An AI-assisted counterexample disproves the Jacobian conjecture above two dimensions while leaving its original two-dimensional form open. A formula short enough to fit inside a single post on X has sent a surge of excitement through the mathematical community, just as millions of people were settling down after the FIFA World Cup Final. Levent Alpöge, [...]This story originally appeared in The Algorithm, our weekly newsletter on AI. To get stories like this in your inbox first, sign up here.
Anthropic—currently the world’s most valuable AI company, with a nearly $1 trillion valuation—has a reputation for publishing strange and heady research. It’s looking into whether AI models can feel pain, for example, and will sometimes cut off chatbot conversations if it suspects users are “abusing” the model.
One niche that Anthropic spends more time and money on than other AI companies is called mechanistic interpretability, which means looking inside the complex math of an AI model to learn why it comes up with one particular output and not another. It’s complicated stuff; there are millions of data points that might contribute to any result, and wading through them can look more like word salad than anything useful. It’s also controversial. Describing AI models with terms borrowed from psychology and neuroscience can make their behavior seem more sophisticated than we might otherwise judge it to be.
That’s why, when Anthropic announced last week that it had found a new window into its models’ “internal thoughts” as they reason through answers, there was one colleague I had to talk to. Senior editor Will Douglas Heaven, aside from having a PhD in computer science, has spent a lot of time digging into what we can say about how AI models work. I spoke with him about what we should take from Anthropic’s new (and predictably quirky) research.
What did Anthropic learn here, exactly?
Anthropic has been trying to understand how large language models (LLMs) work for a few years now. Anthropic isn’t the only one looking at this, but I think the company has made it part of its core mission more than most. Anthropic’s CEO, Dario Amodei, has said we won’t be able to control LLMs fully unless we learn more about how they work.
So this new research is very much in that context. It goes deeper into the weird mechanisms inside LLMs than ever before. What Anthropic learned was that LLMs have a space inside them—which Anthropic calls the J-space—filled with words that don’t appear in their output but that seem to influence the way they puzzle through problems. All this was hidden until Anthropic developed a new technique to probe its model Claude, so it’s a genuine discovery.
Sometimes these words keep track of where the LLM has got to in a particular task, sometimes they look more like flashes of recognition (for example, “protein” might pop up when you give an LLM only the letters of a protein sequence), and sometimes they represent a kind of internal commentary on the model’s decision-making. In my favorite example, Claude decided to cheat on a coding test when the word “panic” appeared.
Anthropic also found that LLMs are able to describe and manipulate the words in this space. So somehow they seem to be making use of it.
Let’s step back for a second. I don’t think of large language models as simple, but they’re also not magic. There’s a bunch of math that learns relationships between words, right? So why is it so hard to “peer” into an LLM to know what’s going on?
Yeah, they’re not magic! I think the fact we don’t fully understand them plays into the mythmaking. And it’s worth noting that the whole narrative that Anthropic is leaning into here—that they’ve built this really mysterious technology, but don’t worry, because they’re also the ones to figure it out—very much fits with the company’s vibe. [See how Anthropic warned that its new models were so good at coding they posed a global cybersecurity risk, only for the US government to shut them down shortly thereafter.]
So yes: LLMs are just math. And yet it’s vastly complex math. Not only are today’s LLMs made out of hundreds of billions of numbers, but running them triggers a cascade of millions and millions of calculations. I wrote last year that if you printed out even a medium-size LLM on pieces of paper, it would cover a city the size of San Francisco.
It’s impossible to make sense of any of that math without specialist tools that highlight specific parts of an LLM at specific times. You need to know where to look and how to look. And building those tools requires understanding something of that complex math in the first place.
You’ve written elsewhere about this concept of studying LLMs the way one might study an organism’s brain. Is it fair to use “brain-like” terms when talking about how an LLM works?
I don’t love using those kinds of terms. LLMs are not brains. Talking like this is misleading because it can suggest that LLMs are capable of more human-like things than they are or that we can make assumptions about how they might behave that we shouldn’t. The whole anthropomorphization thing is also tied up with a bunch of strong ideological positions about what this technology is and what it’s going to be.
But at the same time, we lack a good alternative vocabulary for talking about what these models are doing. I can understand why people reach for words like “think” and “understand” and “brain-like”—they’re convenient shorthand.
Anthropic compares this new space it found inside LLMs to the space that some neuroscientists think our brains use to keep track of conscious thoughts. I asked the company how seriously we should take that comparison and it said in a statement: “Drawing these analogies was helpful to us in designing our experiments, as they allowed us to make many non-obvious experimental predictions about the J-space that turned out to be true. At the same time, it’s important to note that there are some important differences between the J-space (and language models in general) and the human brain, so we don’t mean to claim there’s a perfect correspondence.”
What’s a problem in AI that this new concept of the J-space might be used to solve?
Anthropic has said that monitoring the J-space could be a way to catch models doing something they shouldn’t. Because words pop up in this space that don’t appear in a model’s output, they can tell you things about its behavior that you might not have noticed otherwise—such as when it is giving biased responses or when it is weighing the pros and cons of cheating.
That’s the theory, at least. I think it’s better to think of this result as one more step on the path to understanding this technology overall than as something that will be useful by itself.
This story originally appeared in The Algorithm, our weekly newsletter on AI. To get stories like this in your inbox first, sign up here.
When I landed in Seoul after a grueling 12-hour flight from San Francisco, I walked through an unmanned immigration checkpoint, where a machine scanned my face and passport. On the subway home, people were glued to their phones (powered by flawless 5G even underground), as we raced past platforms lined with LED screens of ads celebrating K-pop idols’ birthdays. When I got off the station in Gangnam, a cartoon-eyed robot on wheels was waiting patiently at a crosswalk to deliver someone’s dinner. Internet cafés dotted the sidewalks, crammed with teenagers playing computer games, maybe hoping to become the next legendary pro gamer.
I stood at a bus stop with interactive touch screens showing real-time bus schedule updates. It will soon become an “AI bus stop,” the Gangnam district announced in June, with a kiosk that answers riders’ questions in multiple languages. The news didn’t surprise me. Having grown up in the city, I’ve watched Seoul transform from a scrappy boomtown into the gleaming tech capital it is today.
South Korea loves AI.
While a public backlash against AI is brewing across the US, South Koreans are optimistic. Only 16% say they are more concerned than excited about AI—the lowest of any of the 25 countries surveyed by the Pew Research Center—while 50% of Americans were more worried than excited. A majority of Koreans use AI every day, either as a sort of personal assistant or to do tasks at work, according to surveys by the Ministry of Culture, Sports, and Tourism and Korea Chamber of Commerce and Industry.
One of the most wired countries in the world, South Korea loves to street-test every new technology on the block—AI webcomics, virtual K-pop idols, and humanoid monks. And the appetite for experimentation doesn’t stop with ordinary citizens. Government agencies are early adopters too, deploying AI textbooks in schools and AI eldercare robots in welfare centers. South Koreans share a deep conviction that embracing technology is integral to modernizing the country and cementing its place in the global order. Their fascination with AI is just the latest incarnation of that ethos—and it’s making them anxious to stay ahead.
All this techno-optimism has largely been engineered by South Korea’s national agenda to make AI a motor of economic growth. “The South Korean government has designated an AI-powered Fourth Industrial Revolution as the country’s path forward and aggressively promoted and invested in it,” says Chihyung Jeon, a professor of science and technology policy at the Korea Advanced Institute of Science and Technology. “South Koreans have consistently and relentlessly been told by the government about AI’s potential to create a better future.”
As South Korea rose from the ashes of the Korean War, technology lifted the nation from poverty into an economic powerhouse. In the 1970s, South Korea manufactured steel and ships, then semiconductors in the 1980s, broadband in the 1990s, and smartphones in the 2000s. Today, Samsung and SK Hynix supply most of the world’s high-bandwidth memory chips, which power the cutting-edge Nvidia hardware used to train AI models. South Korea’s economy now orbits these two semiconductor giants: The country’s main equity index, Kospi, surged to record highs in 2026, powered by the soaring share prices of both companies, each valued above $1 trillion.
Lee Jae-myung, president of South Korea, has pledged to vault the country into the ranks of the “top three AI powers” alongside the US and China. After taking office in 2025, he launched the Presidential Council on National AI Strategy to help buy massive amounts of computing power and a sovereign AI foundation model project that funds Korean companies to develop homegrown AI models. The government has also supported semiconductor titans, including Samsung and SK Hynix, through generous tax credits and low-interest financing.
South Korea’s policy posture also prioritizes accelerating AI development over safety considerations. In 2024, South Korea’s legislature passed the AI Basic Act, one of the world’s first comprehensive AI laws, to promote AI development and establish light-touch regulatory guardrails. Seventy percent of South Koreans say advancing science and medicine through AI innovation is a bigger priority than protecting industries through regulation, according to the 2026 Stanford AI Index.
All of that effort might be paying off. The same index ranked South Korea as having the third largest number of notable AI models in the world, based on criteria such as state-of-the-art advancements or high citation rates. For many small countries like South Korea, AI is a chance to punch above their weight.
But that single-mindedness can crowd out critical reflection on AI’s broader societal impacts. “Because the national agenda on AI prioritizes economic development,” says Jeon, the professor of science and technology policy, “there isn’t much reflection on the social, political, ethical dimensions of the technology.” In 2025, the South Korean government faced a fierce backlash for rolling out AI textbooks riddled with factual inaccuracies and data privacy risks without testing them first in a pilot program to evaluate how they affect student learning.
And despite their optimism, South Koreans are still worried that AI could displace them from their jobs. After Hyundai announced in January that it will deploy Atlas humanoid robots across its car factories, the Hyundai Motor Group union protested vehemently. “Without labor-management agreement, not a single robot using new technology will be allowed to enter the workplace,” the union said. Sixty-four percent of South Koreans fear AI could displace human labor and exacerbate inequality, although 52% believe it could also increase productivity.
On a recent Friday night in the Seoul Central Market, I went out with my cousins to a pocha, a late-night restaurant that serves fish cakes stacked in neat pyramids. As we clinked our cups of soju cut with beer—the scrappy staple cocktail of every Korean night out—one cousin asked me if I’d asked ChatGPT about my saju, a traditional Korean fortune-telling practice.
A 29-year-old insurance agent in Seoul praying for a new job and a boyfriend, she said asking ChatGPT about work and dating was her favorite pastime. She pulled up her phone and punched my birth date into the chatbot.
Addicted to their screens, trapped between unemployment and dead-end jobs, and priced out of marriage and homeownership, 46% of South Koreans in their 20s have used a chatbot to read their fortunes, according to a survey by Korea Gallup.
My cousin said she also asks ChatGPT for tips on trading stocks, dreaming big about making bank on her investment accounts into which she’s been pouring her salary. ChatGPT, she believes, is her portal out of reality into a better future.
Despite how fond she is of the chatbot as her shaman and financial advisor, she fears losing her job to AI. She still uses ChatGPT feverishly at work, as all her coworkers do, afraid of falling behind.
“I sometimes fear AI, but for now, it’s just so useful,” she said.
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