While formalizing Dummit and Foote's algebra textbook in the Rocq proof assistant, a Recurse Center participant found that the book's first proof exercise—claiming a function is injective if and only if it has a left inverse—fails when the domain is empty and the codomain is not. In that case the empty function is vacuously injective but has no left inverse, since no function can map from a nonempty codomain to an empty domain. The author later confirmed the issue is already listed in the book's published errata.
A technical guide walks through configuring a Tor exit node on an Ubuntu 14.04 system, the type of relay that connects anonymous Tor traffic to the regular internet. It outlines the legal and reputational risks operators face, including potential harassment from ISPs and authorities, plus practical hurdles like sites blocking exit node traffic or forcing CAPTCHAs.
Florida's Department of Transportation issued a memo revoking permits for automatic license plate readers, including Flock Safety cameras, on state-controlled roads. Law enforcement agencies have 30 days from August 31 to remove the devices, and the agency says it will stop approving new permit requests going forward.
An Inside Higher Ed analysis found at least 16 nonprofit colleges shut down in 2025 due to falling enrollment and financial strain, following 28 degree-granting institutions that closed in the first nine months of 2024 alone, according to Hechinger Report data. Entrepreneur's coverage argues these closures are not isolated incidents but the culmination of years of compounding pressures — declining tuition revenue, rising costs, debt and accreditation issues.
Researchers report that psilocybin, the psychoactive compound found in magic mushrooms, shows potential to protect cancer patients from developing long-term chronic pain. The finding points to a new therapeutic application for the psychedelic beyond its studied uses in mental health treatment.
Atopile built a benchmark called EEBench to test whether circuits produced by AI models are actually functional, following OpenAI's demo of GPT-6 Astra designing a board in KiCad. Instead of having an AI operate a graphical CAD tool, EEBench has the model write and edit declarative code describing components and connections, then build and simulate the result to check for errors.
The FCC filed a motion to dismiss Disney's lawsuit, defending its decision to launch an early review of the broadcast licenses held by ABC's eight owned stations. The agency argues the review concerns only alleged discrimination tied to Disney's diversity, equity, and inclusion policies, not Chairman Brendan Carr's public threats over Jimmy Kimmel jokes or The View's political content. Separately, two watchdog groups and individual ABC viewers are seeking to intervene in the case, fearing Disney could strike a settlement with the FCC that doesn't serve the public interest, a motion Disney itself opposes.
The Financial Times published a new profile of John Ternus, who this week became Apple's CEO as Tim Cook shifted to Executive Chair. The piece includes commentary from Corning CEO Wendell Weeks, who has worked with Ternus since early iPad development, and notes Apple marked the transition with a party at Apple Park featuring Zane Lowe DJing.
A new survey of homeowners finds that wellness-focused amenities have surpassed energy efficiency and cost savings as the leading reason people choose to buy or upgrade a home. Features tied to physical and mental well-being are reshaping what buyers look for beyond traditional selling points like countertops or finishes.
Security firm Rietta rolled out an emergency hotfix across its client base on July 29, 2026, after a Ruby on Rails ActiveStorage vulnerability—later named KindaRails2Shell and tracked as CVE-2026-66066—jumped from an unrated update to a 9.5/10 CVSS severity score within hours. The flaw, discovered by researchers at Ethiack, allows arbitrary file read and remote code execution through variant processing in Active Storage, a core Rails component used in Rails 8 and newer.
Researchers extracted and sequenced viral DNA preserved in the animal-skin parchment of medieval manuscripts, tracing sheeppox virus's evolutionary history back roughly 3,500 years. The study, published in Science Advances and led by University College Dublin's Louis L'Hôte, demonstrates that parchment can act as a repository for ancient pathogen genomes, not just host DNA.
A NASA satellite positioned nearly one million miles from Earth photographed three powerful tropical cyclones churning simultaneously in the Pacific Ocean, including category 4 and 5 storms occurring at the same time. Scientists attribute the unusual clustering to an especially strong El Niño pattern currently warming Pacific waters.
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