Recaps

Xiao Yi’s team completed and patented the core materials for a high-performance lithium-sulfur solid-state battery, while Liu Xiaodong uncovered anomalous electron movement in carbon nanoporous material and chose to investigate it. After Xiao Yi learned he had become the youngest Changjiang Scholar, three papers revealing the battery breakthrough sent the battery industry and academic community into upheaval.

• Xiao Yi’s team finalized a battery with an energy density of 1,345 Wh/kg, planned patents for its three material technologies, and prepared three papers with Xiao Yi as corresponding author.
• Liu Xiaodong showed Xiao Yi data indicating unusually fast electrons in pores near 26 nanometers, and Xiao Yi encouraged him to pursue the unexplained effect as a new research project.
• Bao Hexin told Xiao Yi that he had been selected as a Changjiang Scholar, and Xiao Yi invited the laboratory to dinner to celebrate.
• News of Xiao Yi’s selection stirred debate in the academic community, where some criticized his rapid rise and others defended his achievements.
• Three papers in JACS and ACS Nano revealed the lithium-sulfur solid-state battery breakthrough, provoking a major upheaval in the battery industry and related academic fields.

Michael Whittingham and ExxonMobil executive Graham verified the three battery materials developed by Xiao Yi and recognized their potential to transform the battery market. As companies and researchers reacted to the breakthrough, consumers celebrated the prospect of longer-lasting devices and electric vehicles.

• Graham showed Whittingham three papers by Xiao Yi's team describing materials for lithium-sulfur solid-state batteries, including a solution to lithium dendrite growth.
• Whittingham and Graham synthesized the materials and assembled a battery that exceeded 900 watt-hours per kilogram; Whittingham judged the technology feasible for consumer use.
• Whittingham predicted lithium-sulfur solid-state batteries would rapidly capture market share, while Graham acknowledged Xiao Yi had filed patents and that Chinese companies already dominated the battery industry.
• After the papers were verified, battery-company share prices fell, companies held crisis meetings, and some corporate-backed research teams were disbanded.
• A Tsinghua University professor posted a popular Zhihu answer predicting much longer device battery life, longer electric-vehicle ranges, and improved performance in extreme cold.

After Xiao Yi’s lithium-sulfur solid-state battery breakthrough drew widespread attention, he rejected ExxonMobil’s $3 billion offer for the patents and traveled to Shangjing to discuss licensing and commercialization. A three-day meeting with government officials and battery-industry leaders set the future direction of the battery industry.

• Netizens praised the batteries’ potential and discussed Xiao Yi’s breakthroughs, his laboratory, and the patents’ significance.
• ExxonMobil president Argyle Bentley offered Xiao Yi $3 billion to acquire the three battery patents, but Xiao Yi rejected the offer and hung up.
• Xiao Yi considered licensing the patents to multiple companies to prevent a monopoly, then accepted Liu Cong’s invitation to discuss commercialization in Shangjing.
• Xiao Yi met Liu Cong, Wang Chuanfu, and Zeng Yuqun, and discussed the future development of lithium-sulfur solid-state batteries.
• Xiao Yi and the industry leaders attended a three-day meeting, after which they left with the future battery landscape essentially decided.

Xiao Yi licensed his lithium-sulfur solid-state battery patents to major companies and other domestic firms, bringing substantial funding to Science Island Laboratory. While developing a plasma-flow model, he encountered a problem that led him to consider proving the existence and smoothness of Navier–Stokes equation solutions.

• Xiao Yi finalized the three-patent licensing deal with Wang Chuanfu and Zeng Yuqun, who each pledged 300 million yuan in funding for Science Island Laboratory.
• Xiao Yi spent 500 million yuan of the licensing proceeds on laboratory research and required licensees to establish factories and create jobs in Hui Province and Fei City.
• Over the following month, about a dozen companies obtained licenses, and Xiao Yi invested 500,000 yuan in a startup founded by Liu Changbo, Pan Ke, and Xu Jin.
• Xiao Yi tallied Science Island Laboratory's available funds and asked Wang Hao to arrange meetings about expanding the facility.
• Xiao Yi combined fluid and multifluid models to study plasma flow, but his derivation revealed possible blow-up solutions and Kelvin-Helmholtz instability.
• Xiao Yi concluded that resolving the model's problem would require proving the existence and smoothness of Navier–Stokes equation solutions.

Xiao Yi began investigating the existence and smoothness of three-dimensional Navier-Stokes solutions after other approaches to his fluid-model problem failed. He realized he needed extensive simulation data to study blow-up conditions, so he used Fei City's Chaohu Mingyue supercomputer and left with more than 300 TB of results to analyze.

• Xiao Yi abandoned other approaches to combining the Navier-Stokes equation with a multi-fluid model and began studying its existence and smoothness problem.
• Xiao Yi examined blow-up singularities and decided he needed data from simulations using many different initial conditions.
• Xiao Yi found that his laboratory servers lacked the computing power to run hundreds of direct numerical simulations, so he planned to expand the computer room and investigate building a supercomputing center.
• Xiao Yi visited the Chaohu Mingyue Supercomputing Center and ran his fluid-mechanics models on its supercomputer.
• Xiao Yi had the simulation data copied onto hard drives, collected more than 300 TB of results, and left the center to analyze them.

After analyzing extensive fluid-mechanics simulation data, Xiao Yi developed the Explosion Trend Discrimination Model to identify initial conditions likely to produce blow-up solutions. He persuaded Tang Fucheng and Shen Gensheng to organize a collaborative effort to improve it, then learned they had come to ask him to take on students.

• Xiao Yi and his laboratory team spent nearly half a month processing more than 300 TB of simulation data, and Xiao Yi identified several factors associated with blow-up solutions.
• After studying the data and imagining a cup of tea exploding, Xiao Yi wrote a paper proposing a model to detect trends that could lead to blow-up solutions.
• Xiao Yi completed the paper and named his approach the Explosion Trend Discrimination Model, then considered gathering more data to improve it.
• Wang Hao brought Tang Fucheng and Shen Gensheng to meet Xiao Yi, and they recognized the significance of his model after reviewing his paper.
• Xiao Yi proposed that the Science Island Laboratory, USTC, and the two schools establish an organization to train a larger model using contributed simulation data, and Tang Fucheng and Shen Gensheng agreed.
• Tang Fucheng and Shen Gensheng asked Xiao Yi to take on students, and Xiao Yi acknowledged that it was time to consider doing so.

Xiao Yi agreed to advise graduate students and began exploring whether Explosion Trend Theory could help prove the Navier–Stokes equation under generalized initial conditions. After USTC coordinated support for his Explosion Trend Discrimination Model, Annals of Mathematics published his paper online, and the surge of attention crashed the journal’s server.

• Xiao Yi agreed to join USTC’s advisor list despite the prospect of interviewing more than a hundred admitted students.
• Xiao Yi decided to submit his paper on blow-up solutions to Annals of Mathematics and began studying generalized initial conditions for the Navier–Stokes equation.
• Tang Fucheng and Shen Gensheng secured Principal Bao’s support, and USTC contacted government offices and companies to help promote Xiao Yi’s model.
• Peter Sanak sent Xiao Yi’s paper to Terence Tao, who praised its findings and urged researchers to develop the model.
• Terence Tao published a blog post describing the paper’s potential impact on mathematics and industry, and Annals of Mathematics posted it online.
• The sudden attention caused the Annals of Mathematics server to crash.

The PDE Industrial Alliance gained momentum after Diaby joined, contributing data to train Xiao Yi’s Explosion Trend Discrimination Model. As the alliance expanded, Xiao Yi faced a less welcome task: online interviews with 120 recommendation-admission students choosing supervisors.

• Sanak watched downloads of Xiao Yi’s paper surge and wondered whether Xiao Yi was preparing to tackle the Navier–Stokes existence and smoothness problem.
• Online commenters speculated that Xiao Yi’s blow-up research aimed at the Navier–Stokes equation and might also help control plasma flows.
• Zhao Zhiqiang told Wang Chuanfu that Xiao Yi’s model could cut Diaby’s computational costs by over forty percent and shorten project timelines by at least ten to twenty percent.
• Wang Chuanfu learned that many institutions and companies were joining the PDE Industrial Alliance, then ordered Diaby to join.
• USTC received more data for training the model as the alliance grew, while Xiao Yi realized he had to interview 120 recommendation-admission students online.

Xiao Yi interviewed Chen Muhua, a talented mathematics student from Shangjing University who had applied to USTC hoping to study under him. After testing Chen with a doctoral-level problem related to the Langlands Program, Xiao Yi encouraged him to deepen his knowledge, leaving Chen eager to pursue mathematics.

• Xiao Yi recognized Chen Muhua's name on the interview list and recalled meeting him in the Joint Examination Group.
• Chen Muhua joked with Xiao Yi during their online meeting, then introduced his academic record and explained his interest in algebraic geometry, number theory, and the Langlands Program.
• Xiao Yi gave Chen a problem about modular forms, Galois representations, and Frobenius traces, but Chen could not complete the proof.
• Xiao Yi explained the solution and advised Chen to broaden his knowledge of number theory and representation theory.
• Chen asked how Xiao Yi had learned so much, and Xiao Yi said he read faster than most people.

Xiao Yi finished interviewing prospective graduate students and selected Liang Qiushi, Chen Muhua, and Sun Yuan as his preferred candidates. Back at his laboratory, he developed a preliminary function space for his NS equation research and realized that its proof was within reach, though a crucial method was still missing.

• After Chen Muhua finished his interview, he joked with his roommates about his chances of becoming Xiao Yi's student, and they playfully attacked him.
• Xiao Yi interviewed dozens of mathematics applicants, ranked Liang Qiushi and Chen Muhua as his top choices, and learned Liang Qiushi had applied to USTC to join his girlfriend, Chen Chunhua.
• After interviewing the physics applicants, Xiao Yi chose Sun Yuan, who had independently published a first-quartile paper on Quantum Chromodynamics, as his sole preferred physics student.
• Xiao Yi submitted the three candidates' names to the school, then returned to his Science Island Laboratory as its second-phase expansion began.
• Xiao Yi created a preliminary function space combining Sobolev and Besov characteristics to study the NS equation, but found that it still needed improvement.
• Xiao Yi concluded that he had found the key to solving the NS equation, although the crucial method for completing the proof remained missing.

Xiao Yi continued researching a new function space while the PDE Industrial Alliance held a major conference without him. Bao Hexin revealed that Xiao Yi was working on a problem that could improve the alliance’s fluid models, prompting speculation that he was tackling the Navier–Stokes existence and smoothness problem.

• Xiao Yi spent two weeks working on a new function space and its regularity properties.
• The recommended postgraduate selections were announced, with Xiao Yi choosing Chen Muhua, Liang Qiushi, and Sun Yuan as his students.
• Tang Fucheng and Shen Gensheng discussed Xiao Yi’s absence from the PDE Industrial Alliance members’ conference and speculated about his research.
• The alliance’s members discussed future arrangements and the coming training of their model, while reporters questioned Xiao Yi’s absence.
• Bao Hexin said Xiao Yi was researching a critical problem that could help optimize fluid models, leading reporters to ask whether he was solving the Navier–Stokes existence and smoothness problem.

Xiao Yi completed his proof of the three-dimensional incompressible Navier-Stokes existence and smoothness problem and uploaded the paper, stunning researchers at the Princeton Institute for Advanced Study. The Ruthless Continuous Study effect reached lv6 and granted him the new Perfect Engineering ability.

• Foreign media attacked the PDE Industrial Alliance and mocked Xiao Yi’s attempt to solve the NS equation, while his supporters defended him online.
• Deligne and Bombieri discussed Xiao Yi’s announced research with Charles Fefferman, who hoped to see the NS equation problem solved in his lifetime.
• Coke announced that Xiao Yi had published a paper proving the NS equation result, and researchers at the Institute for Advanced Study hurried to check his website.
• Xiao Yi’s Ruthless Continuous Study effect reached lv6 after he completed a high-value paper and technology, and he gained Perfect Engineering, which let him grasp information about and simulate modifications to engineering projects.
• Xiao Yi uploaded his paper, “A New Function Space and the Existence and Smoothness of Solutions to the Three-Dimensional Incompressible Navier-Stokes Equations.”

Xiao Yi's proof of the three-dimensional incompressible NS equation under more general initial conditions stunned mathematicians and the media. Terence Tao endorsed the proof and highlighted the new function space's wider potential, while the PDE Industrial Alliance celebrated the boost to its work.

• News outlets prominently reported that Xiao Yi had proved the NS equation problem.
• Terence Tao read Xiao Yi's paper and was astonished that it proved the problem under more general conditions using a new function space.
• James Maynard examined the function space with Terence Tao and recognized its potential for mathematics beyond the NS equation.
• Terence Tao published a blog post praising Xiao Yi's achievement and describing its possible applications to fluid models.
• The mathematical community shared Tao's assessment, and the proof's broader usefulness silenced critics of the PDE Industrial Alliance.
• Tang Fucheng asked Shen Gensheng why foreign countries could not establish their own PDE Industrial Alliance, and Shen explained China's advantages in industrial data and infrastructure.

Xiao Yi developed a new plasma-fluid model and used a supercomputer to show that the Greenwald limit could be increased by 35%. He turned down an invitation to lecture in the United States, announced a March 15 lecture at USTC, and left the Plasma Institute's director stunned by the result.

• Mathematics and physics scholars argued online over whether Xiao Yi was a mathematician or a physicist, while he ignored the debate.
• Tim Bonas invited Xiao Yi to lecture on the NS equation at the Joint Mathematics Meeting, but Xiao Yi declined and invited him to a March 15 lecture at USTC instead.
• Xiao Yi revisited his model combining the NS equation with a multi-fluid model and rebuilt it using Xiao's Space to investigate the Greenwald limit.
• Xiao Yi asked Wang Hao to arrange access to Chaohu Mingyue's supercomputer and announced his NS equation lecture at USTC.
• Xiao Yi ran the new model at Chaohu Mingyue and found that the Greenwald limit could be raised by another 35%.
• Xiao Yi called Zhao Zhanyou to report the result, and Zhao fell silent in astonishment.

Xiao Yi told Zhao Zhanyou that his research had shown the Greenwald limit could be raised by 35%, and explained that proving the NS equation had helped him continue that work. After Xiao Yi published the paper, it drew widespread attention in China and abroad, and the White House decided to monitor his research.

• Xiao Yi told Zhao Zhanyou that the Greenwald limit could be raised by 35% and that he had proved the NS equation's smoothness while investigating the problem.
• Zhao Zhanyou told the Plasma Institute leaders how Xiao Yi's Greenwald limit research had led him to the NS equation, and Academician Li Jiangan urged them to seek cooperation with Xiao Yi.
• Two days later, Xiao Yi uploaded his paper, and the Plasma Institute downloaded it to assess the result and consider testing it with the EAST tokamak.
• Self-media accounts spread news of Xiao Yi's paper, prompting heated reactions from Chinese and overseas netizens.
• The Secretary of State briefed the president about Xiao Yi's nuclear fusion research, and the White House decided to keep an eye on him.

Xiao Yi visited the Plasma Institute to discuss testing his revised Greenwald limit and collected detailed EAST superconducting tokamak plans. After modeling the tokamak in Perfect Engineering, he found that its central challenges lay in extracting fusion energy and handling reactor wear.

• Li Jiangan and Zhao Zhanyou welcomed Xiao Yi and discussed his paper and the upcoming fusion ignition experiment to test the new Greenwald limit.
• Li Jiangan gave Xiao Yi the experimental plan, which aimed to raise plasma density in the EAST superconducting tokamak beyond the original Greenwald limit.
• Zhao Zhanyou handed Xiao Yi classified structural documents for the EAST superconducting tokamak, and Xiao Yi took them back to Science Island Laboratory.
• Xiao Yi spent four days using the documents to construct and study the tokamak in Perfect Engineering.
• Xiao Yi simulated changes to the tokamak's magnetic field and considered problems with energy extraction, blanket replacement, and controlling plasma through an MHD generator.
• Xiao Yi concluded that tokamaks had major problems.

Xiao Yi studied Stellarator designs and attended the Eastern Super Ring’s ignition experiment, where the device exceeded the previous Greenwald limit. After the successful test, he agreed to join the Plasma Institute’s controlled nuclear fusion research.

• Xiao Yi tried several Tokamak designs, concluded that plasma extraction and material wear remained major problems, and began studying Stellarators for ideas.
• The PDE Industrial Alliance gained members, and Xiao Yi’s March 15 presentation on his NS equation proof drew international attention as local governments prepared to host it.
• On February 5, 2024, Xiao Yi took command of the Eastern Super Ring ignition after the vacuum, magnetic confinement, heating, and diagnostic teams reported readiness.
• Xiao Yi ignited the device, which reached 100 million degrees and maintained stable plasma after exceeding the previous Greenwald limit.
• The experiment operated above 100 million degrees for 150 seconds, including 39 seconds at 160 million degrees, and verified a new density limit of 2.12×10^20/m^3.
• Xiao Yi accepted the invitation to become a researcher at the Plasma Institute and join its controlled nuclear fusion research.

After dreaming of humanity’s future collapse when fusion reactor materials ran out, Xiao Yi joined the Plasma Institute and explained that he intended to focus on first-wall materials. His words renewed the institute’s researchers’ commitment as they applauded and pledged to support him.

• On New Year’s Eve, Xiao Yi considered joining the Plasma Institute, preparing his NS equation report, and pursuing controllable nuclear fusion.
• Xiao Yi dreamed that future humanity exhausted the materials needed for fusion reactors, descended into war, and lost a Mars base in a missile strike; he woke shaken and hoped the dream’s vision of scientific progress might come true.
• During the New Year holiday, an elderly neighbor tried to arrange a blind date between Xiao Yi and her unmarried daughter, a teacher at USTC who spent her free time gaming.
• On the third day after the Lantern Festival, Xiao Yi officially joined the Plasma Institute as a Special Appointed Researcher.
• At his welcome ceremony, Xiao Yi said he would devote most of his time to researching first-wall materials and questioned whether fusion could remain viable over the long term.
• Zhao Zhanyou, Li Jiangan, and the other attendees applauded Xiao Yi and promised to support his research.

Xiao Yi researched durable, plentiful first-wall materials for fusion reactors and developed a way to simulate radiation damage in materials. As he prepared for his NS equation presentation, Liu Xiaodong brought him data on anomalous electron acceleration in carbon composites, which Xiao Yi realized might also help identify a carbon first-wall material.

• Li Jiangan briefed Xiao Yi on tungsten and other candidates for fusion-reactor first-wall materials, and Xiao Yi explained why fusion could not depend on a scarce consumable like tungsten.
• Xiao Yi modeled tungsten, steel, and carbon-based materials, then discovered that Material Mastery could simulate how neutron irradiation and plasma affected materials.
• With the NS equation presentation conference one week away, Xiao Yi began preparing his presentation at Science Island Laboratory.
• Liu Xiaodong asked Xiao Yi to collaborate on his discovery that electrons passing through carbon-composite pores around 26 nm wide could accelerate to more than ten times their normal speed.
• Xiao Yi reviewed Liu Xiaodong's experimental data and saw that it might help find a carbon structure suitable for fusion-reactor first walls.

Xiao Yi investigated unexplained electron acceleration in nanoporous carbon and decided to comprehensively analyze carbon, then prepared to present his NS equation work. As the presentation began drawing international attention, Liu Cong asked about Xiao Yi’s prospects for controllable nuclear fusion, and Xiao Yi estimated a twenty percent chance if his current research succeeded.

• Xiao Yi studied Liu Xiaodong’s experiments and concluded that electron acceleration occurred only in porous carbon, though he could not identify its cause.
• Xiao Yi failed to reproduce the acceleration with his model and decided to conduct a comprehensive analysis of carbon’s properties.
• Terence Tao, Charles Fefferman, and Shing-Tung Yau arrived in Fei City for Xiao Yi’s NS equation presentation and discussed whether his research might lead to nuclear fusion.
• Attendees and public interest gathered at the conference center as Xiao Yi waited backstage for his presentation to begin.
• Liu Cong asked Xiao Yi about controllable nuclear fusion, and Xiao Yi said he might have a twenty percent chance if his crucial research succeeded.

Xiao Yi began his lecture on the three-dimensional incompressible Navier-Stokes equations, explaining his analysis of blow-up solutions and turning to the function space needed for his proof. The chapter ended with Xiao Yi developing a new, highly abstract analysis before the audience, including Terence Tao, marveled at his ability.

• Xiao Yi told Liu Cong that fusion depended on developing first-wall materials, which he preferred to call fusion energy exchange materials, and that the research still needed luck.
• Bao Hexin checked on Xiao Yi before the lecture, while Liu Cong left for the audience and Xiao Yi prepared to take the stage.
• Xiao Yi's parents joined the packed audience, and Bao Hexin introduced him as he began his lecture on the Navier-Stokes equations.
• Xiao Yi explained singularities and demonstrated how his data-analysis method identified blow-up characteristics and yielded the blow-up trend.
• Xiao Yi shifted to the NS equation, erased the blackboard, and began analyzing what new function space could accommodate his theory as Terence Tao and Feierman praised his analytical skill.

Xiao Yi presented Xiao's Space and used it to outline a proof of existence and smoothness for solutions to the Navier–Stokes equation. After answering audience questions, he told Terence Tao that he had created the space to describe the complexity of fluids more precisely, then ended the presentation to applause.

• Xiao Yi combined properties of established function spaces with new elements to define Xiao's Space, leaving Terence Tao and Feierman unable to follow how he had conceived it.
• Xiao Yi explained that Xiao's Space provided useful properties for fluid mechanics and used it to present the existence and smoothness proof for the Navier–Stokes equation.
• Xiao Yi answered questions from Jimmy Lawrence and other attendees about the roles of Sobolev and Besov spaces and the properties of his new space.
• Terence Tao asked how Xiao Yi had developed Xiao's Space, and Xiao Yi replied that complex fluids required a more refined description.
• Xiao Yi ended his presentation, and the audience applauded.

After presenting his proof of the Navier–Stokes equation, Xiao Yi declined the Clay Mathematics Institute’s invitation to its award ceremony because traveling abroad was inconvenient and the prize money mattered little to him. He then accepted a Time Magazine interview and argued that education was the most important field because it functioned as a form of knowledge inheritance.

• Xiao Yi ended his presentation to prolonged applause, then joined Terence Tao and other scholars for lunch.
• Thomas Clay invited Xiao Yi to the Millennium Prize Problems award ceremony at MIT, where he would receive a million-dollar prize for solving the mass gap problem.
• Xiao Yi declined to travel outside China, and Jennifer Aikener explained that his Bitcoin software company and battery patents made him worth billions.
• Jennifer asked Xiao Yi to interview for Time Magazine, and he agreed on the condition that he could choose which questions to answer.
• During the interview, Xiao Yi described education as a form of knowledge inheritance that could improve how efficiently people acquired knowledge.

Xiao Yi completed an interview with Jennifer, discussing materials science, nuclear fusion, and humanity’s scientific future. After the interview, he had Jennifer investigated over her questions about fusion; the chapter ended with Time Magazine featuring him on its cover as a scientist on par with Einstein.

• Xiao Yi said materials science was humanity’s most important field and cautioned that nuclear fusion might take decades to achieve.
• Xiao Yi rejected categorizing people by IQ and argued that scientists should have faith in future technological progress.
• Jennifer finished the interview and arranged a cover photo of Xiao Yi for Time Magazine’s upcoming issue.
• Xiao Yi found Jennifer’s contact information, threw it away, and asked Wang Li to investigate whether she had been directed by American departments.
• The academic exchange conference concluded successfully, and the next week Time Magazine’s cover featuring Xiao Yi drew worldwide attention.

Foreign and domestic discussions of Xiao Yi’s Time Magazine interview drew the attention of American officials, who lowered surveillance while keeping nuclear fusion under watch. Xiao Yi returned to studying carbon with Quantum Hodge theory and found an unknown variable that appeared connected to the X particle.

• Foreign netizens praised Xiao Yi’s interview, argued about education and society, and clashed with critics who insulted him.
• Chinese netizens celebrated Xiao Yi’s Time Magazine cover and debated his views, his field, and whether he was researching nuclear fusion.
• The CIA director told the secretary of state that Xiao Yi’s interview suggested he was not researching nuclear fusion, and the secretary ordered surveillance reduced by one level while retaining attention to the topic.
• Wang Li told Xiao Yi that national security investigators had found no proof of Jennifer Aikener’s ulterior motives but considered her nuclear fusion question highly suspicious.
• Xiao Yi used Quantum Hodge theory to analyze carbon and derived an equation for the aperture acceleration phenomenon.
• Xiao Yi examined the equation’s unknown variable and realized it seemed related to the X particle.