Anthropic announced that an advanced prototype of its Claude AI model converted Andrew Wiles' famous proof of Fermat's Last Theorem into a fully computer-verified formal proof, spanning roughly 13 million lines of code. The task, expected to take human mathematicians about a decade, was completed by the AI in just 11 days. Researchers including Alex Kontorovich and Kevin Buzzard called the achievement astonishing given how quickly AI's formalization skills have advanced.
Researchers examined a regulatory protein that controls the cell cycle and found it has an additional, previously unrecognized function tied to breast cancer development. The finding, published via Nature, points to a more complex biological role for this gatekeeper than earlier assumed.
Researchers led by Nikolai Slavov, Magdalena Zernicka-Goetz and Tsui-Fen Chou used single-cell proteomics to analyze the two earliest daughter cells formed after a fertilized mammalian egg divides. They found that these 'alpha' and 'beta' cells already carry distinct protein profiles linked to different developmental fates, with beta cells more often producing viable embryos while alpha cells tend to form supporting extra-embryonic tissue. The team traced these differing identities back to the moment of fertilization.
The authors of the mouse brain stereotaxic atlas study published a correction fixing several errors: a mislabeled gene name in a figure (corrected to 'Emx1-Cre'), an inaccurate Dice score and sample size in Extended Data Fig. 4, and an updated voxel resolution value in the methods section describing whole-head dataset acquisition. The HTML and PDF versions of the paper have been updated accordingly, with the original figure included as supplementary material for comparison.
The publisher has issued a formal author correction to a previously published paper reporting that inhibiting the AhR protein promotes nerve axon regeneration through a stress-to-growth cellular switch. The correction notice itself does not detail what specific errors were fixed, only confirming that changes were made to the original publication.
Portable CarPlay screens typically cost between $50 and $150, offering a cheaper alternative to buying a new car with built-in infotainment. Buyers should weigh screen size (6 to 11 inches), resolution (ideally at least 1280x720), audio output options like Bluetooth, AUX or FM, and whether the unit supports wireless CarPlay rather than requiring a cable.
A new study in AGU Advances models how a rare, extreme geomagnetic storm—similar in scale to the 1859 Carrington Event—would strain the modern US power grid. Researchers found the Northeast and Northern Plains, particularly higher-latitude areas, face the greatest risk of widespread grid failure, with total economic losses estimated at $1.5 to $2 billion per day.
A review of wireless Android Auto examines how the cable-free setup pairs automatically once a car starts, freeing up cabin space and removing the hassle of plugging in a phone each trip. However, it notes that going wireless increases battery drain, can cause noticeable heat buildup on longer drives, and depends heavily on both phone hardware and vehicle compatibility, particularly in older cars.
A tech reviewer compiled a list of 10 connected gadgets designed to improve backyard spaces, covering categories like entertainment, lawn maintenance, lighting and security. The recommendations span both novel devices and smart add-ons that make existing outdoor equipment more automated.
Austin Z. Henley, a Microsoft engineer, built a minimalist Python interpreter written in C that fits within 1024 bytes of code, after an initial attempt at 512 bytes proved too small. The interpreter supports a limited subset of Python syntax—including def, colons, indentation, and parenthesis-free if statements—enough to run a FizzBuzz program, but skips CPython's full tokenizing, AST, and bytecode pipeline in favor of global variables and a fixed-length array.
Mathematicians Wang and Wu of Hunan University released a preprint proving the Spherical Hadwiger Conjecture, an integral-geometry problem unsolved since 1974, using OpenAI Codex to help develop proof details, spot gaps, and draft the manuscript. The authors say they verified all AI-generated mathematical content themselves and take full responsibility for the final result, following disclosure practices similar to the Leiden Declaration guidelines for AI use in research.
Apple's built-in Time Machine utility lets Mac users back up apps, photos, videos and documents to an external hard drive or SSD without paying for cloud storage subscriptions. The initial backup takes longer, but subsequent backups run faster and can be scheduled hourly, daily or weekly. This offers an alternative for users who don't need remote file access but want reliable backups.
GoKawiil