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Anthropic's Claude produces first fully computer-verified proof of Fermat's Last Theorem

Anthropic researcher Tianyi Peng tested whether the Claude AI model could formalize Fermat's Last Theorem in the Lean proof assistant, and over 11 days of largely autonomous work, Claude generated an end-to-end, machine-checked proof. The system wrote roughly 13 million lines of Lean code and proved about 29,500 intermediate theorems, building on decades of prior work including Andrew Wiles's 1995 proof and a community formalization effort led by Kevin Buzzard since 2024.

Casio Leaks Point to New G-Shock GMC-2500/GAC-2500 With Nautilus-Style Case

Leaked images on Notebookcheck and Instagram reveal upcoming Casio G-Shock GMC-2500 (steel) and GAC-2500 (resin) watches featuring pronounced side shoulders reminiscent of Patek Philippe's Nautilus. The resin GAC-2500 line reportedly draws design cues from the original 1983 DW-5000C, while Casio has not confirmed pricing, specs or release date and declined to comment when asked by WIRED.

Nuclear industry veteran details rocky pivot to entrepreneurship after 19-year career

A former commercial nuclear power operator who rose from Reactor Operator to Senior Reactor Operator and into management left his 19-year utility career at 38, relocating from Michigan to Washington, D.C. to chase 'unlimited income potential' through sales and business ownership. He found that the skills that made him excel as an employee inside a large organization did not translate into success running his own venture.

70mai A810 Lite 4K Dual Dash Cam Drops to $89.97 on Amazon

Amazon has discounted the 70mai A810 Lite 4K Dash Cam Front and Rear by 40%, bringing its price down from $149.99 to $89.97. The device offers 4K front and 1080p rear recording, built-in GPS, Wi-Fi 6 connectivity, and ADAS driver alerts, plus optional parking surveillance features when paired with a hardwire kit.

Apple reportedly developing AI-driven home security camera with monitoring service

According to Bloomberg's Mark Gurman, Apple is developing a privacy-focused home security camera and automation device paired with a new monitoring service, expected to launch next year. The camera would reportedly rely on AI analysis rather than raw video footage to track home activity, and it's positioned as part of a broader wave of device launches Apple has planned over the coming years.

Entrepreneur op-ed lists subtle warning signs of eroding workplace culture

An Entrepreneur contributor argues that toxic company cultures rarely announce themselves with dramatic incidents, but instead develop gradually through small, easily overlooked behavioral shifts. The piece identifies quiet indicators—like employees no longer speaking up, volunteering, collaborating, or caring about customers—as early warnings that leadership often misses until the damage is entrenched.

Celleste CEO argues innovation success now hinges on resilience over speed

An opinion piece from the leader of Celleste, maker of the first chocolate bar using cell-cultured cocoa butter, argues that innovation strategy is shifting away from pure speed-to-market toward long-term adaptability. The author draws on experience navigating cocoa supply chains, manufacturing and consumer trust to argue that lasting innovations solve existing industry problems rather than forcing wholesale reinvention.

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