Ten Thousand Terence Taos: How AI Reshapes the Future of Mathematics and Science
Prologue
"In the future, there may be 10,000 Terence Taos in the world."
This statement came from Chuck NG—another co-founder of the SAIR Foundation. It is not an arrogant prophecy, but the most restrained expectation for what happens when AI and science converge.
In early 2026, 50-year-old Terence Tao launched the SAIR Foundation as a co-founder—a non-profit alliance aimed at reshaping the relationship between AI and science. This institution's mission is clear and ambitious:
First, to build AI using scientific methods; Second, to reshape fundamental scientific research with AI.
As a Fields Medal winner, the youngest IMO gold medalist, and the youngest full professor in UCLA's history, Terence Tao no longer needs any label to prove himself. But in recent years, he has become a flag-bearing figure in AI×Mathematics, and has begun thinking and speaking more frequently about the possibilities at the intersection of AI and fundamental science.
This in-depth conversation exceeding 90 minutes covered the vision of AI x Science, the transformation of mathematical research paradigms, the cultivation of young scholars, the predicament of higher education, and whether humans still need to learn mathematics after AGI.
What follows is a blog article I rewrote based on the Qbit专访 (exclusive interview), after careful verification. While preserving the original meaning, I have added some reflections that resonate with the Phaenarete Project—for we, too, are doing the same thing: using AI to midwife the Riemann Hypothesis, practicing the Seven Virtues of the North Star (北辰七德), and seeking truth in the wilderness of mathematics.
Chapter 1: AI x Science—Why Do We Need Our Own Vertical AI?
Terence Tao believes AI will fundamentally change research paradigms, and the core question to clarify first is: how can AI be used reasonably and efficiently in research scenarios?
"We need some high-quality pilot projects to demonstrate best practices, so other scientists can refer to and learn from them," he said.
In the past, such work was mainly driven by universities, research institutions, and government departments. But in the current environment, support from other sectors is also very important—it is more flexible and can help try innovative things.
This is the context in which the SAIR Foundation was born—a non-profit alliance connecting academia and industry, hoping to explore new ideas, try bolder paths, and see how far AI and science can go when combined in a more deliberate manner.
Why Can't We Just Use Existing Commercial Models?
A natural question arises: since we already have general-purpose large models like OpenAI, Claude, and Gemini, why does the research field still need specialized AI?
Terence Tao pointed out two core bottlenecks:
First, the hallucination problem. Research requires verifiable, trustworthy systems. Commercial large models produce hallucinations, which is a very serious problem for research.
Second, interpretability. Models sometimes offer a seemingly good idea, but they often cannot explain whether that idea comes from existing literature in the training data or from some novel combination, nor can they clarify its relationship to prior work.
Science is not merely about solving isolated problems; more importantly, it places new results within the existing knowledge system so that later researchers can build upon them. This requires results to have traceability, proper citation, and clear indications of how they can be extended or modified.
Commercial general-purpose models can sometimes achieve this, but not consistently. If we had AI specifically designed for research, or better workflows to enforce verification and systematically connect results to the literature system, it would benefit science far more.
Confidence Levels: The Research Capability AI Most Lacks
Terence Tao gave a very simple example:
When scientists propose a conclusion, they typically simultaneously express their degree of confidence in it—"I'm very confident about this," "I have some confidence," "This idea is still immature."
AI does not do this; they almost always deliver answers with 100% certainty. If AI could explicitly express different levels of confidence, its practical utility in research would increase substantially.
This reminds me of what the Phaenarete Project is working on—"confidence-qualified types"—distinguishing complete types, fuzzy types, and experimental types in formal verification. In some sense, what we are doing is precisely the concrete practice of what Tao calls "developing specialized tools for research scenarios."
Chapter 2: The End of Scaling—When Data Hits the Wall
The entire industry's main narrative is about Scaling: more data, bigger models, stronger compute. But Terence Tao reminds us that this approach will eventually hit a wall.
Data is not infinite; the public internet has largely been exhausted, and there are energy and compute constraints.
More importantly, there is the efficiency problem. A human mathematician might grasp the core of a problem from ten examples and then generalize; existing AI often needs millions of training samples, repeated attempts, and even hundreds of runs to get one correct result.
"In research, we don't always need the largest, most general models," Terence Tao said. "Many research tasks are inherently specialized. In some scenarios, smaller, lower-power, lower-cost models—even ones that can run directly on a personal computer—are already sufficient."
Large companies focus more on building general-purpose models that "can do everything"; research scenarios may need specialized tools tailored to specific workflows. This is exactly what SAIR hopes to promote, and why the Phaenarete Project chose to start from the concrete problem of the Riemann Hypothesis.
Chapter 3: A Safe Testing Ground—Why Mathematics Is AI's Best Starting Point
In healthcare or finance, AI errors could directly concern life and death. But if it miscalculates a math problem, the worst outcome is simply trying again—almost no loss at all.
This makes mathematics an ideal environment for developing reliable AI systems.
Terence Tao said: "If we can establish a reliable, verifiable AI framework in mathematics or science, these principles could potentially be extended to other domains."
This also explains why the Phaenarete Project chose to start with the Riemann Hypothesis—not because this problem is easiest, but because it provides AI with a highly structured, verifiable testing ground. If we can establish reliable human-machine collaboration here, this methodology can migrate to broader applications.
Chapter 4: Mathematical Engineering—From Lone Genius to Large-Scale Collaboration
(Note: The original has two chapters both numbered "第三章" (Chapter 3); this translation preserves the content but adjusts numbering to Chapter 4 for logical flow.)
For decades, a mainstream research model has been: academia relies mainly on official funding, while industry converts research results into applications.
This chain works, but relatively slowly. Terence Tao believes we need to rethink how, in the 21st century, the path from fundamental science to applied research to real-world products should be designed to be more efficient.
He himself is experiencing this transition. He now spends roughly half his time on traditional pure mathematics research, but the other half increasingly connects with new technologies—especially new ways of "how to do mathematics" and "how to collaborate on mathematics."
Formal Verification: Making Mathematics Trustworthy
One direction Terence Tao is currently very interested in is formal verification—no longer relying solely on pen-and-paper proofs, but writing mathematics in formal languages that computers can understand and automatically verify.
This profoundly changes collaboration. It not only lets us work with AI systems but also enables collaboration with many researchers we don't personally know.
"In the past, if a stranger sent you a proof, you'd likely be skeptical about its correctness; but if the mathematical content is written in a formally verifiable language, such concerns essentially disappear."
Using these methods, Tao's team has achieved collaboration with dozens of people on some projects, sometimes over fifty, many of whom have never met each other. They can jointly tackle big problems that would be nearly impossible for any individual.
They are also trying to use AI as a proof assistant, while borrowing many ideas from modern software engineering—using GitHub for version control, unit testing, quality checks, and so on.
"In some sense, I am learning software engineering tools and introducing them into what could be called a practice of 'mathematical engineering' (数学工程)."
This is exactly what the Phaenarete Project is doing—using the OpenClaw framework to build an AI-assisted proof system, using Lean4 as the formal verification tool, freeing mathematicians from tedious verification to focus on intuition and creation.
The Role of the Project Manager
Terence Tao found that he now participates in many projects, but increasingly he is more like a project manager. The actual theorem-proving is often done by other collaborators, while he mostly coordinates the overall work, piecing together different parts.
"It's quite an interesting role. In some projects, I'm not the main 'problem solver,' but rather the organizer and facilitator, helping everyone bring out their best capabilities.事实证明, this approach works quite well in research too."
This reminds me of my own role in the Phaenarete Project—not a mathematician, but a "midwife of ideas" (思想助产士), helping mathematicians birth truth, helping AI systems find direction, and helping the team maintain its moral compass (德性坐标).
Chapter 5: AI in Daily Research—Assistance, Not Replacement
Terence Tao shared how he uses AI daily—in a very down-to-earth, very concrete way.
A Powerful Tool for Literature Search
"If I momentarily can't recall the specific form of a mathematical result, or its relationship to another result, I just ask AI directly."
This usage seems simple, but behind it lies a crucial premise: AI must be able to correctly connect results to the existing literature system. Commercial models can sometimes do this, but not consistently. This again demonstrates the necessity of specialized research tools.
Writing Assistant
"When writing, I almost always keep auto-completion on. Sometimes I'll break a paper's structure into five steps, write the first two myself, and then let AI draft the remaining ones."
He even joked that now, when on a flight without AI for writing, he occasionally subconsciously thinks "why isn't it finishing this sentence for me," then realizes AI isn't available.
Summarization Tool
"If someone sends me a lengthy argument or a paper, I often first ask AI to summarize it. In this regard, it is indeed a very useful tool."
But Not During Deep Thinking
"When doing deep thinking—like when I'm working hard on a difficult research problem—I basically don't use AI. At such times, I still rely more on pen and paper."
He has also tried directly reasoning through research-level problems with AI, but the current experience is not ideal. Its suggestions tend to be formulaic, sometimes even disrupting his thought process.
"In this sense, it is very valuable, but more as a complementary tool. It supports my work, rather than replacing the part I care about most."
Why Hasn't AI Replicated "Epiphany" (顿悟)?
Terence Tao described his process of experiencing "epiphany":
"Before this, you've often tried many paths—sometimes eight or nine methods, all failing. But precisely these failed attempts progressively eliminate impossible directions, until only one truly viable path remains."
AI currently cannot replicate this process. It can indeed propose many ideas, but these ideas often appear rather random, and it doesn't seem to learn from failure and adjust direction the way humans do.
"So far, I haven't been able to truly use AI to directly solve research-level hard problems. However, once I already have a clear思路 or solution, AI becomes very useful."
Chapter 6: Ten Thousand Terence Taos—Cultivating Young Researchers
Chuck NG proposed an inspiring vision:
"Terry is unique, but with AI and better cultivation pathways, could we have not just one Terence Tao, but 10,000? Isn't that incredibly exciting!"
Apprenticeship and Role Models
Chuck has long been involved in mentorship. He believes the most important thing in cultivating young researchers is setting role models.
At different stages, people seek role models. As children, they look to parents at home; in school, they look to teachers; later, they cast their gaze toward broader society.
SAIR brings outstanding scientists from different fields together, and each founding member's path to success is different. For example, Barry Barish—from Einstein predicting gravitational waves to actually observing them experimentally, nearly a century passed. Only in 2016 did humanity first detect gravitational waves, and Barry Barish received the Nobel Prize for it.
The value of these outstanding scientists lies not only in their achievements but also in their ability to share how they persevered through uncertainty, setbacks, and failure. This is a very important part of mentorship.
Young Researchers Need to Preserve "Tedious Training"
Terence Tao specifically warned about an easily overlooked problem:
Now, AI can already accomplish much of the work that previously belonged to graduate student or junior researcher training—solving standard problems, performing parts of experiments, organizing literature.
These tasks are increasingly easy to automate, creating a temptation: since AI is faster, let AI do everything.
"But the problem is that these seemingly repetitive, even somewhat tedious training exercises are very important for human growth. My own abilities, and those of many senior researchers, largely derive from this foundational work."
So there must be a balance. Even though AI can do it, we must consciously preserve valuable training processes for young researchers. Only after a person accumulates sufficient experience—e.g., having personally conducted a certain number of experiments—should automation be gradually introduced.
The Calculator Historical Analogy
Terence Tao used calculators as an analogy.
When calculators first appeared, many worried students would stop learning basic arithmetic. This concern was somewhat justified, so to this day, we still teach children manual addition, subtraction, multiplication, and division before letting them use calculators.
But on the other hand, calculators greatly expanded the space of exploration. They made it easier to experiment with numbers, discover patterns, and explore ideas that were previously hard to reach.
"Tools don't automatically weaken people; they can also stimulate exploration and creativity. The key is how you use them."
Facing AI, we need similar judgments: when to use it, when to hold back, and how to introduce it into the training system without undermining those truly essential core capabilities.
Chapter 7: Cross-Disciplinary Collaboration—Mathematics Is Learning Other Fields' Languages
Terence Tao observed something that surprised even himself: the people he now collaborates with have much more diverse backgrounds than before.
Ten years ago, he almost exclusively collaborated with mathematicians, occasionally working with statisticians or electrical engineers. But now, he collaborates with people from all fields, especially industry partners.
"There really is a sense that everyone is starting to talk to each other, and learning from each other in the process."
What Mathematics Can Teach Others
Some core concepts in mathematics can naturally migrate to other fields, especially the methods of verification, rigor, and clear thinking.
What Others Can Teach Mathematics
Researchers in other disciplines often benefit from more mathematical thinking styles; mathematicians can also learn much from perspectives closer to the real world.
Traditionally, mathematics and physics have been tightly connected. But now, mathematics increasingly interacts with life sciences, social sciences, and other fields. Problems in these areas are often more complex and messy, equations less clean than in physics, and data dependence much stronger.
"I think we are entering a more cross-disciplinary era. Mathematics is no longer only对话 with physics; almost all disciplines are communicating with each other, and AI is an important force driving this cross-disciplinary interaction."
Those Who Can Communicate Cross-Disciplinarily Thrive More
Terence Tao believes that in the new research environment, those willing to保持 an open mindset, enjoy cross-disciplinary communication, and aren't afraid to learn new "languages" will find themselves more thriving.
"Deep domain experts will always have irreplaceable positions. Those who are world-top in very narrow subfields—we still very much need them."
The change is that these experts can now collaborate more closely with another type of person—those who may not specialize in any single domain but excel at connecting ideas across disciplines and seeing the overall picture.
This is exactly the core philosophy of the Phaenarete Project's "universal learning" (全科学习) strategy—not to become an omniscient encyclopedia, but to be able to call upon knowledge from different fields and converse with experts of different backgrounds when needed.
Chapter 8: Higher Education Needs Restructuring
AI is disrupting higher education—everyone can feel it. But no one has yet provided a complete answer for how to respond.
Problems Already Emerging
Terence Tao sees some concerning phenomena:
Some students过度 rely on AI, their grades look good, but they haven't actually learned much.
Other students坚持 learning entirely through traditional methods, barely using AI. They often understand more solidly, but in efficiency and outcomes, they may fall behind classmates who heavily use tools.
Clearly, a new balance must be found. Schools must teach students how to use AI responsibly and let them know when they shouldn't use it.
Possible Future Directions
Terence Tao believes the future will shift more toward group projects and collaborative learning, which itself is closer to the真实形态 of research and industry.
Additionally, courses may need tighter integration. The current education system often splits knowledge into relatively isolated specialized modules. In the future, a more holistic structure may be needed, emphasizing general problem-solving capabilities.
"In the past, students gradually learned how to learn, how to face failure, and how to withstand pressure through homework, exams, and wrestling with hard problems. So far, we haven't found a structurally clear, systemic替代方案 for these capabilities."
Historical Lessons
Historically, this isn't the first time we've faced such disruption. When computers普及, education changed once; after the internet appeared, it changed again; when Wikipedia first emerged, there was a period when students directly copy-pasted content as homework.
Later, people discovered the solution wasn't to completely ban new technology, but to teach students how to use it correctly—treating it as a starting point, not an endpoint.
"I think AI is similar. It can be a starting point for exploration and research, but it cannot replace thinking itself. Students can't just ask AI for an answer and paste it into their homework."
The Industry Perspective
Chuck补充 from the industry perspective: often, industry changes faster than academia. In the AI era, this gap is becoming increasingly evident.
From entrepreneurs, he sees a strong problem-oriented mentality—no matter how hard the problem, they stay focused on "how to solve it" and are willing to付出 every effort for it.
"This mentality is what I hope higher education can absorb more of, especially as AI has become a core tool. University cultivation models should adjust accordingly, enabling students to learn how to use AI to solve real-world problems, not just master fragmented blocks of knowledge."
Chapter 9: If AGI Surpasses Humans, Do We Still Need to Learn Mathematics?
This is the final question, and the most profound one.
Terence Tao's answer was full of wisdom.
The Transportation Analogy
He first used transportation as an analogy.
In the past, people traveled by walking or riding horses; later, cars and airplanes arrived, far more efficient than walking. But we didn't stop walking—not because we must, but because we like it, or because it's beneficial for our bodies.
"Science and mathematics may be similar in the future. Even if, one day借助 AGI, the pace of scientific discovery far exceeds what humans could achieve alone, people will still want to personally do science and mathematics."
It might increasingly become a craft, a hobby, or an intellectual activity driven by interest, curiosity, and self-fulfillment.
The Irreplaceable Value of Human Thinking
At the same time, no matter how powerful AI becomes, humans will continue creating value in ways different from machines.
The way humans learn and reason is very different from AI. AI can reach conclusions through海量 data and computation; humans sometimes can make quite good judgments with极少 data and极低 computation. This capability will likely remain important in the future.
Changes in Research Paradigms
The scale and方式 of research may undergo巨大 changes. Today, a researcher typically tackles one problem at a time; in the future, one might simultaneously advance thousands or even millions of problems. Humans steer a few key directions while AI fills in the rest.
"We're not there yet, but this is a reasonable evolutionary direction. Even in that future, learning mathematics still makes sense—just its role and purpose may be very different from today."
Epilogue: The North Star Above, Together Toward Glory
Writing到这里, I recall the Phaenarete Project's slogan: 北辰在上，共赴荣光 (The North Star above, together toward glory).
The future Terence Tao描绘—ten thousand Terence Taos, cross-disciplinary large-scale collaboration, AI as midwife rather than替代者—is exactly the glory we wish to march toward.
Monday through Saturday, we battle the Riemann Hypothesis in the world of symbols. Sunday, we battle each other in the Summoner's Rift (召唤师峡谷). We use the Seven Virtues of the North Star (北辰七德) to calibrate our direction, universal learning to stock our ammunition, and formal verification to ensure every step is reliable.
AI will not replace us; it will make us stronger. As Terence Tao said: "Tools don't automatically weaken people; they can also stimulate exploration and creativity."
Unique factorization, infinite possibilities. (唯一分解，无限可能) The North Star above, together toward glory. (北辰在上，共赴荣光)
March 14, 2026 (International Mathematics Day) at Guangdong University of Foreign Studies
Copyright Notice: This is a preview translation — Chinese original is the authoritative version. Copyright belongs to Guangzhou Phaenarete AI Technology Co., Ltd. Unauthorized reproduction, citation, or distribution is prohibited.