An AI Took a Stab at the Riemann Hypothesis

For over 150 years, the Riemann hypothesis has haunted mathematicians. It’s a deceptively simple question about the distribution of prime numbers, and it carries a $1 million bounty for anyone who cracks a general proof. That prize remains unclaimed. But now, an unreleased Anthropic model has made a dent.

On Monday, Anthropic announced that one of its internal models significantly increased the lower bound of solutions for which the hypothesis holds true. That’s not a full proof — nowhere close. But it’s real progress on a problem that has resisted the world’s best minds for generations.

What’s more striking is how it happened. A staffer with minimal mathematical training simply prompted the model to “take a real stab” at the problem, then walked away for a day and a half.

How the Model Worked: 60 Sub-Agents, 650 Ideas, 31 Million Tokens

The scale of the effort is hard to wrap your head around. Over roughly 36 hours, the model tested 650 different approaches, coordinating across 60 sub-agents and burning through 31 million tokens in the process.

According to a footnote in the accompanying paper, the labor split was surprisingly organic:

• 2 sub-agents developed the key mathematical ideas
• 13 contributed supporting ideas to those two
• 30 tried but failed to generate new approaches
• 13 acted as validators, checking the correctness of arguments
• 2 helped write the initial paper

It’s almost like watching a research lab assemble itself. And the results weren’t just hand-waved — Anthropic’s in-house mathematicians confirmed the findings, and the proof was formalized using the open-source proof assistant Lean.

The Growing Wave of AI Mathematical Breakthroughs

This isn’t an isolated event. Over the past year, large language models have been quietly racking up wins in pure mathematics. Several Erdős problems have fallen to AI, and OpenAI recently published ten major results from its internal “Astra” model. Anthropic itself previously disproved the long-standing Jacobian conjecture.

The pattern is clear: as models get more powerful, their mathematical output gets more impressive. But that’s precisely what’s making some mathematicians nervous.

Why Some Mathematicians Are Worried

In June, a group of prominent mathematicians signed a public declaration expressing concern that AI could erode the field’s core values. Their worry centers on attribution — the standard that proofs should be “attributable to specific authors who take credit for their discovery and assume responsibility for their correctness.”

If a model generates a proof, who’s responsible for it? The prompt-writer? The company that built the model? No one at all? Those aren’t just philosophical questions; they have real implications for how mathematics is taught, published, and credited.

Not Everyone Sees It as a Threat

But the mathematical community is far from united. Fields Medal winner Timothy Gowers pushed back on the declaration in a blog post, suggesting the shift might not be as catastrophic as some fear.

“If we arrive at a world where mathematical theorems are no longer associated with mathematicians, maybe that won’t be any more problematic than the fact that stars aren’t named after astronomers and most aren’t named at all,” Gowers wrote.

It’s a compelling analogy. We don’t know who first noticed that the sun rises in the east, and we don’t lose sleep over it. Maybe mathematical discovery will eventually feel the same way.

What This Means for the Future of Discovery

This Anthropic result raises a bigger question: if an untrained staffer can prompt a model into meaningful progress on one of math’s hardest problems, what happens when actual experts start using these tools deliberately?

The answer might be that AI doesn’t replace mathematicians — it accelerates them. Instead of spending months chasing dead ends, researchers could use models to explore hundreds of avenues in a single weekend. The AI sub-agents mathematics approach used here is essentially a brute-force search of idea space, and it worked.

That doesn’t mean the Riemann hypothesis falls tomorrow. The $1 million bounty is still safe. But the fact that a machine can now make a meaningful dent in a 150-year-old problem — largely on its own — should give us all pause. The next breakthrough might not come from a human at all.

Why OpenAI is finally paying attention to teen users

Nearly 90% of teens already use ChatGPT weekly — for homework, research, or just getting their chaotic lives organized. That number is staggering, and it explains why OpenAI has decided to stop treating teenagers as an afterthought.

The company’s latest update isn’t just another content filter slapped on top. It’s a full rethink of how the chatbot behaves for younger users, wrapped around a simple argument: keeping teens away from AI entirely would leave them unprepared for a technology that’s becoming as fundamental as the internet itself.

So what actually changes? Let’s break it down.

Age prediction: the invisible safety net

ChatGPT now uses age prediction to automatically apply a more age-appropriate experience whenever it estimates a user is under 18. If the system isn’t sure, it defaults to the safer teen experience. That means stronger safeguards against graphic violence, self-harm content, unhealthy body image, and those risky viral challenges that sweep through school hallways.

It’s not a perfect system — no AI age detection is — but the default-to-safe approach is a smart move. Teens who lie about their age will still hit the stricter guardrails more often than not.

Break reminders: because teens forget to sleep

Anyone who’s watched a teenager disappear into a screen for four hours knows the struggle. OpenAI is adding more frequent break reminders during long sessions, gently nudging users to step away. It’s a small feature, but for parents fighting the endless battle against bedtime, it’s a welcome one.

Parental controls that actually do something

The expanded parental controls are where this update gets real. Parents can now:

• Set Quiet Hours to block usage during specific times
• Disable Voice Mode entirely
• Manage access to image generation
• Receive notifications in high-risk situations, including signs of potential self-harm

That last one is significant. Real-time alerts about self-harm signals could genuinely help parents intervene early. It’s the kind of feature that moves beyond convenience into genuine protection.

Study Mode: learning instead of cheating

Here’s the part educators will appreciate. OpenAI has rolled out Study Mode, developed alongside teachers and learning experts. Instead of handing over answers, it walks students through problems step by step. The goal is to make ChatGPT a tutor, not a shortcut.

Parents can now turn Study Mode on by default for their teen’s account directly through parental controls. OpenAI has also added new starter prompts built for schoolwork, plus interactive math and science tools that now reach 18 million weekly users across more than 250 topics.

That’s a lot of teens doing actual learning — or at least pretending to while the app guides them through the process.

What this means for parents and teens

The bigger picture here is that OpenAI is acknowledging what most parents already know: banning AI outright doesn’t work. Teens will find ways around restrictions, whether it’s using a friend’s account or a different tool entirely. Building safety features into the experience is a more realistic approach than trying to keep kids away from the technology altogether.

For parents, the new controls offer a middle ground between total surveillance and blind trust. Quiet Hours, voice mode limits, and self-harm alerts give you concrete ways to shape how your teen uses ChatGPT without hovering over their shoulder.

For teens, the trade-off is clear: you get access to a powerful learning tool, but you lose the ability to use it as a 24/7 homework machine with zero oversight. That seems like a fair deal.

As AI becomes more embedded in daily life, expect other platforms to follow OpenAI’s lead. The question isn’t whether teens will use AI — they already do. The question is how we make that use safe, productive, and honest. This update is a solid step in that direction.

If you’re a parent setting up your teen’s account, start by exploring the parental controls in the settings menu. Turn on Study Mode, set your Quiet Hours, and have a conversation about what the self-harm alerts mean. The tools are there — it’s up to you to use them.

A Search Engine That Knows You’re Busy at 7 PM

Ask Google Search for a dinner recommendation, and it might now check your calendar first. That’s the quiet but significant shift the company just announced: AI Mode’s Personal Intelligence can now connect directly to Google Calendar. Not just to read your schedule — but to create events on your behalf.

The feature is rolling out to users in the United States starting now, with a wider international release planned later. It’s a small step in the interface, but a giant leap in what Search is becoming.

Calendar Adds Action to Personal Intelligence

Until now, Personal Intelligence mostly pulled context from Gmail and Google Photos. Those connections made responses more relevant. Calendar changes the game in a different way: it’s the first connected Google app that doesn’t just inform. It acts.

Robby Stein, Google’s Vice President of Product for Search, explained that AI Mode can now understand what’s already on your calendar before answering. Suppose you ask for restaurant ideas. Instead of a generic list, AI Mode might notice you have an evening meeting and recommend a spot that fits your actual window of free time.

And if someone sends you an invitation or mentions a meeting in a message, AI Mode can create the corresponding calendar entry without you ever opening the Calendar app.

From Gmail and Photos to Time Awareness

Gmail and Photos provided context — your emails, your pictures. Calendar introduces something entirely new: time awareness. Two people asking the exact same question could now get completely different answers, simply because their schedules differ.

Google first previewed Calendar integration at Google I/O 2026, though it didn’t announce a timeline then. Now it’s live, joining Gmail and Google Photos in the broader Personal Intelligence ecosystem, which has grown from AI Pro subscribers to nearly 200 countries and 98 languages.

What This Means for Search Results

For decades, the same query produced essentially the same results for everyone. That assumption is crumbling.

Research from SEO firm iPullRank found that connecting Gmail to Personal Intelligence changed which brands appeared in AI-generated responses, even with identical prompts across different accounts. Calendar adds another layer of personalisation that goes beyond preferences — it’s about availability, commitments, and timing.

This raises a fundamental question: if Search answers tailor themselves to your schedule, how do you verify what’s accurate? You’re no longer looking at one definitive result page. You’re looking at an answer shaped by dozens of personal signals that exist only inside your own Google account.

The Road to a Proactive Assistant

The logical next step is obvious. If Google connects apps like Keep, Tasks, Maps, Docs, or even third-party productivity platforms, AI Mode could shift from reactive to proactive. Instead of waiting for you to ask, it might anticipate what you need next.

That’s a very different kind of search experience.

It also makes Google’s AI search updates harder to evaluate. Instead of verifying one result, you’re trusting a system that reasons with your personal data. The trade-off is convenience for transparency.

Is This the Future of Search?

Google’s move suggests the future of Search isn’t about finding the same answer as everyone else. It’s about finding the answer that makes the most sense for you — right now, given your schedule, your commitments, and your time.

For users, that’s genuinely useful. For anyone who relies on predictable search results — marketers, publishers, researchers — it’s a shift that demands attention.

Whether you see it as a helpful assistant or a privacy concern, one thing is clear: Search is no longer just a tool for finding information. It’s becoming a personal planner that knows when you’re free.