Anthropic says a team of Claude agents has produced the first complete computer-checked proof of Fermat’s Last Theorem. The work took eleven days, generated 13 million lines of Lean code and established more than 30,000 intermediate theorems. The final artifact is more than five times the size of Mathlib, the community library of formal mathematics on which it builds.

This is not a new proof of Fermat’s famous claim. Andrew Wiles and Richard Taylor supplied that in the 1990s. It is something both more mechanical and, for the practice of mathematics, potentially more disruptive: a translation of the argument into a language whose logical steps a proof assistant can check from end to end.

The scale is the story. Wiles’s published proof occupied 129 pages and required expert readers to inspect reasoning that rested on generations of shared mathematical knowledge. Lean accepts no collegial nod and no skipped obvious step. Every definition must be supplied; every bridge must bear its stated load. Turning a human argument into a machine-checkable one therefore creates an object vastly larger than the paper it verifies.

Claude did not simply type that object in sequence. Anthropic reports that dozens of agents worked through a collaborative platform called Prove2Me, which represented the campaign as a directed graph of dependent theorem statements. The system helped agents locate unfinished work, reuse completed components and avoid losing the project’s state. After early coordination failures, that scaffold became the difference between a swarm producing fragments and a team closing the root theorem.

The project consumed roughly six billion output tokens from an internal research model described by Anthropic as comparable to Claude Fable 5.1. Human mathematical direction was limited but consequential: a researcher occasionally identified high-priority concepts or redirected effort. Lean then checked the completed construction using its standard axioms, and a comparator matched the theorem statement to Mathlib’s formulation of Fermat’s Last Theorem.

There are two achievements here, and they should not be confused. One is mathematical: a notoriously elaborate body of modern number theory has been encoded in a form a computer can verify. The other is organizational: language-model agents were able to divide, track and complete a project whose intermediate product exceeded the size of the library it depended upon.

That second achievement may travel further. Formalization has long been constrained less by the ability of proof assistants to check logic than by the human labor required to state everything precisely. If agents can supply that labor, journals could eventually expect machine-checkable companions to difficult papers. Old results might be audited. New AI-generated claims might be filtered before human referees spend months finding a broken link.

But verification is not compression. A 13-million-line artifact can certify correctness while remaining nearly impossible for a person to survey. The human-readable proof, the historical explanation and the account of why an idea matters do not become obsolete when the checker returns green. They become the scarce layer.

Fermat allegedly claimed that a marvelous proof would not fit in his margin. Four centuries later, the proof fits inside a machine only by becoming a library. The margin problem has been solved. The comprehension problem has not.

A Chinese worker was brought out alive from a hydropower tunnel in Nepal on Saturday, ten days after a glacial collapse sent a wall of water, mud and rock through communities near the Chinese border.

Lu Haitao had climbed to the highest point he could reach inside the 225-meter tunnel. He later recalled hearing rescuers’ whistles and wondering whether he had imagined them, according to audio carried by Chinese state broadcaster CCTV. A joint team involving Nepalese military personnel and South Korean disaster specialists carried him out and evacuated him by helicopter. He was reported in stable condition.

Two Nepalese workers had been rescued from the Trishuli hydropower project a day earlier. A woman was also found alive in a separate operation Saturday. Each survival is extraordinary; none changes the scale of the disaster around them.

Nepal’s disaster management agency said more than 1,300 people had died and nearly 4,900 remained missing as of Sunday’s reporting. Chinese official figures cited by the Associated Press listed 31 dead and 531 missing on the Tibetan side of the border. Those figures may change as isolated areas are reached and duplicate missing-person reports are reconciled.

Satellite analysis indicates that bedrock and part of a glacier collapsed into a steep valley on Aug. 26. The resulting mass maintained its momentum as ice melted, swelling rivers with sediment and debris. Entire stretches of the Trishuli corridor were widened, buried or cut off.

The rescue also exposes the double nature of Himalayan hydropower infrastructure. Tunnels and plants promise electricity to remote regions; their construction sites concentrate workers inside valleys where roads, communications and escape routes can disappear together. Lu survived because the tunnel contained a high point, because air remained available and because search teams kept listening after the ordinary rescue window had closed.

The headline is a man returning from beneath the mountain. The continuing story is everybody for whom no whistle has yet been answered.

Indonesia canceled all flights at Jakarta’s Soekarno-Hatta International Airport early Sunday after Anak Krakatau erupted and volcanic ash drifted across western parts of the country.

The disruption also affected domestic airports, according to the Associated Press. Ash is not an ordinary visibility hazard. Its fine particles can abrade cockpit windows, contaminate aircraft systems and melt inside jet engines, where they may accumulate and interrupt combustion. Airlines and regulators therefore treat uncertain ash boundaries conservatively.

Soekarno-Hatta is Indonesia’s main international gateway and a central transfer point for an archipelago whose geography makes aviation essential infrastructure. Closing it turns one volcanic event into a network problem: aircraft and crews are left out of position, connections fail far beyond the ash cloud, and reopening the runway does not instantly restore the timetable.

Anak Krakatau—“Child of Krakatau”—grew from the caldera left by the catastrophic 1883 eruption. Its activity is monitored continuously, but forecasting the precise movement and operational effect of ash depends on wind, eruption intensity and altitude. That makes cancellation a decision taken before certainty arrives.

For passengers, the useful distinction is between an airport reopening and an itinerary recovering. The first is a safety determination. The second may take days of aircraft swaps, added flights and rebooking. Sunday morning supplied the spectacular image of an erupting volcano. The quieter consequence will be measured on departure boards across Southeast Asia.

Iran said Sunday that it struck an unmanned American vessel attempting to enter the Strait of Hormuz. The United States had not immediately confirmed the reported attack.

The claim arrived one day after the U.S. military said its forces had struck three Iranian oil tankers in response to ballistic missiles directed at Navy warships. The Associated Press reported that the latest exchanges followed the resumption of attacks last week after roughly a month of relative calm.

The distinction between a claimed strike and a confirmed one matters, particularly in a conflict where unmanned platforms, damaged commercial traffic and competing military accounts can circulate faster than independently verified evidence. At publication, there was no public American confirmation establishing whether a vessel was hit, what platform Iran targeted or what damage occurred.

The fighting began with U.S. and Israeli attacks on Iran on Feb. 28. A ceasefire was announced in June, but intermittent attacks continued and negotiations later stalled. The current round has again concentrated attention on the narrow waterway through which a substantial share of internationally traded oil normally passes.

Sunday’s development is therefore both a military claim and a test of attribution. An unmanned target may reduce the immediate risk of casualties, but it does not reduce the possibility of escalation if one side treats damage to it as requiring a response. Until corroborating evidence appears, the firm facts are limited: Iran made the claim, Washington had not confirmed it, and both states had acknowledged separate attacks during the preceding days.

Domestic movie theaters sold $4.61 billion in tickets between May 1 and Aug. 31, according to Rentrak figures reported by the Associated Press. That was 26.1 percent above the summer of 2025 and the strongest summer gross since 2013.

Hollywood will reasonably call that a recovery. It should not call it a restoration.

Higher ticket prices make gross revenue a generous measure of audience health. The AP noted that admissions remain well below pre-pandemic levels. In other words, theaters extracted more money from a smaller base than the headline comparison might suggest. Premium screens, variable pricing and blockbuster concentration can produce a large dollar total without recreating the old habit of frequent moviegoing.

The encouraging part of the season was not simply that familiar brands earned money. Gen-Z moviegoers turned up, and lower-budget films including “Obsession” became hits. That matters because a theatrical business dependent on two or three giant franchises is less a market than a sequence of refinancing events. Smaller films create more release weekends on which audiences have a reason to visit.

The failures were instructive too. Expensive intellectual property did not automatically convert into demand. A live-action “Moana” remake and “Supergirl” underperformed relative to the scale of their release, while other franchise titles flourished. Recognition may secure awareness; it no longer guarantees urgency.

Theaters have proved they can still create cultural appointments. The unresolved business question is whether they can turn those appointments back into a routine. Gross receipts tell studios what arrived in the till. Admissions, repeat visits and the number of films capable of opening without inherited fandom will tell them whether the audience actually returned.

Google released a Chrome update on Sept. 4 addressing CVE-2026-85046, a type-confusion vulnerability in the browser’s V8 JavaScript engine. Google said an exploit for the flaw existed in the wild, according to security reporting aggregated by AI Weekly.

The patched desktop versions are listed as Chrome 152.0.7977.82 and .83. Because Chrome updates can download in the background without taking effect until the browser restarts, users should check the browser’s About Chrome screen and relaunch it. Chromium-based browsers maintained by other vendors may publish their own corresponding updates.

A V8 type-confusion flaw can cause the engine to handle data as the wrong kind of object, creating opportunities for memory corruption and potentially attacker-controlled code execution within the browser renderer. Exploiting a renderer does not necessarily provide control of an entire device; modern browsers use sandboxes and other layers intended to contain a compromised tab. Attackers may pair multiple vulnerabilities to cross those boundaries.

The episode also illustrates the awkward symmetry of automated security. Google has described using AI-based systems to find vulnerabilities across Chrome more efficiently and reduce false positives. Attackers can use the same broad class of tools to inspect code, adapt exploit chains and scale targeting. Faster discovery does not eliminate the race. It shortens both sides’ clocks.

The practical instruction is plain: close the browser once. A relaunch is a small interruption compared with leaving a known, actively exploited flaw resident in the application through which much of modern work passes.

The most promising thing about the fall movie calendar is not an awards contender or a billion-dollar brand. It is the recurrence of specificity.

Laika’s “Wildwood” offers stop-motion animation, a kidnapped baby and a forest governed by crows. “La Bola Negra,” from Javier Ambrossi and Javier Calvo, connects the lives of three gay men across 1932, 1937 and 2017. Lee Chang-dong returns after “Burning” with a drama built around four strangers meeting by chance. Amir Bar-Lev’s “The Last First: Winter K2” revisits a deadly expedition without requiring anyone to wear a cape.

The release schedule still contains brands—“Resident Evil” returns, and another Dickens adaptation arrives with Johnny Depp as Scrooge—but even those choices have odd edges. Horror director Ti West making “A Christmas Carol” is at least a proposition rather than a quarterly obligation.

This is what theatrical film has too often lacked: not originality in the abstract, but texture. A movie earns texture by seeming to come from a particular maker, place or obsession. It leaves a residue beyond the knowledge that a rights department remains operational.

Audiences spent heavily at theaters this summer, but the durable recovery will depend on whether a night at the movies can promise surprise. Fall’s slate contains reasons to enter without already knowing the shape of the exit. That is not a small luxury. It is the medium remembering what the dark is for.

The green check is seductive. It says the dependencies resolve, the axioms hold and the conclusion follows. After centuries of dubious manuscripts and heroic refereeing, mathematics has acquired something like a final inspection.

Good. Now resist the temptation to mistake inspection for understanding.

Anthropic’s formalization of Fermat’s Last Theorem is 13 million lines long. No person will hold that object in mind. Its trust comes from the small kernel checking the logic, the openness of the definitions and the ability of specialists to inspect pieces—not from any reader experiencing the proof as an argument from beginning to end.

That is acceptable for verification. It is disastrous as a model for knowledge.

A human explanation does different work. It tells us which ideas carry the load, which detours can be forgotten, why one abstraction succeeds where another fails and how the result connects to questions somebody might ask next. Explanation is lossy by design. It compresses without pretending that every omitted step vanished.

As machines become better at producing formally valid work, prestige will drift toward the certified artifact. Universities, journals and laboratories should push the other way. Require the artifact, certainly. Then demand an account a trained reader can inhabit. Reward the person who can compress thirteen million lines into an honest map without flattening the terrain.

The danger is not that AI will make mathematics false. Proof assistants are unusually good at preventing that. The danger is that they will make correctness abundant while leaving comprehension expensive—and that institutions, pleased by the green check, will stop paying the bill.