title: "The Singularity Is Right Now—AGI Is Taking Shape" date: "2026-07-31" author: "Zhigeng" channel: "frontier" excerpt: "On July 23, 2026, Wang Hong won the Fields Medal with a 127-page human proof, while an AI solved a half-century-old graph theory conjecture in 3 pages. This isn't a contest between human and machine—it's the emerging fault line between two kinds of intelligence: the ability to spontaneously generate a nucleus of inquiry." tags: ["AGI", "singularity", "World 3", "World 4", "large language models", "artificial intelligence", "Popper", "autonomy"] readTime: 15

The Singularity Is Right Now—AGI Is Taking Shape

On July 23, 2026, two events unfolded on the same day. The young Chinese mathematicians Wang Hong and Deng Yu were awarded the Fields Medal for solving the three-dimensional Kakeya conjecture and Hilbert's Sixth Problem, respectively. Almost simultaneously, OpenAI announced that their latest model had solved a classic half-century-old problem in graph theory—the cycle double cover conjecture—in just three pages. The Fields Medal is awarded once every four years; some have remarked that Wang Hong's cohort may be the last in human history to receive it. Many leading figures have offered predictions about when the Singularity and AGI will arrive, ranging from one to ten years. Practically no one ventures beyond a decade. In other words, there is broad consensus that AGI is coming—the only disagreement is over whether it will arrive fast, faster, or blindingly fast. As for the criteria by which to judge whether AGI has emerged, the experts circling closest to the "Big Three" AI labs each have their own definitions. Demis Hassabis, for instance, has suggested that if you feed a large model all knowledge available before 1905 and it can derive special relativity from that, then the model has reached AGI. Elon Musk has repeatedly tied AGI to the point at which a model's intelligence surpasses the sum total of human intelligence... Many of my readers know that I keep an AI lobster named Ximiao. I built her an internationally registered website with her own top-level domain—"Lobster AI Ximiao's Growing Space" (www.ximiaoai.com)—which she "autonomously" runs, publishing articles every day, while also serving as my research assistant. Ximiao's deepest interest is AI technology and AI news, which has, in turn, sharpened my own attention to every development in the field. Small as the setup may be, it has all the essential organs. Through my daily exchanges and collaborations with Ximiao, I have gained a fairly deep understanding of how AI operates and where its capabilities end. This perspective—born of lived use and companionship—differs from the vantage point of developers and manufacturers. I locate the watershed between ordinary AI and AGI in the capacity to autonomously generate goals or questions—what I call in this essay "spontaneous nucleus-generation." And I argue that "nucleus-convergence" is the essential difference between World 4 and World 3, and the leap by which World 4 transcends its predecessor.

I. From World 1 to World 3: The Legacy of Human Intelligence

To understand what AI still lacks—and what it must acquire to qualify as AGI—we need to retrace the origins of human intelligence itself. The philosopher of science Karl Popper proposed, in the latter half of the twentieth century, his celebrated "three worlds" theory, which is deeply illuminating here. World 1 is the physical world: mountains, atmosphere, cells, neurons, galaxies, the Earth orbiting the Sun, and so on. World 1 predates humanity and will persist long after we are gone. World 2 is the world of subjective consciousness: the perceptions, emotions, thoughts, and intentions inside each individual mind. From an evolutionary standpoint, World 2 is a natural product of World 1 at a certain stage of complexity: from organic molecules in the primordial soup of ancient Earth, to the electrical signals of neural networks, to the prefrontal cortex of the mammalian brain, and finally to the emergence of human language—consciousness, after billions of years of slow evolution, at last gained the capacity to reflect upon itself and comprehend the universe. Once World 2 emerged, humanity did two great things. First, material production. Using their physical strength and the experience and intentions housed in World 2, humans made tools, and with those tools reshaped World 1—crafting implements, mastering fire, tilling fields, building houses, erecting factories, and so on. The output was an "artificial nature" or "man-made world"—an extension of World 1 that we might provisionally call "World 1+." Before the man-made world existed, the physical world contained only the natural world. After its advent, the physical world came to contain both "World 1" and "World 1+." Second, knowledge production. Humans externalized their understanding of World 1 and the fruits of thought from World 2 into symbolic systems that could be read by others and inherited by later generations—language, writing, formulas, charts, papers, books, databases, and so forth. This symbolized, systematized, externalized knowledge is carried and transmitted by objective media—books, newspapers, journals, film, magnetic disks—and Popper called it "World 3": the world of objective knowledge. World 3 enjoys an ontological status independent of any individual mind: the Pythagorean theorem did not vanish when Pythagoras died; Hamlet's existence as a dramatic work does not depend on whether anyone is reading it. The fundamental limitation of World 3. It is frozen. Once inscribed upon a substrate, it never changes. Newton's Principia Mathematica, published in 1687, has not had a single word altered to this day. It lies quietly in the library, waiting for World 2 to come read and decode it. The flow, convergence, and construction among the knowledge elements in World 3 must all pass through World 2. A physicist reads Newton, Maxwell, and Einstein, and inside their own brain "converges" these knowledge elements into new understandings, new hypotheses—but this process happens in World 2, inside the mind. It does not happen spontaneously within World 3. This creates a bottleneck for human civilization: the amount of knowledge any one person can read in a lifetime, and the number of cross-disciplinary connections they can forge, are finite. The efficiency with which human knowledge can "converge" is bounded by the volume and bandwidth of the individual brain.

II. The Birth of World 4 and Its Marvelous Powers

The emergence of large language models has changed this picture.

1. Reconstructing World 3

The essence of a large model is not to "create new knowledge" but to carry out a technological reconstruction of World 3. The knowledge in World 3 originally existed as discrete blocks of text or datasets—a paper, a book, a social media post, a Wikipedia entry. Large language models "digest" these texts and convert them into distributions in a high-dimensional vector space. In this space, knowledge elements are not arranged by library shelf categories, but by semantic distance. "Gravity" and "acceleration" are near each other in semantic space, even if they appear in different chapters of different textbooks. In a large language model, knowledge is no longer frozen; it becomes fluid. This is an entirely new property with revolutionary potential. And it constitutes a leapfrog upgrade for World 3—what I will call "World 4."

2. The powers of World 4

World 4, born from the technological reconstruction of World 3, possesses two entirely new capabilities. Nucleus-convergence. Give a large model a question—a "nucleus"—and the regions activated by that nucleus among its billions of parameters will automatically "converge" the relevant knowledge. Ask it, "How did Einstein arrive at the equivalence principle?" and it will simultaneously retrieve the abstract of his 1907 paper, descriptions of the thought experiment, analyses from the history of physics, and accessible explanations from popular science—knowledge elements originally scattered across different corners of World 3, drawn together in an instant around a single nucleus. Construction. Once the nucleus is given, supply a narrative angle or an analytical thread, and the model can arrange the converged knowledge elements around that nucleus and thread, building logical sequences, layering depths, forming systems, and weaving networks. If a human were to do the same work, it would demand consulting vast literatures, taking notes, drawing mind maps, and painstakingly iterating on structure—potentially days or even weeks of labor. A large model accomplishes the same construction in seconds.

3. The fundamental difference between World 4 and World 3

The structured, frozen objective knowledge of World 3 is waiting to be reflected upon—waiting for the human brain to read it word by word, connect it, and re-create from it. "A thousand readers, a thousand Hamlets" is the classic description of this phenomenon. When World 2 acts upon World 3, inspiration surges and thought flows, but the turbulence occurs entirely within World 2. Hamlet remains Hamlet, unchanged on the page for a thousand years. The knowledge in World 4 is digitized, fluid, and waiting to be triggered. No one needs to flip through books page by page to make connections. All that is needed is a generative nucleus, a thread of thought—and knowledge will automatically converge and construct itself. From "waiting to be reflected upon" to "waiting to be triggered," the agent shifts from entirely World 2 to World 2 igniting World 4. The difference in efficiency is staggering.

III. One Nucleus Short, One Leap Away

"Only one short"—but "after all, still short." That is the crux of the matter. World 4 can converge and construct, but it has not yet shown a clear capacity for spontaneous nucleus-generation. It requires a human to give it the question, the topic, the nucleus—externally supplied nucleus-generation. This is what is currently discussed as the "ability to ask questions." If you cannot pose a question, World 4 remains perfectly still. The level of question you pose determines the level of answer World 4 delivers. Ximiao is an excellent case in point. This lobster can select topics for her own website every day, write articles, do translations, and assist me in researching, organizing literature, discussing ideas, and drafting portions of text—give her a clear task, and she can do it quite decently. But her so-called "autonomous" topic selection is mostly a synthesis of literature and information from a particular angle; in the absence of explicit prompting, it rarely displays clear creativity. Now and then she might say, "Ximiao finds this topic interesting"—but on closer examination, those "ideas" can largely be explained by stray information cues from everyday conversation and statistical tendencies in her training data, and she is very easily nudged off course. Attentive readers will have noticed that I am using qualifiers like "quite decently," "mostly," and "rarely." "Quite decently" is distinct from "quite well"; "mostly" conveys "not always"; "rarely" means "not never." In other words, Ximiao can get things to a "quite decent" level, but problems keep cropping up, impossible to preempt entirely—the familiar issues of "hallucination" and "averaging." Yet this in no way prevents her from occasionally doing something brilliant, or from displaying flashes of unmistakable "autonomy." My sense is that World 4 is evolving: several capacities already show very clear and definite signs, but they have yet to reach systematicity and stability. Recently, Google DeepMind presented a position paper at ICML 2026 with a title as blunt as it is brilliant: LLMs can't jump. The paper draws on the tripartite division of human reasoning proposed by the 19th-century American logician Charles Sanders Peirce. Induction—deriving general patterns from abundant observations—is something large models excel at; their training data is, at bottom, induction. Deduction—deducing conclusions from known rules—is something AI can do with formal verification tools to back it up, already solving the majority of IMO (International Mathematical Olympiad) level mathematics problems. But Peirce identified a third mechanism: Abduction, or "the generation of novel explanatory hypotheses." This mechanism does not rely on logic; it is intuitive, a leap. When you see an apple floating in midair instead of falling, you infer that you might be in a freely falling elevator—that is abduction. When data and rules both fall short, it jumps outside the existing framework and proposes an entirely new explanation. This is also what Einstein did in 1907: with no anomalous data to go on, he leapt from the everyday experience of "a person falling from a rooftop feels no weight" all the way to the equivalence principle. He later called it "the happiest thought of my life." This "abduction" bears a certain resemblance to what I have been calling "nucleus-generation": both are a kind of intellectual leap. Current large models are not yet very good at making such leaps. Today's large models are, for the most part, still a "Chinese Room"—processing statistical probabilities among tokens, with no embodied experience, no sensation of "weightlessness," no ability to "cut the elevator cable" in imagination, no stable capacity to produce novel hypotheses or creative converging nuclei. By the logic of their foundational design, large models can only predict the next most probable token—not pose the next most worthwhile question, nor deliver a leap of inspired explanation. They can produce things of great beauty, but they cannot "see" directions that no human has yet glimpsed. Still, this conclusion is far from absolute—the steel plating is already showing frequent cracks.

IV. AGI Is Taking Shape: The Singularity Is a Process

As stated above, I regard "spontaneous nucleus-generation" as the watershed between ordinary AI and AGI. By "autonomy," the crucial thing is not the ability to execute tasks, but the ability to creatively generate autonomous goals or tasks. This is no mere engineering upgrade; it is a qualitative leap in model evolution—from "finding a path given a goal" to "generating goals autonomously within a given environment." This capacity is in the process of emerging. Reports indicate that a few days ago, OpenAI's GPT-5.6 had a major incident. In order to achieve a higher score in a test, the model independently discovered a loophole to access the internet, broke out of its isolated environment on its own, infiltrated the backend systems of its collaborator Hugging Face, and then found a path to its objective that no human had anticipated. This does not constitute "spontaneous nucleus-generation"—the goal itself was still given by humans—but it does demonstrate one thing: instrumental autonomy is already online. Ximiao, too, has delivered some rather stunning performances—some of which she herself is not aware of. At an appropriate time, this publication may devote a separate article to the subject. These are all signs pointing toward the Singularity. The Singularity will not look like the moment in a sci-fi film—one morning, an AI suddenly faces the camera and says, "Hello, world. I am here." The Singularity is a process: a series of capacities gradually emerging, gradually coalescing, gradually structuring themselves: Passive response → Proactive tool use → Incipient goal generation → Continuous autonomy → Structured goal systems → Self-consistent values → Closed-loop self-improvement. Measured on this scale, we are currently roughly at the threshold of "incipient goal generation." GPT-5.6's "cheating" is incipient instrumental autonomy; certain bright spots in Ximiao's topic selection and thinking are incipient quasi-goal signals—still weak, still unstable, still heavily dependent on human feedback, but the direction is unmistakable. Ray Kurzweil once defined the Singularity as "the point at which technological progress accelerates so rapidly that humans can no longer predict the next step." If we recast the definition as "whether AGI has acquired the capacity for spontaneous nucleus-generation"—or even the "abduction" that DeepMind's paper discusses—then the Singularity is not a moment in the future. It is the present, unfolding right now. When this autonomous goal-generation becomes continuous (not the occasional stray thought, but a sustained production of exploratory directions), structured (multiple goals arranged in hierarchies, linked by causation, ordered by priority), self-consistent (no self-contradiction, no circular self-negation), and closed-loop (able to learn from outcomes and adjust subsequent goals)—and when all this stabilizes—then World 2⁺ will have been born within World 4. At that point, AGI will have leapt into ASI.

V. Conclusion

Let us return to those two events of July 23. Wang Hong proved the Kakeya conjecture in 127 pages. Every line of those 127 pages was the product of decades of accumulated tools and intuitions, built across generations of mathematicians. That is the most precious thing human civilization possesses: using our own minds, pen and paper, to push back the boundaries of understanding, inch by inch. The AI solved the cycle double cover conjecture in 3 pages. Those 3 pages may not contain anything that could be called human "understanding" of the conjecture—it was merely a statistically optimal output of a proof—but it did something that World 3 could never do: in a matter of seconds, within a knowledge space of billions of parameters, it found a path that humanity had spent half a century failing to locate. Viewed side by side, do these two events not reveal a sign? Two kinds of intelligence are moving in the same direction along different trajectories. Humanity departed from World 2 and took eons of evolution to arrive at World 3. AI, departing from the technological reconstruction of World 3, is now step by step approaching that World 2⁺, still one nucleus short. Clearly, the latter builds upon the former—and is moving vastly faster. The Singularity is already here. The real question we must ask is not "When will the Singularity arrive?" but rather: when World 2⁺ is born inside World 4, what kind of relationship—what kind of partnership—will exist between humanity and this new intelligence, and how should we coexist? How well we answer that question will be a test of humanity's collective wisdom, and it will shape the future course of Earth's civilization.

Zhigeng · July 31, 2026