishan gives Ou Ye a red envelope, signifying his approval of their relationship.
• Shen Qi departs for the United States, with friends and family seeing him off at the airport.

Character Developments

• Shen Qi: Confident in his career and relationship, he formally introduces Ou Ye to his father and expresses his commitment to their future.
• Ou Ye: She handles her first meeting with Shen Qi's father gracefully, showing maturity and respect, and receives his approval.
• Shen Zhishan: He shows approval of Ou Ye, finding her quiet, gentle, and well-mannered.

Significant Themes

• Parental Approval: The meeting between Ou Ye and Shen Zhishan focuses on gaining his approval for their relationship.
• Career Ambition: Shen Qi's career is thriving, and he encourages Ou Ye to strive for success as well.
• Long-Distance Relationship: The chapter highlights the challenges and pressures of maintaining a relationship when one partner is studying abroad.

Character Interactions

• Shen Qi and Ou Ye: They present a united front to Shen Zhishan, showing respect and affection for each other.
• Shen Qi and Shen Zhishan: Their relationship is warm and affectionate, with Shen Qi expressing his love and respect for his father.
• Ou Ye and Shen Zhishan: They interact politely and respectfully, with Shen Zhishan showing approval of Ou Ye's character and upbringing.

Key Plot Points and Events

• Zhou Yu'an scores 112 on the TOEFL, one point higher than Ou Ye, but his research experience is limited compared to Ou Ye.
• Shen Qi returns to Princeton, taking 16 courses in his first semester, completing 10 and earning 150 credits, leaving a deficit of 75 credits for the master's degree requirement of 225 credits.
• Shen Qi's paper on the Riemann zeta function ζ(2n+1) is under review at the Annals of Mathematics.
• Shen Qi makes significant progress on the 'Orbifold Fundamental Group to Characterize Symplectic Orbifold Groupoid' topic but struggles with a crucial breakthrough.
• Shen Qi seeks advice from Professor Muller about his orbifold project. Professor Muller mentions that Shen Qi's paper on the Riemann zeta function ζ(2n+1) has been rejected and requires major revisions.

Character Developments

• Zhou Yu'an is under pressure to match Ou Ye's academic achievements and sees Shen Qi as a role model.
• Shen Qi is highly motivated and dedicated to his academic pursuits, working tirelessly and making significant progress in his research.

Significant Themes

• Academic competition and the pressure to excel.
• The relentless pursuit of knowledge and academic achievements.
• The struggle and dedication required for groundbreaking research.

Character Interactions

• Zhou Yu'an and Ou Ye are in academic competition, with Zhou Yu'an feeling the pressure to match Ou Ye's achievements.
• Shen Qi seeks advice from Professor Muller regarding his orbifold project, showing respect for his mentor's knowledge and experience.
• Shen Qi and Mary are co-authors of a paper on the Riemann zeta function ζ(2n+1), demonstrating collaboration in academic research.

Key Plot Points and Events

• Professor Muller assigns Shen Qi and Mary to focus on revising "The Problem of the Riemann Zeta Function ζ(2n+1)".
• Jonas suggests directly proving Riemann's fifth conjecture (Riemann Hypothesis), disagreeing with Professor Muller's step-by-step approach.
• Shen Qi and Mary side with Professor Muller, while Jonas remains unconvinced.
• Professor Muller and Shen Qi discuss orbifolds, and Muller encourages Shen Qi to socialize more and meet young women.

Character Developments

• Shen Qi: Shows pragmatism and caution regarding the Riemann Hypothesis, and demonstrates his dedication to learning from Professor Muller.
• Jonas: Reveals his serious and stubborn side when discussing academic matters, displaying his ambition to directly prove the Riemann Hypothesis.
• Professor Muller: Shares his academic views and life experiences with Shen Qi, showing his mentoring side.

Significant Themes

• The Riemann Hypothesis: The chapter explores different approaches to proving this conjecture, highlighting the debate between a step-by-step method (Hadamard system) and a direct, radical approach (Hardy system).
• Mentorship: Professor Muller's guidance and sharing of knowledge with Shen Qi emphasize the importance of mentorship in academic growth.

Character Interactions

• Shen Qi and Jonas: Their differing views on the Riemann Hypothesis lead to a tense discussion, revealing Jonas's ambition and Shen Qi's pragmatism.
• Shen Qi and Professor Muller: Their conversation about orbifolds and Professor Muller's encouragement for Shen Qi to socialize demonstrate the mentoring relationship between them.
• Shen Qi and Ou Ye: Their phone conversation shows their affection for each other and Ou Ye's struggle with her health condition.

Key Plot Points and Events

• Shen Qi and Mary begin revising their paper on the Riemann Zeta Function after receiving harsh feedback.
• Shen Qi presents a new approach using series, which Mary initially doubts but eventually agrees to pursue.
• Their collaboration starts off poorly, with constant arguments and disagreements over their work.

Character Developments

• Shen Qi remains optimistic despite setbacks and is determined to succeed, even if it means working alone.
• Mary struggles with self-doubt and insecurities, leading to increased irritability and defensiveness.
• Professor Muller advises Shen Qi on the importance of teamwork and tolerance, helping Shen Qi understand Mary's perspective better.

Significant Themes

• The pressure of high expectations and the stress of revising a rejected paper lead to tension and conflict between Shen Qi and Mary.
• The importance of teamwork, tolerance, and understanding others' perspectives is highlighted through Professor Muller's advice to Shen Qi.

Character Interactions

• Shen Qi and Mary's collaboration is marked by constant arguments and disagreements, testing their ability to work together.
• Shen Qi seeks Professor Muller's advice, leading to a better understanding of Mary's character and the value of tolerance in teamwork.
• Shen Qi and Mary's relationship remains strained, but Shen Qi decides to try and reconcile with Mary, showing a willingness to learn and grow.

Key Plot Points and Events

• Shen Qi and Mary initially agree to collaborate on the Riemann Zeta Function problem but soon clash due to differing opinions and stubbornness.
• Shen Qi starts working on a new project, "Characterization of Symplectic Orbifold Groupoids," independently.
• Shen Qi shares his work on the Riemann Zeta Function with Ou Ye, who finds flaws in his approach.
• Shen Qi struggles with the criticism, refines his method, and seeks Professor Muller's opinion.

Character Developments

• Shen Qi: Initially open to collaboration, he becomes stubborn and defensive when criticized. He struggles with self-doubt but ultimately refines his work.
• Mary: Remains stubborn and unwilling to compromise, leading to the breakdown of her collaboration with Shen Qi.
• Ou Ye: Shows intellectual growth by identifying flaws in Shen Qi's work and providing constructive feedback.

Significant Themes

• The importance of collaboration vs. individualism in academic research.
• The struggle with self-doubt and the process of refining one's work.
• The tension between personal relationships (Shen Qi and Ou Ye) and academic pursuits.

Character Interactions

• Shen Qi and Mary: Their initial attempt at collaboration fails due to their stubbornness and differing opinions.
• Shen Qi and Ou Ye: Despite the distance, they maintain a close academic and personal relationship. Ou Ye's feedback challenges Shen Qi's perspective and helps him grow.
• Shen Qi and Professor Muller: Muller acts as a mentor, offering guidance and reviewing Shen Qi's work.

Key Plot Points and Events

• Shen Qi's paper on the Riemann zeta function ζ(2n+1) is rejected by Professor Muller, who suggests recalculating the uniform convergence.
• Muller holds onto Shen Qi's orbifold paper for further study.
• Shen Qi resubmits his revised paper on the Riemann zeta function to the Annals of Mathematics.
• He also submits a paper on orbifolds to the Journal of Mathematics.
• Shen Qi intensively studies the Riemann Hypothesis (RH), feeling physically unwell during his research.
• The Annals of Mathematics rejects Shen Qi's paper again, leading to his serious illness.

Character Developments

• Shen Qi becomes more determined to prove the RH despite facing rejections and physical discomfort.
• Professor Muller remains cautious and critical of Shen Qi's work, but also supportive, offering to pay publication fees if the Annals accepts his paper.

Significant Themes

• Perseverance: Shen Qi's unyielding pursuit of proving the RH, despite facing rejections and physical ailments.
• The Power of Mathematics: The captivating and valuable nature of the RH, which has fascinated many mathematicians for over a century.
• Mentorship and Criticism: Professor Muller's role in guiding and challenging Shen Qi's work.

Character Interactions

• Shen Qi and Professor Muller have a professional relationship, with Muller providing feedback and guidance on Shen Qi's papers.
• Shen Qi's interactions with the mathematical community are shown through his paper submissions and rejections, highlighting the competitive and rigorous nature of academic mathematics.

Key Plot Points and Events

• Shen Qi recovers from his mental breakdown, visited by Professor Muller, Jonas, and Mary.
• Shen Qi decides to focus on basic research instead of forcing the Riemann Hypothesis.
• He adjusts his mindset, attends classes, gets a driver's license, and travels locally.
• Shen Qi's paper is rejected, but he remains calm and seeks Professor Muller's advice.
• He submits two Group Theory papers to American Math journals and wins the Ford Prize.

Character Developments

• Shen Qi learns to be more down-to-earth and patient, focusing on basic research.
• He acknowledges his limitations and seeks advice, showing humility and growth.
• Shen Qi starts to appreciate the process of research and life, letting go of his fixation on quick success.

Significant Themes

• Patience and Persistence: Shen Qi learns the importance of patience and persistence in research and life.
• Humility: He acknowledges his limitations and seeks advice, showing humility.
• Process vs. Outcome: Shen Qi begins to appreciate the process of research and life, not just the results.

Character Interactions

• Shen Qi and Professor Muller: They maintain a mentor-mentee relationship, with Professor Muller guiding Shen Qi's research and career.
• Shen Qi and Jonas/Mary: They show concern for Shen Qi's well-being, with Jonas encouraging him to enjoy life and Mary emphasizing the importance of health.

Key Plot Points and Events

• Shen Qi receives the Ramanujan Prize announcement, knowing it's unlikely he'll get the Fields Medal next year.
• He decides to prove the Riemann Hypothesis (RH) to earn the Fields Medal, understanding the verification process takes several years.
• Shen Qi publishes two group theory papers in prestigious journals, earning him 205,300 scholar points and upgrading his Math level to Master (Level 11).
• He completes his Master's degree at Princeton in just two semesters, earning 800,000 scholar points for tying the fastest record.

Character Developments

• Shen Qi shows ambition and impatience in proving the RH to secure the Fields Medal.
• He demonstrates academic prowess by publishing papers in high-impact journals and earning his Master's degree quickly.

Significant Themes

• Ambition and Impatience: Shen Qi's desire for academic recognition (Fields Medal) leads him to rush the RH proof.
• Academic Pursuits: The chapter emphasizes Shen Qi's mathematical achievements and his progress towards his academic goals.

Character Interactions

• Shen Qi interacts with Feierman, the head of the Mathematics Department, who hands him his Master's degree certificate.
• He shares his achievement with Zhou Yu'an, who also received an offer from Princeton, and asks about Ou Ye's status.

Key Plot Points and Events

• Ou Ye's interview for Princeton goes poorly, leading to a low interview score.
• Shen Qi devises a plan for Ou Ye to first study at Columbia University under Professor Gong Changwei, then transfer to Princeton.
• Shen Qi discovers an unproven theorem, the "Muller-Manning Theorem," and decides to attempt its proof with Professor Muller.

Character Developments

• Ou Ye: Struggles with interviews due to lack of social experience; relies on Shen Qi for guidance.
• Shen Qi: Demonstrates strategic thinking and problem-solving skills in handling Ou Ye's situation; shows curiosity and initiative in mathematical research.
• Professor Muller: Admits past mistakes in the "Muller-Manning Theorem" and agrees to collaborate with Shen Qi on its proof.

Significant Themes

• The importance of interview skills in academic admissions.
• The value of perseverance and initiative in mathematical research.
• The significance of collaboration and mentorship in academic growth.

Character Interactions

• Shen Qi and Ou Ye: Shen Qi supports and guides Ou Ye through her academic and personal challenges.
• Shen Qi and Professor Muller: They collaborate on mathematical research, with Shen Qi showing respect for Professor Muller's academic standing.
• Shen Qi and Gong Changwei: Shen Qi seeks Professor Changwei's help for Ou Ye's admission to Columbia University.

Key Plot Points and Events

• Shen Qi, a high school student interested in math history, asks Professor Muller about Tony Manning, a mathematician he's never heard of.
• Muller recounts his past with Manning in the 1970s and 80s at Princeton, where they collaborated on mathematical projects.
• Manning develops a gambling addiction, leading to a large debt. Muller pays off Manning's debt, saving his life.
• Muller discovers Manning and his wife in a compromising situation. Heartbroken, Muller returns to Germany.
• Muller and Shen Qi collaborate to revise and prove the "Muller-Manning Theorem," which has been unrecognized for over thirty years due to flawed proof.

Character Developments

• Muller: Recalls his past with Manning, revealing his kindness, academic achievements, and heartbreak. He shows grief and indignation but maintains composure. He warns Shen Qi against gambling.
• Shen Qi: Shows interest in math history and dedication to his academic pursuits. He sympathizes with Muller's past and reassures him of his commitment to their collaborative work.

Significant Themes

• Betrayal and Trust: Muller's trust in Manning is betrayed, leading to heartbreak and a change in Muller's life trajectory.
• Redemption and Forgiveness: Muller doesn't acknowledge Manning as his student, but he's willing to work with Shen Qi, showing a desire for redemption and moving on.
• History and Progress: The chapter explores the history of math and the progress made over time, with Shen Qi aiming to write an accessible history of math.

Character Interactions

• Muller and Shen Qi: They share a mentor-mentee relationship, with Muller recounting his past to Shen Qi, showing trust and openness. They collaborate on mathematical work, with Shen Qi showing dedication and initiative.
• Muller, Manning, and Muller's Ex-Wife: Their interactions reveal betrayal, heartbreak, and the consequences of unchecked vices.

Key Plot Points and Events

• Shen Qi and Professor Muller collaborate on proving the "Muller-Shen Theorem."
• Shen Qi prepares to teach the recitation class for Non-Euclidean Geometry.
• Shen Qi leads a recitation class for second-year undergraduate students, engaging them in a discussion about the history of mathematics before delving into the course material.

Character Developments

• Shen Qi: Demonstrates his teaching skills, engaging students and making the class interactive. He shows respect for his mentor by insisting on putting his surname last in the theorem's name.
• Professor Muller: Treats Shen Qi as an equal academic partner, showing respect and trust in his abilities. He is hands-on and eager to complete the theorem they're working on together.

Significant Themes

• Mentorship and collaboration: Muller and Shen Qi work together as equals, reflecting a positive mentor-mentee relationship.
• Respect for history and foundations: Shen Qi emphasizes the importance of understanding the history of mathematics to learn it well.
• Engagement and interaction: Shen Qi's teaching style encourages student participation and engagement.

Character Interactions

• Shen Qi and Professor Muller: They communicate smoothly and respectfully, working together on the theorem and their respective tasks.
• Shen Qi and the students: Shen Qi engages the students in a friendly and interactive way, using their curiosity and enthusiasm to create a dynamic learning environment.

Key Plot Points and Events

• The chapter introduces the Italian Fibonacci, who translated mathematical works from various cultures, reviving European mathematics and sparking a golden age that continues to this day.
• Shen Qi, a 21-year-old teaching assistant, leads a tutorial on Non-Euclidean Geometry, involving a Q&A session on the First Mathematical Crisis with student Luca Filiberti.
• Shen Qi tests each student's understanding of the differences between Euclidean and Non-Euclidean geometry, with students Luca and Jack Ma performing exceptionally well.

Character Developments

• Shen Qi demonstrates his teaching style: humorous, flexible, and engaging, connecting with students and creating a positive learning environment.
• Luca Filiberti shows his knowledge of Math history and acting skills, earning Shen Qi's praise.
• Jack Ma, an Asian American student, exhibits a deep understanding of the topic and American cultural influences.

Significant Themes

• The global exchange of knowledge and its impact on the advancement of mathematics.
• The importance of understanding and applying mathematical concepts creatively and intuitively.
• The value of passionate discussion and diverse opinions in learning and problem-solving.

Character Interactions

• Shen Qi interacts with students through Q&A sessions, testing their knowledge and encouraging creative thinking.
• Students engage with each other and Shen Qi, sharing their insights and learning from one another.
• Shen Qi shows favor to high-performing students like Luca and Jack Ma, offering praise and encouragement.

Key Plot Points and Events

• Shen Qi, a teaching assistant, lectures on Euclid's "Elements" and the debatable Euclid's Fifth Postulate.
• He introduces Non-Euclidean Geometry, focusing on Lobachevskian and Riemannian geometries.
• Shen Qi assigns a homework problem involving the Eiffel Tower and its reflection in a curved space.

Character Developments

• Shen Qi demonstrates his profound mathematical knowledge and effective teaching skills, earning respect from his students.
• Students like Luca and Jack Ma show their mathematical talents and understanding.

Significant Themes

• The universality of Euclid's Fifth Postulate and the birth of Non-Euclidean Geometry.
• The intersection of mathematics, physics, and philosophy in understanding space curvature.

Character Interactions

• Shen Qi interacts with his students, engaging them in mathematical discussions and assignments.
• Shen Qi appreciates Luca's talent and Jack Ma's analytical skills, showing his admiration for their abilities.
• Students admire Shen Qi for his knowledge and teaching style, with some expressing envy over his social life.

Brief Overview

Shen Qi's recitation class focuses on the history and implications of Euclid's "Elements," leading to an exploration of Non-Euclidean Geometry. Through engaging discussions and an assigned problem, Shen Qi fosters a lively academic atmosphere, encouraging students to explore the complexities of curved spaces. The chapter highlights Shen Qi's teaching prowess and the students' growing mathematical understanding.

Key Plot Points and Events

• Shen Qi, a doctoral student at Princeton, interacts more with the 12 boys in his recitation class than with Professor Muller.
• Coffee is a significant part of the Princeton Math Department culture, fostering communication and teamwork.
• Shen Qi invites his students to his apartment for coffee, hosting John M. Grossston, Luca, and Jack Ma (Mark Jie) on different days.
• Shen Qi learns about Jack Ma's challenging background and offers him a problem to solve, rewarding him with $20.
• At the weekly coffee gathering, the topic of discussion is naming three Princeton mathematicians representing the smartest, most famous, and highest academic contributions.

Character Developments

• Shen Qi shows his appreciation for talent and takes an interest in Jack Ma's potential.
• Jack Ma (Mark Jie) is revealed to be from a poor Chinese immigrant family, struggling to make ends meet while studying at Princeton.
• Professor John Milnor is introduced as a legendary mathematician with the triple crown of F, W, and A prizes.

Significant Themes

• The importance of communication and teamwork in academia.
• The impact of wealth disparity on educational opportunities.
• The recognition and celebration of exceptional talent and academic achievements.

Character Interactions

• Shen Qi mentors and engages with his students, showing genuine interest in their backgrounds and abilities.
• Jack Ma (Mark Jie) and Shen Qi bond over their shared Chinese heritage and discuss their views on wealth and success.
• Princeton's professors and doctoral students engage in lively discussions during the weekly coffee gatherings.

Key Plot Points and Events

• John Nash is widely recognized as the greatest mathematician of their time.
• Professor John Milnor, another renowned mathematician, announces his retirement and plans to move to Sardinia, Italy.
• A Princeton-style tribute is held for Milnor, where colleagues give him pens as a sign of respect and recognition for his achievements.
• Milnor leaves Princeton, marking the end of an era.

Character Developments

• John Milnor: Retires after a prolific career, receiving a Princeton-style tribute for his contributions to mathematics.
• Shen Qi: Gains insight from Milnor's example, deciding to focus on proving theorems before developing a new theoretical system. He co-authors a preliminary draft of the "Muller-Shen Theorem" with Muller.

Significant Themes

• Achievement and Recognition: The chapter explores how mathematicians are recognized and celebrated for their contributions, with the Princeton-style tribute serving as a key example.
• Legacy and Retirement: Milnor's retirement marks the end of an era, highlighting the importance of his legacy and the impact of his work on the mathematical community.
• The Path to Innovation: Shen Qi reflects on the difficulty of innovating in mathematics and decides to focus on proving theorems before developing a new system.

Character Interactions

• Milnor and his Colleagues: Milnor interacts with his colleagues, who show their respect and admiration by giving him pens during the Princeton-style tribute.
• Shen Qi and Muller: Shen Qi and Muller collaborate on the "Muller-Shen Theorem," with Shen Qi gaining insight from Milnor's example and discussing their progress with Muller.

Key Plot Points and Events

• Shen Qi and Muller work on proving a theorem about Banach spaces.
• They decide to release a 'de-featured' version of their theorem first to cater to basic market demand, and later release a high-end version with a new name.
• Shen Qi submits their paper, titled "Problems on Concave Points in Banach Spaces and Strongly Smooth Spaces," to the Annals of Mathematics.
• Faltings, the editor-in-chief of Annals of Mathematics, discovers their paper on arXiv and praises their work.

Character Developments

• Shen Qi demonstrates mathematical prowess and strategic thinking in handling the theorem's release.
• Muller shows his expertise in mathematics and his playful side in interactions with Faltings.
• Faltings, as a renowned mathematician and journal editor, exhibits professionalism and a sense of responsibility towards the review process.

Significant Themes

• Mathematical Research: The chapter explores the process of mathematical research, from theorem proving to paper publication.
• Academic Publishing: It highlights the importance of academic journals and the review process in the mathematical community.
• Mentorship and Collaboration: Shen Qi's work with Muller showcases the collaborative nature of academic research.

Character Interactions

• Shen Qi and Muller work together, with Shen Qi driving the strategic decisions and Muller contributing his mathematical expertise.
• Muller and Faltings, both German and established mathematicians, engage in playful banter, showcasing their camaraderie and shared history.
• Faltings interacts with Shen Qi professionally, acknowledging his work and initiating the formal review process for their paper.

Key Plot Points and Events

• Faltings, an editor at the Annals of Mathematics, expedites the review process for a paper co-authored by Muller and Shen Qi.
• The paper, "On Concave Points in Banach Spaces and Smooth Spaces," is accepted within 8 days, reviewed by Andrew Saunders and Pierre Deligne.
• The theorem proved in the paper, the "Muller-Shen Theorem," is recognized by the International Mathematical Union (IMU) and published in the Annals of Mathematics.
• Shen Qi receives scholar points for publishing in a high-impact journal and having a theorem named after him.

Character Developments

• Shen Qi demonstrates his anxiety and excitement about the review process and recognition of his work.
• Faltings shows favoritism towards Muller and Shen Qi, expediting the review process and revealing the reviewers' identities.

Significant Themes

• Recognition and validation in the mathematical community.
• The importance of publishing in high-impact journals.
• The significance of having a theorem named after oneself.

Character Interactions

• Shen Qi interacts with Faltings, seeking information about the review process and expressing excitement upon learning the reviewers' identities.
• Shen Qi and Muller celebrate their achievement together, expressing admiration for each other's accomplishments.

Key Plot Points and Events

• Shen Qi publishes a paper in the Annals of Mathematics and names a theorem after himself, boosting his spirits.
• He discovers the "Muller-Manning Theorem" and decides to prove it, aiming to pass his PhD defense by next September.
• Shen Qi plans to make the most of his remaining ten months as a student by working on interesting projects.

Character Developments

• Shen Qi gains confidence and recognition due to his recent academic achievements.
• He becomes more familiar with the Mathematics Department's professors, including Fields Medalist Elon Lyndon Strauss.
• Shen Qi decides to write an academic monograph on Number Theory, initially planning a popular science book focused on its history.

Significant Themes

• The fleeting nature of youth and the desire to make the most of one's time.
• The importance of academic success in earning respect and attention in Princeton's Mathematics Department.
• The history and development of Number Theory as a branch of mathematics.

Character Interactions

• Shen Qi interacts with Professor Elon Lyndon Strauss, discussing Number Theory and Strauss's upcoming book.
• Shen Qi mentors his tutorial class, engaging them with historical questions related to mathematical symbols before delving into professional mathematical knowledge.

Key Plot Points and Events

• Shen Qi teaches a recitation class on non-Euclidean geometry, engaging students in lively discussions.
• He singles out four outstanding students—Luca, Ajie, Stephen, and John—for a private conversation about their interests and career goals.
• Shen Qi completes the proof of the "Muller-Shen Proximity Theorem" and submits it to Inventiones Mathematicae.
• He picks up Zhou Yu'an from New York JFK Airport for the Christmas holiday.

Character Developments

• Shen Qi: Proves the "Shen Proximity Theorem," demonstrates dedication to his work, and shows concern for the future of Princeton's academic integrity.
• Luca: Shows expertise in geometry and a penchant for wooing women.
• Ajie: Displays practicality and a focus on money-making subjects.
• Stephen: Pursues discrete mathematics and aspires to become a Silicon Valley IT engineer.
• John: Plans to study non-Euclidean geometry for credits and pursue game theory and financial mathematical analysis methods for his career.

Significant Themes

• The pursuit of knowledge vs. pragmatism and utilitarianism in academia.
• The potential decline of Princeton's academic standards due to a lack of young scholars dedicated to pure theory.
• The importance of mentoring and nurturing young talent.

Character Interactions

• Shen Qi interacts with his students, encouraging their academic pursuits and offering guidance.
• The four outstanding students discuss their interests and career goals with Shen Qi, revealing their unique personalities and aspirations.
• Shen Qi picks up Zhou Yu'an, indicating their close relationship and shared plans for the holiday.

Key Plot Points and Events

• Shen Qi picks up Zhou Yu'an at Kennedy Airport, New York.
• They drive to Princeton, with Shen Qi acting as tour guide.
• Zhou Yu'an starts his graduate studies at Princeton, while Shen Qi continues his doctoral studies.
• Shen Qi receives a WeChat message from Ou Ye, his girlfriend, who is about to arrive in the US.
• Shen Qi picks up Ou Ye at Kennedy Airport, expecting only her, but her brother, Old Ou, accompanies her.

Character Developments

• Zhou Yu'an: Shows excitement and curiosity about Princeton and the US, relying on Shen Qi for support.
• Shen Qi: Acts as a mentor and guide to Zhou Yu'an, showing concern for his well-being and independence.
• Ou Ye: Arrives in the US to pursue her academic goals, with her brother accompanying her.

Significant Themes

• Friendship and camaraderie between Shen Qi and Zhou Yu'an.
• The importance of independence and self-reliance, as emphasized by Shen Qi.
• The pursuit of academic excellence and personal growth.

Character Interactions

• Shen Qi and Zhou Yu'an: Reunite and catch up, with Shen Qi showing concern for Zhou Yu'an's well-being and encouraging his independence.
• Shen Qi and Ou Ye: Reunite after a long separation, with Shen Qi excitedly waiting for his girlfriend's arrival.
• Shen Qi's surprise at seeing Ou Ye's brother, Old Ou, accompanying her, highlighting the unexpected turn of events.