Terence Tao

Biodata

Feature	Information
Name	Terence Tao (陶哲轩)
Alias(es)	Professor Tao
Gender	Male
Affiliation	UCLA 109 110
Occupation/Role	Mathematician; professor; reviewer of major mathematical work 91 110
First Appearance	Mentioned in Chapter 7 7

Background / History

Terence Tao is initially invoked as a benchmark for the difficulty of an IMO problem that Xiao Yi solves under Liu Bin's guidance; the problem is described as one Tao could not solve. 7

As Xiao Yi's work gains international attention, Tao becomes one of the prominent mathematicians evaluating, discussing, and publicly responding to its implications. He later hosts Xiao Yi at UCLA for research discussions following the Princeton Annual Mathematics Conference. 87 109 110

Personality

Tao is intellectually curious and willing to openly seek insight from Xiao Yi. After Xiao Yi presents his proof concerning Navier–Stokes solutions, Tao asks how Xiao's Space was derived rather than simply treating the result as an opaque achievement. 223

He retains a competitive, youthful drive toward difficult problems. Following political pressure surrounding the Riemann Hypothesis, he responds with frustration and renewed determination to tackle the challenge. 278

Tao also shows frank admiration for exceptional work. He describes Xiao Yi's Riemann Hypothesis proof as a work of art and acknowledges that Xiao Yi's mode of thought exceeds his own capabilities. 264 286 287

Abilities & Skills

Mathematical Research

Tao is an active researcher capable of assessing advanced work in number theory, PDEs, and problems connected to the Riemann Hypothesis.

• Discusses the consequences of Xiao Yi's proof of the Elliott–Halberstam conjecture for prime-number problems with James Maynard. 87
• Serves on the high-level review committee for Xiao Yi's papers submitted to the Annals of Mathematics. 91
• Proposes combining elliptic inverse analytic continuation with the Artin Conjecture as an approach to the Riemann Hypothesis, though he finds the route extremely difficult. 279
• Quickly studies Xiao Yi's Hailstone Conjecture paper and publishes a blog post praising its innovative approach and relevance to the Langlands Program. 264

Interdisciplinary Communication

During the UCLA research project, Tao helps translate highly abstract mathematical ideas into practical implications for computer-science problems.

• Explains Xiao Yi's solutions concerning classification-sieve attacks and secure cross-chain transactions to Professor Leonard Kleinrock. 114
• Works with Xiao Yi and Maynard on research involving information security, blockchain transactions, and cryptographic applications. 110 113 115
• Reacts with Maynard to the computer-science community's intense interest in Xiao's Polynomial Expansion. 123

Relationships

• Xiao Yi — Fellow mathematician, collaborator, host, and admirer. Tao houses Xiao Yi at UCLA, researches with him, publicly supports his work, and seeks to understand Xiao's methods. 109 110 223 264 287
• James Maynard — Research collaborator and discussion partner; they jointly examine the implications of Xiao Yi's number-theory breakthroughs and work alongside Xiao Yi at UCLA. 87 110 123
• Professor Leonard Kleinrock — Interdisciplinary collaborator during the multiparty-security and cross-chain transaction project; Tao helps explain the mathematical solutions to him. 110 114
• Enrico Bombieri — Fellow reviewer of Xiao Yi's Annals of Mathematics submissions and one of the mathematicians discussing Xiao Yi's work. 87 91
• Pierre Deligne — Fellow reviewer and mathematician who joins Tao in discussing Xiao Yi's later Navier–Stokes achievement. 91 213
• Zhang Yitang — Shares responsibility for guiding Xiao Yi during his United States stay after the Princeton conference. 109

Story Role / Major Arcs

Evaluation of Xiao Yi's Early Breakthroughs

Tao joins Maynard in assessing Xiao Yi's papers on the Elliott–Halberstam conjecture and related prime-number questions. He considers possible extensions of Xiao Yi's theory while recognizing limits to its use on the Twin Prime Conjecture. 87

He is subsequently named to the high-level committee reviewing Xiao Yi's papers for the Annals of Mathematics. 91

UCLA Collaboration

Following Xiao Yi's Twin Prime Conjecture presentation, Tao arranges a UCLA dormitory for him and plans research discussions. 109

At UCLA, Tao, Maynard, and Xiao Yi collaborate on mathematical proofs and on the security implications of the Parity Check Classification Sieve. 110 Tao later assists Kleinrock in understanding Xiao Yi's countermeasures against sieve-based attacks on RSA encryption and the proposed cross-chain transaction protocol. 114

Riemann Hypothesis Competition

Tao reacts strongly to the U.S. President's confidence that American mathematicians can solve the Riemann Hypothesis, treating it as a challenge worth pursuing. 278

Within the Prime Pioneer Project, he proposes an approach combining elliptic inverse analytic continuation with the Artin Conjecture, but cannot overcome its complexity. Other researchers regret that Xiao Yi is not part of the project. 279

After Xiao Yi publishes five papers proving the Riemann Hypothesis, Tao is among the first mathematicians to publicly endorse the work, calling the papers works of art and expressing confidence in the proof. 286 287

Later Recognition of Xiao Yi's Work

Tao is interviewed in support of Xiao Yi following Xiao Yi's Fields Medal win. 176

He later acknowledges the perfection and significance of Xiao Yi's generalized proof of the Navier–Stokes equation with Maynard. 214 At Xiao Yi's report on the proof, Tao directly asks about the conceptual origin of Xiao's Space. 223

When Xiao Yi solves the Hailstone Conjecture, Tao immediately reads the paper and publicly praises its originality and importance. 264