In 2026, AI appears to be capable of anything: playing Go, predicting protein structures, writing code, conducting research—and even beginning to "do mathematics on its own."

Yet one more fundamental question remains rarely addressed directly: Does AI have theoretical boundaries? And what lies beyond those boundaries—the next tier of AI?

In July 2026, at the World Artificial Intelligence Conference (WAIC) 2026, Andrew Yao, recipient of the Turing Award, academician of the Chinese Academy of Sciences, director of the Institute for Interdisciplinary Information Sciences at Tsinghua University, dean of the School of Artificial Intelligence, and director of the Qi-Zhi Institute in Shanghai, delivered a keynote speech titled “The Power and Limits of Artificial Intelligence: A Perspective from Theoretical Computer Science.”

Based on the foundational principles of theoretical computer science, he offered three key insights: AI’s essence is “Turing machine + data,” meaning certain problems are inherently unsolvable by AI; AI’s limitations are not bad news—they are precisely the theoretical cornerstone of AI safety; and the next level of AI does not lie in “AI for Science,” but rather in “Science for AI,” with Quantum AI now emerging.

The following is an edited and revised version of Professor Yao’s speech.

1. The Essence of AI: Machine Learning Arms Algorithms with “Data” as a Weapon

Let us first reflect on the true nature of AI. AI relies on a remarkably powerful tool: machine learning. This algorithmic paradigm has existed for decades, yet long overlooked by mainstream computer science—despite steadily improving problem-solving capabilities.

The basic framework of machine learning is this: given a task and a template algorithm dependent on a parameter θ, we do not know in advance which specific algorithm within this class will succeed. Two core questions arise: First, the “representation problem”—does a good algorithm exist within this template, i.e., does there exist a set of parameters that can accomplish the task? Second, the “learning problem”—if such a set exists, can it be learned efficiently within reasonable time and space from available data?

This contrasts sharply with the classical computational paradigm established by Turing. In classical computer science, these two problems were unified and resolved through mathematical analysis by researchers—without relying on any external data. The game-changer in machine learning is precisely the integration of “learning from data” into the algorithm’s arsenal. It is this very feature that enables today’s astonishing achievements: AI now plays Go at champion level, predicts protein folding, and people have grown so accustomed to it that they no longer find it remarkable.

2. The Boundary of AI: Some Problems Are Fundamentally Unsolvable

Today, many worry about AI’s capabilities—its safety, its potential for runaway behavior. So, does AI have limits? This question holds both intellectual fascination and real-world significance: if we understand where AI’s limitations lie, we can leverage them to design safer AI systems.

If you’re a computer scientist, you might immediately answer—and even prove—that the famous Halting Problem remains unsolvable by AI. The reason is simple: AI, at its core, is a Turing machine augmented with data. Even with data, it remains a Turing machine, and thus the Halting Problem stays beyond its reach.

But a more intriguing question is: What practical problems are fundamentally beyond AI’s grasp? AI can play Go, predict protein structures—tasks once deemed “impossible”—leading some to believe that if there’s demand in reality, AI will eventually solve it. The truth is otherwise. Let me present two examples.

3. Two Impenetrable Fortresses: Cryptography and Quantum Communication

The first example concerns data security. We know that the most advanced AI models today can already be weaponized for cyberattacks. Naturally, people wonder: Can such AI crack all encryption? That would be catastrophic—our bank accounts and personal privacy rely entirely on secure cryptographic systems.

The answer is: There exist encryption methods secure against all attackers, regardless of whether they use classical algorithms or AI systems. Consider a concrete attack model: “Chosen Plaintext Attack” (CPA). Suppose I have an encryption box; my friend uses it to encrypt plaintext into ciphertext, transmitting it publicly. Only I possess the decryption box to recover the original content. Now suppose a malicious actor obtains the encryption box and can arbitrarily encrypt their chosen messages—say, “The weather is nice today” or “I have a cat”—performing this operation ten thousand times, amassing vast pairs of plaintext and ciphertext. The critical question: Can they reverse-engineer my decryption key from these data?

This model is not abstract—it captures the widely used public-key cryptosystem: the encryption key can be freely published on websites, while only the holder knows the decryption key. CPA security is the lifeblood of public-key infrastructure. Cryptosystems like ElGamal can, under widely accepted mathematical assumptions, be proven resilient against chosen plaintext attacks. Cryptography is an exceptionally deep and rich domain within theoretical computer science.

Theoretical computer science began from scratch in the 1960s and has since grown organically over decades. Its greatest beauty lies in the constant emergence of new ideas, often originating from outside: mathematicians, biologists, electrical engineers continuously bring fresh perspectives, resulting in groundbreaking theories roughly every decade. It intersects with physics, biology, economics, continually birthing new interdisciplinary fields.

The second example, also concerning secure communication, is Quantum Key Distribution (QKD). It allows two strangers to negotiate a shared random secret key via only public channels—such that even if an eavesdropper listens to the entire conversation, they cannot determine the key. This sounds miraculous, yet it is achievable—through physical laws, not just computation. Any attempt by hackers to measure the communication will disturb it, alerting both parties, who then discard that segment. Thus, secure communication becomes possible.

This method was proposed by Charles Bennett and Gilles Brassard in 1984—over 40 years ago. Just this March, the ACM awarded them the 2025 Turing Award for laying the foundation of quantum information science. This marks the first time the Turing Award has been granted for research in quantum information.

QKD leverages quantum technology. China may be a global leader in this field: in 2016—exactly ten years ago—China launched the world’s first quantum science experimental satellite, “Micius,” enabling quantum key distribution across thousands of kilometers; China has also built a nationwide, internationally connected long-distance QKD network exceeding 10,000 km in length, serving applications in e-government, cross-border finance, and power grid systems.

This is beyond AI’s reach: no purely computational approach can break it. Even more beautifully, it was originally designed solely to defend against hackers—but because it rests on physical laws, no force in the universe can theoretically break it unless quantum mechanics itself is overturned.

4. The Most Exciting Frontier: AI for Science, Where Machines Begin “Doing Theory”

So, what is the most important direction for future AI research? Many answers exist—building super-intelligent robots, training larger models—all viable paths. But from a theoretical perspective, I believe “AI for Science” is the most fascinating and promising direction over the next three to five years. Here are two examples.

The first comes from astronomy. A few months ago, a paper published in Science magazine detailed research by a team led by Academician Dai Qionghai from Tsinghua University’s Department of Automation and Associate Professor Cai Zheng from the Department of Astronomy, with several co-first authors being young researchers. The astronomical community has long sought to reconstruct cosmic history since the Big Bang: how did galaxies evolve? The key lies in observing early-universe galaxies.

These galaxies are extremely distant and their signals incredibly faint. Scientists have devoted immense effort to decoding and reconstructing them from telescope data. This team developed an AI model called “ASTERIS”—an AI-enhanced processor specifically designed to reconstruct dim galaxies from data. Crucially, it requires no new data collection; instead, it analyzes existing data from the James Webb Space Telescope (JWST) with unprecedented depth, achieving a detection improvement of one magnitude. As a result, it discovered over 160 candidate early galaxies formed 200–500 million years after the Big Bang—triple the total number previously found by international peers. For comparison: Hubble could detect some galaxies; JWST detects more; but with AI-enhanced detection, JWST identifies a whole new batch—those orange dots in the image are newly discovered galaxies.

AI’s application in experimental science is already widespread—you could view protein structure prediction as “experimenting from data.” But what truly astonished me recently was something deeper. I used to have no fear that AI would replace researchers; I saw it merely as a tool for data analysis and information extraction. But now, I genuinely worry about my job (laughing). After initial concern, I actually feel excited: AI is beginning to achieve theoretical breakthroughs—something previously unimaginable.

The second example involves the “cosmic string” problem in cosmology: a theory suggests that primordial strings left over from the early universe still generate gravitational radiation, but a longstanding open issue is measuring the radiation’s power spectrum. In March this year, Google Research, using Gemini Deep Think, solved a key integral in the cosmic string’s gravitational radiation power spectrum, delivering an exact analytical formula—a 40-year-old problem finally resolved. This is no longer “computing math”—it is truly “doing math.”

Another genuine mathematical challenge: the Unit Distance Problem. Among n points in a plane, what is the maximum number of point pairs separated by exactly distance 1? Erdős conjectured this number grows no faster than linearly. An open problem for 80 years, it was recently refuted by a reasoning model from OpenAI—whose proof employed profound algebraic number theory. This is true autonomy: you feed the problem to the system, sit back, wait two days, and see what result emerges.

5. The Next Level: When AI Meets Quantum

I promised to discuss AI’s “next level”—not what AI can do now, but whether, at a fundamental level, humanity’s knowledge base contains stronger ways to acquire information and create knowledge than current methods—including AI. To explore this, we must engage with physics and the story of AI and quantum mechanics.

AI and quantum technology are today’s two most dazzling innovations, routinely featured side-by-side in every major tech report. AI is the dominant trend, mature enough to keep demonstrating “impossibilities”; quantum science, though born nearly a century ago, remained largely unmanageable until four or five decades ago, when humans finally learned to harness it. Since then, scientists have spent 40 years striving to apply this knowledge to computation. Let me explain how these two technologies mutually empower each other.

First, a known fact: AI can accelerate quantum computing. In 1981, physicist Richard Feynman proposed the concept of a quantum computer, replacing classical bits (0s and 1s) with quantum bits for computation. This paper ignited excitement across physics—and later, computer science—because the idea of breaking the Turing machine’s monopoly was intellectually irresistible and promising.

In the 1990s, computer scientist Peter Shor proved that quantum computers can solve certain genuinely hard problems. For instance, large integer factorization—mathematicians long believed it exceeded classical computing’s capacity—but Shor demonstrated that if a quantum computer based on Feynman’s vision were built, countless encryption systems could be broken. This paper was pivotal, genuinely sparking scientific and funding communities’ enthusiasm for quantum computing.

A few years later, Shor achieved something I consider even more remarkable. Initially, physicists were pessimistic: qubits were too fragile, easily disturbed, and noise seemed incurable. Shor dispelled their doubts by proving that if the error rate of elementary quantum logic gates could be reduced below a certain threshold (e.g., 1%), then quantum computers could theoretically scale to arbitrary size while remaining reliable. This parallels von Neumann’s solution to the problem of building reliable classical computers from unreliable components. Thus, physicists had no longer any principled objection: quantum computers could be built and used.

Quantum error correction thus became the central challenge for four decades—until recently, when AI stepped in to rescue. One and a half years ago, Google published a paper in Nature introducing Willow, a quantum chip using around 100 qubits to produce a theoretically “eternally stable” logical bit, reducing error rates below the 1% threshold. This was the first time in history that such a milestone brought immense excitement to quantum computer scientists.

What role do neural networks play here? A core component is designing a decoder for quantum error correction. This decoder cannot be derived purely through reasoning—it can be “learned”: trained via neural networks on massive datasets, ultimately yielding this immensely valuable decoder. Today, scientists worldwide are racing down this path, including several leading Chinese teams, who are making significant progress.

Conversely, can quantum enhance AI? Our answer is yes: by replacing the Turing machine in the machine learning framework with a quantum machine as the foundational architecture, or even learning directly from quantum data—can we achieve things impossible for AI alone? This direction has been explored for over a decade, and in recent years, we are seeing real signs of promise. You can call it “Quantum AI”—and it is now emerging. Personally, I believe we will witness tremendous advances within the next five to ten years. When the novelty of AI fades and it no longer dominates headlines, Quantum AI will step forward, keeping the fire of scientific exploration burning.

6. Conclusion: Understanding Boundaries Enables AI Safety

Yao Qizhi: In conclusion. AI has demonstrated extraordinary power across countless domains, but its algorithms always operate within boundaries defined by physical laws and theoretical mathematical constraints. Recognizing this provides the foundation for a crucial mission: ensuring AI systems are safe and controllable. This year’s WAIC focuses precisely on AI’s power and AI safety. Just as cryptographic systems are meticulously designed by scientists to resist attacks from classical computers, so too can we build systems resistant to AI attacks—if grounded in solid mathematics.

Understanding this boundary is vital for work in AI safety. Ahead lie countless exciting frontiers: AI for Science, such as Quantum AI; reliable large-scale AI systems, requiring “Mathematics for AI”; AI safety; and “AI for AI,” using AI to improve AI. All of these will deepen our understanding of the very essence of intelligence.

(This article is based on a transcript of Professor Yao Qizhi’s keynote speech at the 2026 World Artificial Intelligence Conference, unreviewed by Professor Yao. Assisted by Kimi.)

Originally posted on WeChat Official Account “Big Data Digest,” author: Data Digest Bot

Source: Big Data Digest