What is the technological singularity?

“Singularity” was first a word from math and physics. In a 2001 essay, Kurzweil explained that in math it means “the explosion of value that occurs when dividing a constant by a number that gets closer and closer to zero.” Divide 1 by 0.1 and you get 10; by 0.01, 100; by 0.001, 1,000. The closer the divisor gets to zero, the bigger the answer, and at zero it cannot be calculated.

In physics, the best-known example is the center of a black hole. According to NASA, general relativity (Einstein’s theory of gravity) predicts that the very center of a black hole contains a point where matter is crushed to infinite density. Whether it is a real physical thing or only something in the math, astronomers do not yet know. Light cannot get out from inside the “event horizon,” which you can think of as the black hole’s surface, so nothing about what happens inside can reach an outside observer.

In a January 1983 column in Omni magazine, Vinge wrote that when we create intelligences greater than our own, human history will reach “a kind of singularity, an intellectual transition as impenetrable as the knotted space-time at the center of a black hole” (as quoted by Quote Investigator, which checked scans of the magazine). In his 1993 essay, he called the Singularity “a point where our models must be discarded and a new reality rules.” The name borrows both pictures: a value that grows without limit, and a boundary we cannot see past.

Both Vinge and Kurzweil quote a 1958 passage as an early use of the word (Kurzweil’s 2001 essay, without naming Ulam, quotes it as von Neumann’s words from the 1950s). The mathematician Stanislaw Ulam wrote a long article for the Bulletin of the American Mathematical Society looking back on the mathematician John von Neumann (1903–1957), who had died the year before. In it, he recalled one of their talks: “One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”

These are not von Neumann’s own written words; they are Ulam’s account of a conversation. And “essential singularity” is a technical term from mathematics.

In 1965, the British mathematician I. J. Good wrote that if a machine that could far surpass any person designed even better machines, there would be an “intelligence explosion.” The idea is close, but the word Good used was “intelligence explosion.”

The person who spread “singularity” as a word about the future of technology was Vernor Vinge, a mathematician and science-fiction writer at San Diego State University. His own list of writings calls a January 1983 opinion column in Omni magazine his “first in-print fling at the Singularity.” He also used the word in his 1986 science-fiction novel Marooned in Realtime (according to Kurzweil’s essay), and in March 1993 he presented the essay “The Coming Technological Singularity” at a symposium sponsored by NASA and others.

The inventor Ray Kurzweil brought the idea to a wide audience with his 2005 book The Singularity Is Near (its Japanese edition came out in 2007). In a question-and-answer piece that went with the book, he wrote, “I set the date for the Singularity—representing a profound and disruptive transformation in human capability—as 2045,” and said that the nonbiological intelligence created in that year would be “one billion times more powerful than all human intelligence today,” meaning in 2005.

Underneath this is a view he calls the “law of accelerating returns.” In a 2001 essay, he wrote that because technological change speeds up exponentially, the 21st century will see not 100 years of progress but “on the order of twenty thousand years of progress — at today’s rate of progress.” Because the speed of progress itself keeps rising, progress that would take 20,000 years at today’s speed gets packed into 100 years. He keeps a separate date for computers reaching human-level intelligence: by 2029 (according to the publisher of his 2024 sequel).

His 2024 sequel, The Singularity Is Nearer (a Japanese edition came out the same year), still points to 2045. The publisher’s description says that “by 2045, we will be able to connect our brains directly with AI, enhancing our intelligence a millionfold,” and that “this is the Singularity.”

In Japan, because of that year, the idea is also called the “2045 problem” (2045-nen mondai). For example, a 2013 paperback by Takuya Matsuda is titled 2045-nen Mondai: Konpyuta ga Jinrui o Koeru Hi (“The 2045 Problem: The Day Computers Surpass Humanity”).

The three overlap, but they point to different things. “Superintelligence” is a thing: an intelligence far smarter than the smartest people in nearly every field. An “intelligence explosion” is an event: AI building smarter AI, so the speed of getting smarter suddenly shoots up. “Singularity” usually names a point: the boundary beyond which we cannot see.

In a 2007 essay posted on the site of the research institute MIRI, Eliezer Yudkowsky sorted the meanings of “singularity” into three “schools.” “Accelerating Change” (Kurzweil and others): technological change follows smooth, typically exponential curves, so we can predict with fair precision when new technologies will arrive. “Event Horizon” (Vinge): once smarter-than-human intelligence exists, the future after it is unpredictable. “Intelligence Explosion” (Good and others): smarter minds build even smarter minds, in a loop.

Yudkowsky wrote that the three schools are “logically distinct,” and that while their core claims support each other, their strong claims “tend to contradict each other.” For example, a strong form of Accelerating Change says we can predict exactly when new technologies will arrive, which clashes with the Event Horizon idea that the future beyond that point cannot be predicted (this example is our own). He also wrote that the original meaning is the Event Horizon idea of Vinge, “who coined the word” (Ulam’s 1958 article already has a similar phrase). For more, see the “Intelligence explosion” and “Superintelligence” pages.

No one knows. The singularity is about a future that has not happened, so whether it will come, and when, are predictions. In 1993, Vinge wrote, “Within thirty years, we will have the technological means to create superhuman intelligence,” and “I’ll be surprised if this event occurs before 2005 or after 2030.”

Vinge himself thought it might not come. In the same 1993 essay he wrote, “Well, maybe it won’t happen at all,” and in 2007 he gave a talk titled “What If the Singularity Does NOT Happen?” Even there, though, he called the Singularity “the most likely non-catastrophic outcome for our near future.”

Some experts doubt it. In a 2008 IEEE Spectrum special report in which ten people gave their views, Gordon Moore, known for Moore’s Law (the prediction about the growing number of components on a semiconductor chip), said, “I am a skeptic. I don’t believe this kind of thing is likely to happen, at least for a long time.” Steven Pinker, a professor of psychology at Harvard, said, “There is not the slightest reason to believe in a coming singularity.”

In 2011, Microsoft cofounder Paul Allen and computer scientist Mark Greaves wrote, “While we suppose this kind of singularity might one day occur, we don’t think it is near.” Building the complex software that would allow the singularity to happen, they argued, first requires a detailed scientific understanding of how the human brain works, enough to use as a guide, or else creating it all from scratch; and with the brain, “the more we learn, the more we realize there is to know.” They called this the “complexity brake.”

AI smarter than humans at nearly everything is considered not to exist yet. A paper by researchers at Google DeepMind (Google’s AI lab; September 2025 version) sorts AI into levels and lists artificial superintelligence (ASI), AI that outperforms all people across a wide range of tasks, as “not yet achieved.” So the trigger of Vinge’s singularity has not arrived.

On the other hand, some AI company leaders write that it has already started. Sam Altman, the head of OpenAI (the company that makes ChatGPT), opened his June 2025 blog post “The Gentle Singularity” with “We are past the event horizon; the takeoff has started,” and wrote that “the singularity happens bit by bit” (this is a company head’s view).

So the same black-hole image is used in different ways: Vinge used it for a boundary we cannot see past, while Altman says we have already crossed it and that, so far, it is “much less weird than it seems like it should be.” It helps to check who is using the word and in what sense. How much AI is already helping with AI research is covered on the “Intelligence explosion” page.