Chapter Summaries

Xiao Yi agreed to carry out three simulations for Luo Mingya’s research project and partnered with Luo Mingchuan to operate Yishui Bit. After the New Year’s Day holiday, the software launched from Luo Mingchuan’s data center and attracted more than three hundred thousand mining machines.

• Xiao Yi offered to handle the doping, molecular dynamics, and mechanical simulations, and Luo Mingya promised him co-first authorship if he completed them.
• Luo Mingya introduced Xiao Yi to her brother Luo Mingchuan, who ran a data center, and Xiao Yi proposed that he provide servers and personnel in exchange for a 40 percent stake in Yishui Bit.
• Luo Mingchuan accepted the deal and agreed to prepare the contract, which he signed with Xiao Yi the next day.
• Xiao Yi delayed Yishui Bit’s launch again, then promised Boss Huang it would launch after the New Year’s Day holiday.
• Yishui Bit moved into Luo Mingchuan’s data center, and more than three hundred thousand mining machines connected to its servers on January 16, which the chapter also called February 27.

After returning to his dorm, Xiao Yi heard that Yishui Bit had passed 500,000 users, while the sudden influx of mining rigs overwhelmed Luo Mingchuan’s servers and drew global attention to the platform. Xiao Yi left the business to Luo Mingchuan and spent the next half month researching Computational Materials Science.

• Xiao Yi reunited with Ye Cheng and the other roommates, told them about his recent work, and agreed to treat them to dinner.
• Luo Mingchuan told Xiao Yi that Yishui Bit had surpassed 500,000 users and was dominating crypto discussions.
• A surge of mining rigs, including Bitmain’s, filled Yishui Bit’s servers, so Luo Mingchuan activated backup capacity and prepared for overseas users.
• Crypto forums spread news of Yishui Bit’s algorithm, Bitmain’s plans to adopt it, and a miner who had earned 6.25 Bitcoin with three rigs.
• Yishui Bit’s popularity spread overseas, while Xiao Yi left its management to Luo Mingchuan and focused on Computational Materials Science for half a month.

Xiao Yi completed three computational models and found that their results closely matched experimental data. As the group prepared further simulations, he proposed a new computational framework combining quantum path integrals with Markov chain Monte Carlo.

• Xiao Yi brought his completed models to Luo Mingya's lab, where the group compared their results with experimental data and found very small errors.
• Luo Mingya praised Xiao Yi's work and led the group to the Entrepreneurship Center to run simulations under different conditions.
• Liu Chao presented a joking proof about π cubed being greater than 31, and Xu Ming teased him with a mock score of zero.
• Xiao Yi returned Luo Mingya's books and said existing material-prediction methods struggled to balance accuracy and computational cost.
• Xiao Yi asked Luo Mingya whether path integrals and Markov chain Monte Carlo could be combined into a new computational framework, leaving her astonished.

Xiao Yi explained his Absolute Electronic Computation idea to Luo Mingya, who offered Materials Science data and assistance. After Luo Mingya left to continue her group’s project, Xiao Yi returned to developing the new method, considering how to combine path integrals with multiscale modeling.

• Xiao Yi described using path integrals, Markov chain Monte Carlo, and machine learning to predict material properties, and Luo Mingya said the approach was credible but difficult to implement.
• Luo Mingya offered to help Xiao Yi with Materials Science questions and provide data, while Zhao Yuanyuan struggled to follow their technical discussion.
• Xu Ming announced that the results showed comparable band structures and similar bulk plasmon peak energies among the studied polytypes.
• Luo Mingya took her fellow students back to the lab to find TMD-based heterostructures and told Xiao Yi to focus on his research, promising he would not be excluded from first authorship.
• Xiao Yi reviewed his derivations for Absolute Electronic Computation and considered combining path integrals, Molecular Dynamics, and finite element analysis into a multiscale framework.

Xiao Yi completed the theoretical model for Absolute Electronic Computation and joked with his roommates after they mistook a project meeting with Luo Mingya for a date. Zhang Yitang then called him during a Princeton presentation, where Xiao Yi answered Manjul Bhargava’s question about controlling higher-order terms in the Circle Method Expansion.

• Xiao Yi finished the theoretical model for Absolute Electronic Computation and planned to begin implementing it on a computer.
• Ye Cheng, Song Ziyang, and Luo Qiao confronted Xiao Yi with a photo of him dining with Luo Mingya, but Xiao Yi explained they had met to discuss their project.
• Xiao Yi bribed Song Ziyang and Luo Qiao with dinner, and they helped him subdue Ye Cheng before he tickled him.
• Zhang Yitang called Xiao Yi from Princeton University after Manjul Bhargava asked how their Circle Method Expansion controlled errors from higher-order terms.
• Xiao Yi explained an adaptive weighting method combined with a sieve method, and Manjul Bhargava accepted the answer.

Xiao Yi demonstrated how his method could control high-order terms in Fourier expansion, then finished training version 1.0 of his Absolute Electronic Computation model. Initial tests on silicon and copper produced results with less than one percent error, leaving him impressed by the model’s accuracy and speed.

• Xiao Yi explained how his method could reduce accumulated errors in Fourier expansion, with Zhang Yitang writing the steps on the blackboard.
• Xiao Yi answered no further questions, then told Zhang Yitang and the assembled scholars that he was working on an important project with practical applications.
• After the livestream ended, Xiao Yi joked with Ye Cheng, Song Ziyang, and Luo Qiao about speaking before hundreds of people.
• The next day, Xiao Yi completed version 1.0 of Absolute Electronic Computation and ran it on his server using experimental data from Luo Mingya.
• A week later, Xiao Yi found training complete and tested silicon and copper; the model’s calculated values differed from measured results by less than one percent.

Xiao Yi tested Absolute Electronic Computation on complex materials and found it produced highly accurate predictions. After Luo Mingya used the model to uncover new questions in her WS2 project, she canceled the celebration and returned to the laboratory with her students.

• Xiao Yi began calculations on methylammonium lead iodide and Yttrium Barium Copper Oxide to test his model on complex materials.
• Luo Mingya and Xu Ming told Xiao Yi their project was finished and an editor at Nature had invited them to submit their paper.
• Xiao Yi reviewed the new calculations, which closely matched experimental results for both materials, and Luo Mingya asked him to test WS2.
• Luo Mingya saw discrepancies in the WS2 results that suggested further research and canceled the celebration dinner so her students could resume experiments.
• Luo Mingya praised Absolute Electronic Computation as a revolutionary achievement and left with her students to continue their work.

Xiao Yi submitted his new Absolute Electronic Computation paper to arXiv while continuing to work on the Goldbach Conjecture. After Manjul Bhargava and Ali Yazdani read the paper’s startling results, Yazdani left to verify them in the lab.

• Xiao Yi posted his Absolute Electronic Computation paper in arXiv’s physics section.
• Bhargava told Yazdani that Xiao Yi had recently pursued applied mathematics and might produce useful results.
• Students nearby noticed Xiao Yi’s new paper, prompting Bhargava and Yazdani to look it up.
• Bhargava and Yazdani read that the model predicted properties of complex materials, including YBCO, with errors under ten percent.
• Yazdani was shocked by the results and said he would return to the lab to verify them.

Researchers in Materials Science and Condensed Matter Physics tested Xiao Yi’s Absolute Electronic Computation model and reported highly accurate predictions for complex materials. At UC Berkeley, Paul Alivisatos told his students that the model could transform research as a valuable experimental tool and defended Xiao Yi’s mathematical expertise.

• Yazdani hurried away to verify the potential of Xiao Yi’s work while Balgava watched him go.
• Researchers in Materials Science and Condensed Matter Physics devoted time and resources to testing Absolute Electronic Computation, with some launching dedicated projects.
• Laboratories at ETH Zurich, Princeton, and elsewhere reported that the model’s predictions for superconductors, topological insulators, and other complex materials closely matched experimental results.
• UC Berkeley students debated the model’s likely impact, and Paul Alivisatos said it could change laboratory habits by assisting experiments without replacing them.
• Paul Alivisatos explained that Xiao Yi’s mathematical methods enabled the breakthrough and suggested that his students improve their mathematics, leaving them horrified.

A week after Xiao Yi published his paper on Absolute Electronic Computation, physicists debated whether the method could be extended to particle research, while scientists weighed its promise against the risks of relying too heavily on computation. Xiao Yi stayed out of the debate and finally attended Luo Mingya's research group's celebration banquet.

• Particle physicists discussed using Xiao Yi's method to simulate collider experiments and asked Edward Witten to assess whether it could be extended to other particles.
• Edward Witten said the mathematical problems were difficult, praised Xiao Yi's ability to unite disparate methods, and suggested asking Xiao Yi to study Theoretical Physics.
• Domestic researchers discussed Absolute Electronic Computation, with some laboratories preparing to adopt it widely and critics warning that it could cause scientists to overlook unknown mechanisms and undervalue experiments.
• Xiao Yi declined to weigh in on how the scientific community should use his method and trusted researchers to make their own decisions.
• Xiao Yi attended Luo Mingya's research group's celebration banquet.

At a celebration dinner, Xiao Yi received invitations from top journals to submit his Absolute Electronic Computation paper, then returned to his mathematics work. He combined Xiao's expansion with the circle method and prepared to improve Chen's Theorem, aiming to turn “1+2” into “1+1.”

• Luo Mingya credited Xiao Yi's simulations and Absolute Electronic Computation model with helping their project paper gain immediate approval from Nature's editor.
• Xiao Yi received submission invitations from the editor-in-chief of JACS and the editor-in-chief of Physical Review Letters, and decided to submit his paper to JACS rather than shorten it for PRL.
• After returning to the entrepreneurship center, Xiao Yi reviewed results on the Goldbach Conjecture and recalled Chen Jingrun's paper and its lemmas.
• Xiao Yi realized he could combine Xiao's expansion with sieve methods and the circle method, then completed the new combined theory.
• Xiao Yi set out to formally improve Chen's Theorem and turn its “1+2” result into “1+1.”

After developing his Circle Method Expansion theory, Xiao Yi proved the Goldbach Conjecture and considered where to submit his paper. The chapter left him preparing for the worldwide attention he expected once the proof became known.

• Xiao Yi joined Ye Cheng, Song Ziyang, and Luo Qiao for Number Theory class and helped Ye Cheng with his paper on sheaf cohomology.
• Professor Wang and the students persuaded Xiao Yi to teach, so he lectured on sieve methods and connected them to the circle method and the Goldbach Conjecture.
• Xiao Yi presented his Xiao's expansion and outlined how it could help turn Chen Jingrun's 1+2 result into 1+1 before class ended.
• Four days later, Xiao Yi finished writing a proof that every even number greater than 2 was the sum of two primes.
• Xiao Yi decided to submit his Goldbach Conjecture paper to a journal rather than post it on arXiv, hoping to rest before the proof drew worldwide attention.

Annals of Mathematics editor Peter Sarnak reviewed Xiao Yi’s submission and judged that it proved the Goldbach Conjecture, prompting the journal to assemble an expert review committee. After a month of review, the committee officially confirmed the proof.

• Editors Ron and Beck found two submissions titled “Goldbach Conjecture,” and recognized Xiao Yi as the author of the second paper.
• Ron and Beck alerted Peter Sarnak, who began reviewing Xiao Yi’s paper and confirmed it was his work.
• News of Xiao Yi’s claimed proof spread through Princeton and the mathematical community, where many doubted it because the paper was not on arXiv.
• After reading the paper, Sarnak announced that the proof appeared valid and organized a review committee of six number theory experts.
• The committee began reviewing Xiao Yi’s paper and officially announced one month later that the Goldbach Conjecture had been proven.

After Xiao Yi’s proof of Goldbach Conjecture was verified, Academician Xun Yong invited him to present it at the Great Hall of the People, where the report would also serve as his undergraduate graduation defense. The announcement sparked nationwide excitement, and the chapter ended as the lecture date approached.

• You Kun watched the news that Goldbach Conjecture had been proved and decided to attend Xiao Yi’s report with Chen Jingrun’s photo.
• Xiao Yi guided Song Ziyang through a proof involving the Mountain Pass Theorem and the PS condition while Ye Cheng joked about no longer calling him “Godfather.”
• Professor Liu Bin told Xiao Yi that Academician Xun Yong had come to invite him to give a Goldbach Conjecture report in Shangjing.
• Xun Yong invited Xiao Yi to present at the Great Hall of the People, and the dean proposed making the report Xiao Yi’s undergraduate graduation defense.
• Xiao Yi agreed to the arrangements, and news of the report spread across China, prompting overwhelming demand for attendance reservations.
• The reservation website crashed, then available places sold out quickly as the lecture date drew near.

Guo Xiaoming livestreamed from the Great Hall of the People before Xiao Yi’s Goldbach Conjecture report and undergraduate defense, then watched as Xiao Yi presented his new mathematical methods and began proving the conjecture. The report was still underway as Xiao Yi’s derivations left most of the audience unable to follow, while mathematicians discussed where he might pursue graduate studies.

• Guo Xiaoming told viewers that unclaimed seats might let people into Xiao Yi’s report and explained that Xiao Yi would present in Chinese.
• On May 29, more than ten thousand people filled the Great Hall of the People, where Xiao Yi’s report was also announced as his undergraduate graduation defense.
• Liu Cong encouraged Xiao Yi backstage and promised him a surprise after the report.
• Xi Lan opened the event, and Xiao Yi began his presentation by discussing Chen Jingrun’s theorem and the history of the Goldbach Conjecture.
• Xiao Yi introduced his Parity Check Classification Sieve, Xiao’s Polynomial Expansion, and the Circle Method Expansion before beginning his proof of the Goldbach Conjecture.
• Hu Guangde told Xi Lan that Xiao Yi might pursue graduate studies in China, and Xi Lan suggested recruiting him to the Mathematics Research Institute.

Xiao Yi completed his Goldbach Conjecture defense to a huge audience, drawing praise and recruitment offers from leading mathematicians and physicists. At the reception afterward, he met Chen Jingrun's family and accepted an Outstanding Young Scholar application, leaving with a special route to research funding and expectations for his future work.

• Xiao Yi finished his defense, and the committee members praised his achievement while Xi Lan and Pang Cheng competed to recruit him for their institutes.
• Xi Lan delivered the closing remarks as the auditorium applauded, and the presentation became a major online event with its relativity joke trending.
• Xiao Yi met Chen Jingrun's widow and son, who thanked him for fulfilling Chen's wish and easing the son's regret about the Goldbach Conjecture.
• Liu Cong gave Xiao Yi an Outstanding Young Scholar application, explained its benefits, and Xiao Yi signed it immediately.
• Liu Cong told Xiao Yi that his research funding would use a special channel and encouraged him to produce further achievements before leaving to attend to other matters.

After graduating with bachelor's and master's degrees, Xiao Yi agreed to pursue doctoral studies in both mathematics and physics and joined Pang Cheng's high-temperature superconductivity project. He arrived at the Institute of Physics, where Pang Cheng welcomed him and showed him his new dormitory, leaving Xiao Yi ready to begin the next stage of his research.

• Xi Lan and Pang Cheng argued over Xiao Yi's future studies, and Hu Guangde proposed that he pursue doctorates at both institutes; Xiao Yi agreed.
• Pang Cheng invited Xiao Yi to join a project investigating why FeSe superconductivity rose on an SrTiO3 substrate, and Xiao Yi agreed to join after completing his graduation procedures.
• Xiao Yi returned to Fei City, completed his remaining exams and credits, and received his bachelor's and master's degree certificates.
• Xiao Yi took graduation photographs with his teachers and remembered that he had also joined his high school classmates for their graduation photo.
• On June 15, Pang Cheng welcomed Xiao Yi to the Institute of Physics and showed him his spacious researcher dormitory; Xiao Yi planned to begin work the next day.

Xiao Yi joined Pang Cheng’s condensed matter research group and proposed using hydrogen to create iron vacancies in FeSe/SrTiO3 monolayers. Pang Cheng judged the method highly promising, leaving the team eager to test Xiao Yi’s idea.

• Xu Zhiqiang escorted Xiao Yi to the Shangjing Condensed Matter Physics Research Center and revealed that his family owned a chain of hotels.
• Pang Cheng welcomed Xiao Yi to the lab, and Xu Zhiqiang learned that Xiao Yi’s company was valued at hundreds of millions and that Xiao Yi had been selected as an Outstanding Young Scholar.
• Pang Cheng introduced Xiao Yi to the research group, then rebuked Cui Yuanhao for criticizing Xiao Yi’s award and funding allocation.
• Guo Ding explained the team’s project on finding an iron-vacancy-ordered parent compound for FeSe/SrTiO3 monolayer superconductors.
• After examining the experimental data, Xiao Yi proposed using hydrogen to lower iron atom migration barriers and produce vacancies, and Pang Cheng praised the method’s potential.

Xiao Yi proposed the Hydrogen Power Method to introduce iron-vacancy defects into FeSe/SrTiO3 monolayer superconductors, and Guo Ding’s simulation confirmed it could work. The research group successfully reproduced the defects in the laboratory and continued toward studying the transition to the insulating parent phase.

• Xiao Yi explained to Guo Ding how hydrogen could lower the energy barrier for iron atoms to migrate and create vacancies in the FeSe layer.
• Guo Ding simulated the method, confirmed it could introduce iron vacancies and produce a transition to the insulating parent phase, then informed Pang Cheng.
• At the group meeting, Pang Cheng announced Xiao Yi’s method, and Xiao Yi explained it while Guo Ding presented the simulation results.
• Pang Cheng led the group through experiments using calculated hydrogen conditions, and the team confirmed iron-vacancy defects with a Scanning Tunneling Microscope.
• Pang Cheng offered Xiao Yi first authorship on a paper combining the method with the group’s final results, and Xiao Yi agreed to publish them together.

Xiao Yi received an invitation to deliver a one-hour plenary lecture at the 2022 International Congress of Mathematicians and wondered what to present. After the congress's speaker list was announced, mathematicians debated whether he should receive the 2022 Fields Medal, and he led an online poll by a wide margin.

• Xiao Yi received an invitation from the International Mathematical Union to give a one-hour plenary lecture at the 2022 International Congress of Mathematicians in Saint Petersburg.
• Guo Ding learned about Xiao Yi's invitation, then left the laboratory to help Academician Tang's research group at the Institute of High Energy Physics.
• Xiao Yi continued helping in the laboratory and studying papers and experimental results after Guo Ding left.
• The International Mathematical Union announced the invited speakers, and mathematicians marveled that Xiao Yi was the youngest one-hour plenary lecturer in ICM history.
• Mathematicians argued online over whether Xiao Yi should receive the 2022 Fields Medal, and his poll support climbed from 44% to nearly 60%.