Chapter Summaries

Wang Qi settled into a routine in Divine Capital while repeatedly defeating Myriad Dharma Sect disciples who challenged him. Feng Luoyi then showed him Pang Jialai’s paper On Constructive Computation, revealing a new challenge to the Master of Computation’s approach.

• Wang Qi defeated another Myriad Dharma Sect True Disciple, though the opponent’s stronger Sword Qi eventually knocked the sword from his hand.
• Wang Qi spent the month working with Chen Feng and Chen Youjia, receiving guidance from Feng Luoyi, and training his cultivation and swordsmanship.
• Wang Qi continued defeating Myriad Dharma Sect challengers under Feng Luoyi’s orders, building a reputation as the disciples fled from their bouts.
• Feng Luoyi showed Wang Qi Pang Jialai’s paper On Constructive Computation, and Wang Qi recognized it as a counterattack against the Master of Computation’s line and the Goting school.

Wang Qi recognized the Master of Calculation Pang Jialai’s new constructive algorithm as a major breakthrough that could redirect Divine Land mathematics toward practical applications. Feng Luoyi then confronted Wang Qi with Master Xi’s question about why he had abandoned finitism in his later research, leaving Wang Qi pressed to explain whether he had foreseen a dead end or concealed a discovery.

• Wang Qi studied Pang Jialai’s paper and realized its constructive algorithm surpassed the School of Separation in practical value.
• Wang Qi reflected on how Pang Jialai had reached the breakthrough despite the different course of mathematical history in the Divine Land.
• Feng Luoyi asked Wang Qi what he thought of the paper, and Wang Qi praised its importance for applied mathematics.
• Feng Luoyi explained that Master Xi felt blocked while pursuing completeness and asked why Wang Qi had shifted from finite methods to transfinite methods.
• Feng Luoyi asked whether Wang Qi had anticipated the impasse or was hiding a discovery.

Xiboche confronted the limits of his research against Master Pang’s new paper, then learned that Aike Man and Wang Qi had made rapid progress on arithmetic consistency using transfinite methods. When Feng Luoyi asked Wang Qi how he had found that path, Wang Qi feared revealing Gödel’s Incompleteness Theorems would destroy the School of Separation, but a sudden association gave him an idea.

• Xiboche told the Mathematicians to present their work and judged their results far weaker than Master Pang’s paper.
• Feng Luoyi asked Aike Man for his paper, and Aike Man submitted four papers coauthored with Wang Qi on the transfinite method.
• Xiboche praised the direction’s rapid progress and asked Feng Luoyi to find out how Wang Qi had conceived it.
• Wang Qi considered revealing Gödel’s Incompleteness Theorems, then rejected the idea because it could shatter the School of Separation.
• Wang Qi connected the Bourbaki school with Principia Mathematica and was struck by a flash of inspiration.

Wang Qi convinced Feng Luoyi that his work on completeness had grown from an ideal of unifying mathematics through structural methods. Xiboche decided to pursue Wang Qi’s approach for a month, while Wang Qi realized he had accidentally invited others to expect him to develop work he could not do.

• Wang Qi answered Feng Luoyi’s questions by presenting his goal of gathering mathematics into one discipline through structural methods.
• Feng Luoyi praised Wang Qi’s line of thought but remained uncertain about his approach to proving its foundations.
• After observing the exchange, Xiboche decided his group would pursue Wang Qi’s axiomatization approach for one month and promised to compensate him.
• Wang Qi panicked at his desk because he had directed attention toward Bourbaki-style work in fields he could not develop.

Wang Qi’s work fueled a mathematical revolution as the Gottingen Sect pursued formalizing all of mathematics, while he began receiving merit and unknowingly gained Feng Luoyi’s protection. At a Myriad Dharma Sect council meeting, the Grandmasters debated giving Wang Qi the Daoist Artifact Award, but one Grandmaster objected.

• The Gottingen Sect announced its plan to reconstruct mathematics as a unified formal system, and Pang Jialai’s papers let him contend with the sect’s research.
• Wang Qi became a recurring name in the debate, while his pseudonym, “Anonymous,” appeared on Gottingen Sect papers and earned him merit.
• Feng Luoyi learned that the Gottingen Sect would pursue the Bourbaki school’s ideas and quietly decided to protect and guide Wang Qi.
• Wang Qi received his first installment of merit and planned a prosperous New Year celebration.
• Divine Lord Bai Ze opened a Myriad Dharma Sect council meeting and raised Wang Qi’s nomination for the Daoist Artifact Award.
• Bo Yage supported the award, but an unnamed Grandmaster stood and objected.

Divine Lord Bai Ze defended Wang Qi’s qualifications for the Daoist Artifact Prize and brought the dispute over the Math Sovereign and Math Master to a decision. He told Su Junyu that Wang Qi had won at sixteen, while Pang Jialai would voluntarily return to his post and withdraw from the Divine Land’s mathematical debates for three years.

• Zhang Jinsong objected to Wang Qi receiving the prize, questioning the practical value of his Law of Completeness and his youth.
• Bo Yage defended the mathematical logic behind Wang Qi’s work, and Divine Lord Bai Ze rejected the objections and asserted his impartiality.
• Divine Lord Bai Ze shifted the meeting to deciding the positions of the Math Sovereign and the Math Master.
• Su Junyu waited outside the council hall as snow began to fall, then asked Divine Lord Bai Ze for the outcome.
• Divine Lord Bai Ze told Su Junyu that Pang Jialai would return to his post and avoid the Divine Land and foundational mathematics debates for three years.
• Divine Lord Bai Ze revealed that Wang Qi had won the Daoist Artifact Prize, making him the youngest winner in the history of the Divine Land.

As the year-end celebrations filled Divine Capital, Wang Qi realized that he had become unusually idle and showed Chen Youjia the artifact he had been refining. After joining Chen Feng and his colleagues for a meal, Wang Qi came up with a new story idea for Chen Youjia.

• Wang Qi left Chen Feng's laboratory and reflected briefly on his lingering sense of estrangement during the New Year season.
• Chen Youjia arrived with snacks, noticed Wang Qi had been idle, and examined his belt-buckle computing artifact and Telepathy Bottle.
• Chen Feng welcomed his subordinates and the children who had brought him year-end gifts, then invited Wang Qi and Chen Youjia to eat.
• Wang Qi teased Chen Feng about his affection for children, and Chen Feng defended his teaching hobby as a source of happiness and research efficiency.
• Wang Qi told Chen Youjia that he had another story for her, about a Modern Method preacher during the war between the Ancient Method and Modern Method.

Wang Qi told the Sky Spirit Ridge disciples a science-fiction story that drew mixed reactions, then learned Chen Feng wanted him to teach children in a village as part of a free school. Wang Qi reluctantly accepted after Chen Feng mentioned girls with catlike features, and Chen Feng agreed to apply for the assignment.

• Wang Qi finished his interstellar-war story, and Chen Youjia called it wondrous before leaving.
• An outer disciple questioned the story’s scale, and the cultivators debated whether the Immortal Heaven had a Star Sea.
• Chen Feng teased Wang Qi about tailoring stories to impress Chen Youjia and revealed that she had a poor relationship with her parents.
• Chen Feng asked Wang Qi to teach at a village school, explaining that teaching children served his pursuit of the Dao.
• Wang Qi resisted until Chen Feng mentioned little girls who went meow-meow, then agreed to take the job.
• Chen Feng said he would apply to the Immortal Alliance for the assignment and reminded Wang Qi to collect data.

Wang Qi received an invitation to the Feast of Completed Artifacts, where he might receive the Daoist Artifact Prize, and chose Huangfu Lian and Mo Zhenzhen as his companions. The three set off by spirit vessel for Fusang, with Wang Qi anticipating the journey.

• Liu Yunxiang presented Wang Qi with an unopened invitation from the Thousand Machines Pavilion to the Feast of Completed Artifacts.
• Wang Qi told the Myriad Dharma Sect disciples that he thought his chances of winning the Daoist Artifact Prize were fifty-fifty, and the invitation passed around the courtyard.
• Wang Qi asked Chen Feng and Chen Youjia to accompany him, but both declined because they wanted to avoid trouble and pressure from the sect.
• Wang Qi chose Huangfu Lian and Mo Zhenzhen as his two companions for the trip.
• The Immortal Alliance sent a spirit vessel, and Wang Qi, Huangfu Lian, and Mo Zhenzhen departed the Divine Capital for Fusang.

Wang Qi, Huangfu Lian, and Mo Zhenzhen arrived in Fusang and met Wu Chengdao, Thousand Machines Pavilion’s foremost True Disciple, who escorted them toward the sect in a Mechanism Beast. Wu Chengdao explained that Wang Qi’s Law of Completeness could greatly improve computational artifacts, leaving Huangfu Lian to reconsider Wang Qi’s importance.

• Wang Qi and his companions found the Thousand Machines Pavilion disciple waiting for them at the air harbor.
• Wu Chengdao recognized Wang Qi and asked him to inscribe a copy of the Gottingen Sect’s mathematical collection.
• Wu Chengdao assembled an eight-legged Mechanism Beast and carried Wang Qi, Huangfu Lian, and Mo Zhenzhen through the forest.
• Huangfu Lian quietly asked Wu Chengdao whether Wang Qi was truly formidable.
• Wu Chengdao said Wang Qi’s Law of Completeness would inevitably enhance computational artifacts, as Thousand Machines Pavilion’s Supreme Elder had stated.

Wang Qi and his companions explored the ruins of the Ancient Demon Race in Fusang and learned about its sun-worshipping theocracy and sacred architecture. Wu Chengdao revealed that the Immortal Alliance still released Di Liu Jiang into the ancient waterways, which might bring the dying waterway demon back to life.

• The group spotted a huge flat-topped pyramid, and Wu Chengdao explained that the Ancient Demon Race had used it as its main hall and imperial court.
• Wang Qi noted that the pyramid’s steps matched a solar calendar, and Wu Chengdao explained that the Demon Race worshipped the sun and followed a form of the Path Method.
• Wu Chengdao described the sacred thousand-mile light and sunflower, which represented the Ancient Demon Race’s highest officials and the Demon Emperor’s personal guards.
• The Mechanism Beast carried the group through ruined residences, temples, and clinics toward the pyramid, where they saw the ancient waterways still carrying clear water.
• Wu Chengdao explained that Di Liu Jiang had once been diluted through the waterways to awaken beasts, and said the Immortal Alliance still periodically released it into them.

Wang Qi and his companions learned how the Immortal Alliance used Di Liu Jiang to make Fusang’s demons loyal to humans, then entered the automated outer region of Thousand Machines Pavilion. Wu Chengdao drove them at dangerous speed through its bronze-colored streets.

• Wang Qi and Huangfu Lian drew their swords when they learned the Immortal Alliance regularly released imitation Di Liu Jiang in Fusang, but Wu Chengdao explained that newly intelligent demons regarded humans as their innate teachers and would not attack them.
• Wu Chengdao described the Immortal Alliance’s plan to enlighten Fusang’s demons and incorporate them into its civilization, while Wang Qi reflected on the transformation of the once-hostile region.
• Wang Qi, Huangfu Lian, Mo Zhenzhen, and Wu Chengdao passed through ancient ruins and reached bronze-colored buildings modeled on Ancient Demon Race civilization.
• Wu Chengdao explained that the Immortal Alliance had rebuilt the ruins to link humans with the relics in the minds of newly born demons.
• Wu Chengdao’s eight-legged Mechanism Beast transformed into a wheeled vehicle on the metal road, and he sped through the automated district despite Huangfu Lian’s warning about the danger to pedestrians.

Wang Qi visited Sanjiang Hall at the Thousand Machines Pavilion and bought Yu Liu Type 3 Mechanism Beasts for research. He spent the rest of the day quietly preparing, and the Feast of Completed Artifacts began the next morning.

• Wu Chengdao brought Wang Qi, Mo Zhenzhen, and Huangfu Lian to the Thousand Machines Pavilion before the feast officially opened.
• Wang Qi asked to visit the mechanism shop, and Wu Chengdao escorted him to Sanjiang Hall because many disciples might confront him.
• Wu Chengdao showed Wang Qi the shop’s mechanisms and explained why spirit armor had failed as a practical product but became popular through stories and Mirage Plays.
• Wang Qi bought ten Yu Liu Type 3 Mechanism Beasts for his research.
• Wang Qi stayed in his room refining mechanisms and cultivating, and the Feast of Completed Artifacts began the next day.

At the Artifact Completion Banquet, Wang Qi entered the inner tier and drew the attention of the Myriad Dharma Sect’s grandmasters and peers. He met the Math Sovereign, who gave him a sword manual, while Xiboche asked whether he was prepared for what would happen next.

• Wang Qi arrived at the Thousand Machines Pavilion’s ceremonial hall with Huangfu Lian, Mo Zhenzhen, and Wu Chengdao for the Artifact Completion Banquet.
• Wu Chengdao led Huangfu Lian and Mo Zhenzhen to the outer tier and sent Wang Qi into the inner tier, where his reputation attracted curious, jealous, and hostile looks.
• Wang Qi examined the ancient Demon Race murals and discussed their strange symbols with an elderly Myriad Dharma Sect cultivator.
• The elderly cultivator identified himself through Wang Qi’s realization as the Math Sovereign, Mr. Pang, and left him a sword manual derived from his theories.
• Xiboche told Wang Qi that Mr. Pang had come to meet the man who had helped the Gottingen Sect and asked whether Wang Qi was prepared for what would happen that night.

At the Daoist Artifact Award gathering in Fusang, Wang Qi drew the Gottingen Sect’s favor and spoke with Bo Xiaoya and Su Junyu about his unfinished work on probability. The ceremony began with Turing’s formal address, while Wang Qi and his friends quietly discussed the event.

• Xiboche urged Wang Qi to study another school's swordsmanship and left, prompting others to see him as a future member of the Gottingen Sect.
• Bo Xiaoya confronted Wang Qi over leaving her with an unfinished formula, and Su Junyu explained that Patriarch Baize disliked probability despite discovering the law of large numbers.
• Su Junyu remarked on Wang Qi's rapid progress and asked whether a Gottingen Sect Xiaoyao had guided him; Wang Qi kept the identity secret and agreed to spar later.
• Wang Qi told Bo Xiaoya he intended to continue researching the law of large numbers because it could support several researchers’ work.
• Turing appeared on the ceremonial platform, reviewed recent mathematical developments, commented on the debate between the Arithmetic Lord and the Arithmetic Master, and began the formal proceedings.

Wang Qi received the Myriad Dharma Sect’s Daoist Artifact Award for establishing the completeness of mathematics and uniting the Dao of Calculation with the Dao of Heaven. After accepting the Seeking Dao Jade, he shared his conception of mathematics with the gathered disciples.

• Su Junyu explained that Wang Qi’s achievement had earned him the Daoist Artifact Award and that the crowd’s resentment came from losing their chance at the honor.
• Wang Qi learned that Su Junyu had also been nominated for his paper, “Wuding Card Tactical Algorithms and Methods of Computational Demonstration.”
• Divine Lord Bai Ze announced that Wang Qi would receive the award for his mathematical achievements.
• Wang Qi accepted the Seeking Dao Jade from Divine Lord Bai Ze as the hall applauded.
• Wang Qi described mathematics as abstract structures that gained power by shedding their original intuitive content and accepting new interpretations.

Wang Qi presented a structuralist program for mathematics, arguing that its unity came from connections among fields and shared concepts rather than formal logic alone. His speech left the mathematicians of the Divine Land sensing that mathematics was about to turn a new page.

• Wang Qi explained the divide between discrete arithmetic and continuous geometry and described earlier efforts to unify mathematics.
• Wang Qi argued that mathematicians should seek connections among mathematical fields and prioritize problems that could advance the wider discipline.
• Feng Luoyi noted that Wang Qi’s approach dismissed the value of Chen Jingyun’s Dao, while Xiboche defended its systematic account of ideas others had also considered.
• Wang Qi concluded that axioms and formal logic supplied mathematics with a framework, while shared concepts gave it unity.
• Xiboche applauded Wang Qi, and the cultivators in the hall sensed that mathematics in the Divine Land was entering a new era.

After the Artifact Completion Banquet, Wang Qi examined his new Dao-Seeking Jade and spent several days training and exchanging spells with his friends. A True Disciple challenged him over his future prospects before Wang Qi boarded a spirit vessel to return.

• After the banquet, Wang Qi persuaded Su Junyu and Bo Xiaoya to stay and talk mathematics, and Xiang Qi joined them.
• Wu Chengdao suggested inspecting the Dao-Seeking Jade, and Wang Qi showed the group the portable Treasure Weapon and learned about its advanced functions.
• Wang Qi bought or commissioned small Mechanism Beasts and sparred with Su Junyu, Bo Xiaoya, and Xiang Qi, learning from their tactics and spells.
• A middle-aged Myriad Dharma Sect True Disciple warned Wang Qi that he would never pass the Primordial Spirit heavenly gate, and Wang Qi asked for his name without taking offense.
• The next day, Wang Qi boarded a spirit vessel for the return journey.

After returning to Divine Capital with the Seeking Dao Jade, Wang Qi endured his fellow cultivators’ attention and was drawn into the city’s social circle. On the ninth day of the first month, Du Bin brought him to meet a group of ancient Dharma descendants, where a burly perfected Golden Core cultivator greeted him as a brother.

• Wang Qi returned to Divine Capital with the Seeking Dao Jade, and Liu Yunxiang led the outer sect cultivators in welcoming him.
• Wang Qi moved next door to Chen Youjia to escape his fellow disciples’ constant attention, while Chen Feng granted his verifiers a long New Year holiday.
• After the third day of the first month, Du Bin began visiting Wang Qi regularly with gifts, and Chen Feng explained that Divine Capital cultivators viewed Wang Qi as a Transcendent Immortal.
• On the ninth day of the first month, Zhen Chanzi insisted that Wang Qi meet the ancient Dharma descendants, so Wang Qi went with Du Bin to a restaurant.
• A burly modern-Dharma Golden Core cultivator pulled Wang Qi into the private room and greeted him as a brother.

Wang Qi met seven other Banished Immortals, who described their backgrounds and shared their frustration at being unable to advance beyond Golden Core perfection. Zhao Qingfeng warned Wang Qi that the Immortal Alliance could not be relied upon and urged him to hear their experiences.

• Wang Qi entered a private room and found seven powerful cultivators who said they were Banished Immortals.
• Zhao Qingfeng explained that they had gathered to meet Wang Qi and called Banished Immortals frustrated souls with no hope of attaining a Primordial Spirit.
• Zhao Qingfeng, Lu Wan, Shu Rongrong, and the others introduced themselves and recounted how they had been identified as Banished Immortals.
• Wang Qi questioned what made someone a Banished Immortal, but Zhen Chanzi admitted that he did not know.
• Wang Qi tried to leave to ask Chen Feng about Banished Immortals, but Zhao Qingfeng stopped him and warned that all of them had failed to break through Golden Core perfection.