Recaps

Xiao Yi’s extraordinary mathematical ability brought him into USTC’s Young Scholars Program and drew the attention of Professor Liu Bin and Academician Hu Guangde. After topping a major joint exam, he secured permission and resources to organize his studies and pursue Hu’s challenge to write a mathematics paper before university.

• USTC students found Xiao Yi’s elegant solutions to Liu Bin’s blackboard problems, and Liu invited him to join the Young Scholars Program and pursue the Gifted Class.
• Xiao Yi’s teachers learned of his opportunity, and his parents approved his application while Liu Bin waited for the monthly exam results.
• Xiao Yi earned 700 points and first place in the grade, including perfect scores in mathematics, physics, and chemistry, and Liu Bin brought him advanced mathematics books.
• Xiao Yi rapidly studied advanced mathematics, impressed Hu Guangde by identifying an error in a research paper, and accepted Hu’s challenge to write a paper suitable for a domestic Core Journal before enrolling.
• Xiao Yi ranked first in the Nine Provinces Joint Examination with 725 points, and Principal Liu Songlin agreed to let him arrange his study time and use a self-study room.
• Liu Songlin approved Xiao Yi’s request to use a computer and phone, awarded him a scholarship, and agreed to cover the paper’s publication fees before taking him and Luo Penghua to the flag-raising ceremony.

Xiao Yi topped the Gaokao, chose USTC, and proved a difficult conjecture in an independently written paper that drew attention from leading mathematicians and IHES. As his paper entered expert review, he sat USTC’s joint mathematics exam and quickly worked through problems drawn from famous research papers.

• Principal Liu announced Xiao Yi’s first place in the Nine Provinces Joint Examination and presented him with a 10,000-yuan scholarship, after which Xiao Yi arranged to study independently.
• Xiao Yi chose a difficult number theory topic involving the Absolute Remote Abelian Conjecture and promised his classmates he would become the Gaokao top scholar.
• After Xiao Yi scored 741 and topped the science stream, he committed to USTC’s Gifted Class despite recruitment visits from Shangjing University and Tsinghua University.
• Xiao Yi finished a 25-page proof of the Absolute Remote Abelian Conjecture, and Professor Liu Bin and Academician Hu Guangde confirmed its rigor and value.
• Xiao Yi translated the paper and submitted it to Publications mathématiques de l'IHES, where Editor Evans and Editor-in-Chief Bojielun sought Peter Scholze’s review.
• Xiao Yi prepared for USTC’s joint mathematics exam, which required applicants to identify methods in research papers and apply them to new problems.
• Xiao Yi solved the morning exam’s three questions in twenty minutes, astonishing Professor Xu and the other examinees.
• During the afternoon exam, Xiao Yi recognized excerpts from Chen Jingrun’s Goldbach Conjecture work and Zhang Yitang’s Twin Prime Conjecture paper, then began answering while Ye Cheng struggled with the first passage.

Xiao Yi’s paper drew international attention and brought him to a conference where he identified the flaw in Shinichi Mochizuki’s IUTT theory. After the mathematical community praised his work, Xiao Yi sought advice on his twin-prime research and returned to China to give a report.

• Xiao Yi finished the USTC examination early, and Wang Jianxin recognized that his solution improved Zhang Yitang’s twin-prime method.
• Peter Scholze confirmed Xiao Yi’s paper was correct and valuable, and IHES accepted and published it online.
• Xiao Yi ranked first in the joint examination, completed USTC’s interview, and received Peter Scholze’s invitation to a conference in Germany.
• At the conference, Xiao Yi showed that Mochizuki’s Hodge Theater reasoning conflicted with the Mochizuki Theorem, and Mochizuki admitted IUTT theory did not hold.
• Mochizuki apologized for the dispute over his theory, while Faltings offered Xiao Yi advice on his Twin Prime Conjecture research.
• Xiao Yi explained his mathematical achievement to international media and discussed approaches to the Elliott-Halberstam Conjecture with Faltings, Deligne, Bombieri, and Schultz.
• Xiao Yi returned to China with Hu Guangde, agreed to report on the conference and Mochizuki’s theory, and remembered that he needed to email Professor Maynard.

Xiao Yi connected Far Abelian Geometry with Automorphic Forms, proved the Elliott-Halberstam Conjecture, and developed a sieve theory that he used to claim a proof of the Twin Prime Conjecture. His papers passed review, and he accepted an invitation to present his sieve at Princeton as mathematicians awaited a definitive assessment of his proof.

• Xiao Yi emailed James Maynard a proposal that raised θ to 0.65, then developed the connection between Far Abelian Geometry and Automorphic Forms for his lecture in China.
• Xiao Yi presented his new functor and showed how the Kuznetsov Trace Formula raised θ to 0.75, announcing that he would soon publish a proof of the Elliott-Halberstam Conjecture.
• Xiao Yi uploaded his papers, and Bombieri, Deligne, Maynard, Tao, and other mathematicians judged his proof correct and explored its implications for prime gaps.
• Xiao Yi returned to USTC, where Peter Sarnak invited him to submit his papers to Annals of Mathematics and leading mathematicians began reviewing them.
• During Liu Bin’s class, Xiao Yi used the Selberg Sieve in a third solution and began investigating how sieve methods could address the Twin Prime Conjecture.
• Xiao Yi developed a classification of the parity problem in sieve theory, attracting attention from mathematicians including Tao Quan, Henrik Iwaniec, and Zhang Yitang.
• Xiao Yi completed a proof claiming that infinitely many twin prime pairs existed, reached lv4, and wrote the paper “Parity Check Classification Sieve and the Twin Prime Conjecture.”
• Zhang Yitang verified Xiao Yi’s sieve method and used it in his own research, while Princeton arranged a special presentation and Sarnak invited Xiao Yi to deliver a lecture there.