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OpenAI has published an update describing how its AI systems are advancing in mathematics, a field long seen as a benchmark for reasoning ability. The post outlines the company's approach to evaluating and sharing progress on math problems. The item drew strong attention on Hacker News, where readers are debating what these mathematical capabilities signal about the state of AI reasoning more broadly.

Mathematician Terence Tao is arguing that "Math 2.0" — the emerging era of mathematics shaped by AI and new collaborative tools — will require valuing mathematical progress more holistically, not just through traditional metrics like published proofs. His remarks are drawing wide attention among technologists and researchers debating how AI is changing how mathematical knowledge is created and judged.

AbemaTV is drawing attention in Japan with a program featuring a single father raising four children alone after divorcing over his wife's infidelity. He answered candidly when asked whether he would meet his ex-wife if she said she wanted to see him, sharing his honest feelings about the breakup and solo parenting.

Weather forecasts for tomorrow point to a split across France: grey, overcast conditions in the north with sunshine in the south, before cooler air returns later in the week. In central regions, forecasters warn of heavy rain and thunderstorms expected this evening and tomorrow, while the north stays sunny. People are checking the outlook as the recent mild spell gives way to a fresher pattern.

A federal judge, described in court as furious, has halted tree removal connected to a plan to upgrade a Washington, D.C. golf course tied to Donald Trump. The judge paused the work and demanded that officials provide answers about the project, raising fresh scrutiny of how the plan was approved and its environmental impact.

Thunderbird 158, Mozilla's open-source email client, has been released with a faster, more responsive Quick Filter and a batch of additional bug fixes. The update is drawing attention across free and open-source software communities, particularly among Linux users who follow each release of the long-running email application.

Indian opposition leaders are marching to the Supreme Court in Delhi to demand the resignation of the country's chief election commissioner. The protest escalates a growing standoff between opposition parties and India's election authorities over the conduct and credibility of the electoral process, drawing wide national and international attention.

OpenAI has withdrawn three mathematical results, according to a post from an OpenAI researcher announcing the retraction. Details on which results were pulled and the reasons for the withdrawal have not yet been made widely available. The news is drawing attention from researchers following the reliability of AI company claims in mathematics.

Actor Nana Patekar has been given a state funeral in Maharashtra, with the state bidding farewell to one of Indian cinema's most respected figures. NDTV reported on the ceremony, which drew significant public attention. Details about the date, location and attendees remain limited, but the honour reflects his standing in Marathi and Hindi film.

Penguin Mail, a new open-source email client written in Rust for Linux, is drawing attention for its built-in AI features. The project has been shared on developer forums, where commenters are weighing its performance and privacy credentials against established clients. Interest centers on the combination of a memory-safe Rust codebase, native Linux support, and integrated AI assistance in a free, open-source package.

Mathematician Terence Tao has published a new essay on his blog examining the Lean theorem prover, focusing on questions of reliability and the role of artificial intelligence in formal proof verification. The piece is aimed at mathematicians weighing whether to adopt Lean in their work and how AI-assisted proof tools fit into trustworthy mathematics.

Hundreds of thousands of people have taken to the streets across France to demand reform of the country's education system. The demonstrations, described by some outlets as France being 'on fire,' represent one of the larger protest mobilizations in the country recently. Details about the specific reforms being demanded and the organizers have not yet been fully reported.

Dutch cycling media are discussing the Simac Ladies Tour, with organiser Simac reportedly giving the women's stage race room to develop further within the Eneco Tour framework. Roxane Knetemann, the Dutch former professional rider and commentator, is also being searched and talked about in connection with Dutch cycling coverage.

A US senator is formally demanding information about a license plate surveillance program run out of the White House, following a 404 Media investigation that exposed the initiative. The inquiry raises questions about the legality and scope of mass vehicle tracking by the executive branch, and is likely to fuel a broader debate over privacy, government overreach and the lack of oversight surrounding automated license plate reader networks.

OpenAI has released a collection of mathematical manuscripts alongside supporting proof artifacts on its public code repository. The materials document formal proofs and written mathematical work produced by the company's AI systems. Hacker News readers are sharing the repository, with discussion focusing on what the releases indicate about AI capabilities in formal mathematics and rigorous proof generation.

Mikayla Demaiter, a Canadian former ice hockey goaltender turned social media model, is trending after headlines about her meeting a new 'tall guy' while accompanying her boyfriend, golfer-turned-influencer friendship circles. A Daily Star article highlighting her 'unlikely admirer' has driven fresh searches, with readers reacting to her ever-growing fanbase and glamorous photos.

A writer has described another failed attempt to move his personal notes out of Emacs, returning to the editor after trying something else. The post, shared on Hacker News, is part of a familiar debate among Emacs users about whether its plain-text workflow is worth the lock-in compared with newer note-taking apps.

A reference guide on the mathematics of geothermal energy is drawing attention, covering the equations and models used to quantify heat extraction, power output and efficiency from geothermal resources. The item arrives amid renewed interest in geothermal as a low-carbon, always-on power source, with readers debating how its physics and costs compare to solar, wind and other renewables.