Chapter Summaries

Xiao Yi gave a talk demonstrating applications of his expansion across several areas of mathematics, including progress on the Riemann Hypothesis. During the Q&A, Turing Award winner Silvio Micali asked how the expansion might improve blockchain security, leaving Xiao Yi surprised by the audience’s computer science questions.

• Xiao Yi explained that his factorization sieve solution had made RSA encryption more secure and reduced the key length needed to match ECC.
• Xiao Yi showed how his expansion could push the Riemann Hypothesis critical-line result from 61% to 62.5%, then explored the Bohr-Landau theorem and other mathematical applications.
• Xiao Yi finished his thirty-minute presentation and opened the floor to questions, with more than a hundred attendees raising their hands.
• Silvio Micali introduced himself as an MIT professor and Turing Award winner, then asked whether Xiao’s expansion could strengthen blockchain cryptocurrencies and other blockchain applications.
• Xiao Yi was surprised to learn that the audience’s questions would extend beyond pure mathematics.

Xiao Yi discussed blockchain design with Silvio Micali and answered questions about applying Xiao's expansion to cryptography at his mathematics talk. The session ran overtime, and Micali concluded that Xiao Yi's abilities exceeded his reputation as the audience applauded.

• Silvio Micali asked Xiao Yi about applying Xiao's expansion to blockchain encryption, then explained Algorand's approach to the blockchain trilemma.
• Mathematicians learned that Xiao Yi's recent work had addressed concerns about RSA security, while Terence Tao and Maynard discussed their World Bank proposal being accepted and its ten-million-dollar prize.
• Xiao Yi and Micali exchanged knowledge about blockchain construction and cryptography, and Xiao Yi demonstrated how Xiao's expansion could be adapted to ECC, though with worse results than for RSA.
• Xiao Yi answered questions from mathematicians and computer scientists until Hales Carl signaled that the talk had gone overtime, and the audience applauded as the session ended.
• Prabhakar Raghavan praised Xiao Yi, while Silvio Micali said Xiao Yi exceeded his reputation, prompting Raghavan to consider inviting him to join Google.

After his presentation, Xiao Yi answered dozens of questions and met prominent figures who praised his work and offered opportunities. He turned down Google’s $500,000 annual offer because he wanted to focus on pure mathematics, then learned the offer had been part of a bet.

• Xiao Yi stayed after his presentation to answer scholars’ questions until late in the evening.
• Silvio Micali exchanged email addresses with Xiao Yi, and Brian Winston introduced himself as a World Bank Chief Information Officer and arranged to expedite the $10 million prize payment.
• Prabhakar Raghavan offered Xiao Yi a Google position with a $500,000 base salary, education support, bonuses, and help obtaining a U.S. green card.
• Xiao Yi declined the offer because he preferred pure mathematics, and Raghavan admitted he might be dismissed if his research never produced profits.
• Raghavan collected money from Winston and Micali after revealing they had bet that Xiao Yi would reject Google, then shared part of his winnings with Xiao Yi.

Xiao Yi became a global sensation after rejecting Google's unusually generous offer, as people discussed his mathematical and computer science achievements. The Joint Mathematics Meeting then reached its closing ceremony, where Hales Carl began announcing the awards.

• Xiao Yi turned down Google's offer despite its $500,000 starting salary and other benefits because he wanted to pursue his own research.
• News of Xiao Yi's rejection spread worldwide, with media and social media users debating his decision and his reputation in Japan and China growing.
• A highly rated Zhihu answer explained that Google's offer reflected Xiao Yi's work on Xiao's System and a cross-blockchain transaction protocol developed with Terence Tao, James Maynard, and Leonard Kleinrock.
• Computer science researchers and students discussed how Xiao Yi's mathematical methods could benefit information security and secure multiparty computation.
• The Joint Mathematics Meeting in San Jose approached its conclusion, and Hales Carl opened the awards ceremony by announcing the Cole Algebra Prize.

Xiao Yi received the Cole Algebra Prize for proposing the automorphic theory of étale algebraic varieties, then learned that his contribution to the World Bank project had earned him $6 million. He planned to travel to Santa Barbara before returning home for the New Year.

• Hales Carl presented Xiao Yi with the Cole Algebra Prize and its $5,000 award at the Joint Mathematics Meeting.
• After the meeting ended, Xiao Yi prepared to travel to Santa Barbara and received the $5,000 prize money in his bank account.
• Xiao Yi posted a photo of his prize certificate on QQ, where Song Ziyang, Ye Cheng, and Luo Qiao eagerly asked him to treat them to a meal.
• Xiao Yi ignored a former classmate's flirtatious comment on his post.
• Xiao Yi received a $6 million deposit from the World Bank project and realized his share of the $10 million prize was now in his account.

After receiving their project payments, Xiao Yi said goodbye to Terence Tao and James Maynard and traveled with Zhang Yitang to Santa Barbara. They reviewed the remaining obstacles to the Landau-Siegel Zero Conjecture and began working on them at UCSB.

• Xiao Yi, Terence Tao, and James Maynard confirmed that their project payments had arrived, and Kleinrock thanked Xiao Yi for helping speed up the transfer.
• Terence Tao and Maynard said goodbye to Xiao Yi, who left with Zhang Yitang for Santa Barbara.
• On the drive, Xiao Yi mistook a passing mounted police officer for a reminder of the game Road Rash, then reviewed Zhang Yitang’s research notes on the Landau-Siegel Zero Conjecture.
• After reaching UCSB and settling into the student dormitories, Xiao Yi and Zhang Yitang went to Zhang Yitang’s office to discuss the conjecture’s remaining problems.

Xiao Yi combined the circle method with Xiao's expansion to break through the central obstacle in the Siegel-Zero Conjecture. After he and Zhang Yitang resolved the remaining minor issues over the following days, they completed the proof and established that no Landau-Siegel zero existed.

• Xiao Yi shifted from their earlier approach and began applying the circle method to the problem.
• Xiao Yi combined the circle method with Xiao's expansion, revealing a way past the main obstacle in the proof.
• Zhang Yitang realized the breakthrough had brought them close to a complete proof and decided to continue working with Xiao Yi.
• Xiao Yi returned to his dormitory and studied how the circle method and Xiao's expansion might lead to further techniques, including for the Goldbach Conjecture.
• Over the next several days, Xiao Yi and Zhang Yitang resolved the remaining issues and completed the proof of the Siegel-Zero Conjecture.

After Xiao Yi and Zhang Yitang concluded that Landau-Siegel zeros do not exist, they reflected on the discovery and began preparing a paper. While Zhang Yitang organized their proof, Xiao Yi continued studying the circle method and Xiao's expansion and found a possible connection to prime factorization.

• Zhang Yitang and Xiao Yi finished their proof and concluded that the Landau-Siegel zero does not exist.
• Xiao Yi and Zhang Yitang discussed how unexpected discoveries could lead to major advances in mathematics and physics.
• Zhang Yitang explained that he would organize the paper, and Xiao Yi offered to help if problems arose.
• Over the following days, Zhang Yitang worked on the paper while Xiao Yi studied the circle method and Xiao's expansion.
• Xiao Yi unexpectedly realized that the method might help with prime factorization.

Xiao Yi turned his new prime-factorization method into the basis for Bitcoin mining software and planned how to charge miners for using it. After Zhang Yitang submitted their joint paper on the Siegel-Zero Conjecture, he offered to introduce Xiao Yi to a mining-farm owner who could help promote the software.

• Xiao Yi combined the circle method with Xiao's expansion to devise an efficient method for factoring prime numbers.
• Xiao Yi began developing mining software with usage fees and a one-percent mining commission, while considering how to protect and promote it.
• Zhang Yitang handed Xiao Yi his paper, and Xiao Yi found typos and citation errors that they corrected together.
• Zhang Yitang uploaded their joint paper to arXiv and invited Xiao Yi to give talks, but Xiao Yi declined.
• Xiao Yi told Zhang Yitang he was writing Bitcoin mining software, and Zhang Yitang offered to introduce him to a mining-farm owner with more than thirty thousand rigs.

Xiao Yi arranged for mining-company owner Huang Houping to test his upcoming mining software, while Zhang Yitang announced that their proof of the Landau-Siegel Zero Conjecture was on arXiv. The paper passed review and was released, leaving mathematicians eager to examine its proof.

• Zhang Yitang introduced Xiao Yi to Huang Houping, who agreed to test Xiao Yi’s mining software free for three days once it was finished.
• Xiao Yi learned Huang Houping’s mining company could help spread the software if it improved mining profits.
• Zhang Yitang announced that his and Xiao Yi’s paper, “The Nonexistence of Landau-Siegel Zeros,” had been uploaded to arXiv.
• Joey Ayton visited Zhang Yitang and learned that Xiao Yi had helped solve the Zero Conjecture in less than a day.
• Mathematicians gathered on arXiv, and the paper passed review and was publicly released.

Terence Tao and James Maynard reacted to Zhang Yitang and Xiao Yi’s proof of the Landau-Siegel Zero Conjecture, praising its new methods but complaining about its abbreviated proofs. After the pair returned to China, Zhang Yitang found that mathematicians had flooded him with comments telling him to stop writing papers, and he prepared to argue back.

• Terence Tao read Zhang Yitang and Xiao Yi’s proof of the Landau-Siegel Zero Conjecture and recognized Xiao Yi’s contribution to Xiao’s Circle Method Expansion.
• James Maynard called Terence Tao, and they discussed the proof’s speed and Zhang Yitang’s difficult writing style.
• The proof spread through the mathematical community, where scholars admired its methods but criticized its abbreviated proofs.
• Zhang Yitang and Xiao Yi landed at Shangjing International Airport, and Zhang Yitang found numerous comments telling him to leave paper-writing to Xiao Yi.
• Zhang Yitang vowed to scold his critics, and he and Xiao Yi left the plane and stepped out into familiar surroundings in China.

After returning to China, Xiao Yi reunited with his parents for Lunar New Year and used his earnings to plan a new home for them. Once the holiday ended, he returned to school to set up his mining software server and apply for university startup support.

• Xiao Yi declined to present at the Mathematics Research Institute and flew back to Fei City on Lunar New Year's Eve.
• Xiao Yi reunited with Father Xiao and Mother Xiao, shared his recent experiences, and persuaded them to buy a home in Emerald Court with his earnings.
• Xiao Yi transferred twenty million yuan to his parents for the house and renovations after they visited relatives during the holiday.
• Xiao Yi returned to campus on the eighth day of the Lunar New Year and told Liu Bin he wanted to get his server running.
• Liu Bin gave Xiao Yi an entrepreneurship application form, and Xiao Yi applied for funding for Blockchain Technology Innovation Practice under the company name Yishui Technology.

Xiao Yi got his blockchain mining software approved for a university entrepreneurship space, then configured its server and launched a test with Boss Huang’s mining rigs. His overnight solo test unexpectedly earned 6.25 Bitcoins, leaving him eager to prove Yishui Bit’s algorithm at scale.

• Cao Nan approved Xiao Yi’s blockchain software project and showed him the university space for his server.
• Xu Ming and Junior Brother Hu discovered that the server they had hoped to borrow belonged to Xiao Yi.
• Xiao Yi configured the server and contacted Boss Huang to prepare his mining rigs for Yishui Bit.
• Boss Huang logged in with 3,000 mining rigs, and Xiao Yi confirmed the software was running normally.
• Xiao Yi saw that his overnight test had earned 6.25 Bitcoins, worth about 2.23 million yuan.

Huang Houping tested Xiao Yi’s Yishui Bit mining software and discovered that it raised his mining rigs’ earnings by about 86%. He switched his farm to the software, invested in cloud mining, and offered to pay and promote it, while Xiao Yi refused to sell the algorithm.

• Huang Houping ordered 3,000 mining rigs to join a mining pool through Yishui Bit and test its new algorithm.
• After the first block was mined, Huang Houping and his employees saw average earnings rise from 0.00031229 to 0.00058212 Bitcoin per rig and were stunned.
• Huang Houping monitored the results for about an hour, confirmed earnings stayed near 0.00058 Bitcoin, and ordered the farm to switch its rigs to Yishui Bit and rent cloud servers.
• Huang Houping offered to pay for the software and promote it to mining farms, but Xiao Yi said he would not sell the software or algorithm.
• Xiao Yi agreed to make Yishui Bit available for download in a few days, and Huang Houping offered to help spread the word among miners.

Xiao Yi agreed to let Luo Mingya's materials science research group rent his server and join their computational materials project. He also realized his server was nearing capacity as Huang Houping prepared to promote Xiao Yi's mining software.

• Xiao Yi accepted Huang Houping's offer to promote his software after granting the promised three free days.
• Luo Mingya and four graduate students from the School of Materials Science asked to rent Xiao Yi's server for their research simulations.
• Luo Mingya invited Xiao Yi to join her Computational Materials Science research group, and he agreed.
• Luo Mingya assigned Xu Ming responsibility for data processing, while Xiao Yi's server usage reached 78 percent.
• Xiao Yi explained his mining software project to the students, who were surprised that a major mining boss was already using it.

Xiao Yi visited Luo Mingya’s materials science laboratory and learned about its equipment and unusual advisor-student dynamic. Luo Mingya gave him tensile-test data from metal alloy samples, and he began analyzing it by proposing a Fourier Transform.

• Xiao Yi agreed to expand his server setup and help Xu Ming with data analysis, while Luo Mingya assigned Xu Ming lab cleanup duties for a month.
• Luo Mingya invited Xiao Yi to visit the School of Materials Science laboratory, where he saw her impressive academic poster and toured the lab with Zhao Yuanyuan.
• Xiao Yi watched Luo Mingya confront her advisor, Sun Lina, for playing a Switch instead of working.
• Luo Mingya gave Xiao Yi stress-strain data from alloy tensile tests and asked him to investigate why some samples were weaker.
• Xiao Yi said they should use a Fourier Transform to process the data.

Xiao Yi used Fourier analysis to identify unusual oscillations in Zhao Yuanyuan’s metal samples and linked them to lattice defects, helping Luo Mingya confirm the cause. The findings advanced the project, and Luo Mingya invited Xiao Yi to join research on defects in two-dimensional materials.

• Xiao Yi suggested converting the samples’ stress-strain data into frequency-domain spectra, and Luo Mingya led the students to analyze it on a computer.
• Xiao Yi and Luo Mingya found that abnormal samples had distinct oscillation peaks, and Xiao Yi connected them to possible lattice defects or dislocations.
• Luo Mingya inferred that lattice defects were responsible and directed Zhao Yuanyuan and the other students to conduct further experiments.
• Xiao Yi explained his reasoning to Xu Ming and Liu Chao, then quickly proved that pi cubed was greater than 31 using an estimate and a written calculation.
• Zhao Yuanyuan reported that the team had confirmed a lattice-defect problem and offered to buy Xiao Yi milk tea.
• Luo Mingya invited Xiao Yi to officially join the project studying defects in two-dimensional materials using Density Functional Theory and first-principles calculations.

Luo Mingya explained the lab’s WS2 nanomaterials project to Xiao Yi and asked him to review its computational algorithm. Xiao Yi proposed optimizations and began modifying the code, while Luo Mingya explained that the calculations required more computing power than the school’s old server could provide.

• Luo Mingya introduced TMD materials and described the project’s goal of calculating the optoelectronic properties of 2H/3R polytypes in WS2 nanomaterials.
• Sun Lina stopped playing Breath of the Wild after Luo Mingya threatened to complain about her, and the two joked about the lab’s funding and an expensive server.
• Xiao Yi asked about first-principles calculations and learned that the project involved quantum physics and computational materials science.
• Xu Ming showed Xiao Yi the lab’s theoretical model and algorithm, and Xiao Yi recommended a more efficient iterative solver, multigrid methods, and adaptive mesh refinement.
• Xiao Yi backed up the existing code and began modifying the algorithm for a small-scale test, while Luo Mingya explained that the calculations demanded more computing power than the school’s antique server could provide.

Xiao Yi optimized the lab’s algorithm and began studying computational materials science, while Luo Mingya’s team continued its research. He also watched his new server cluster being installed and received payment from Boss Huang, who reported strong interest in Yishui Bit.

• Xiao Yi optimized the lab’s algorithm, and a small-scale simulation showed over twenty percent better resource utilization along with improved convergence speed and accuracy.
• Luo Mingya teased Sun Lina with a recording, then the team returned to work on their projects while Xiao Yi began studying Density Functional Theory and related topics.
• Xiao Yi spent several days studying computational materials science and considered whether mathematical optimization could improve exchange-correlation functionals.
• Workers began assembling the five-million-yuan server cluster Xiao Yi had purchased at the startup center.
• Boss Huang told Xiao Yi he had transferred 1.5 million yuan in Yishui Bit usage fees and said he had promoted the software, with at least two hundred thousand mining rigs potentially set to use it.

Xiao Yi expanded his server capacity and arranged a possible data-center partnership as Yishui Bit prepared to launch. He then helped Luo Mingya improve her research calculations, leaving Xu Ming and Liu Chao amazed by his expertise.

• After Boss Huang predicted at least two hundred thousand Yishui Bit users, Xiao Yi ordered another three million yuan in servers from Manager Yu.
• Manager Yu suggested server hosting and financing, and Luo Mingya offered to connect Xiao Yi with her brother Luo Mingchuan, who ran a data center.
• Luo Mingya tested her research algorithm on the newly assembled server cluster, but the calculated energy-loss spectrum differed from experimental results.
• Xiao Yi suggested doubling the number of bands to account for bulk plasmon peaks, and the revised calculation produced results closer to the experimental values.
• Xiao Yi proposed doping, molecular dynamics, and mechanical-property simulations, leaving Xu Ming and Liu Chao stunned by how much he knew.