AI and Mathematics: OpenAI says its models produced proofs challenging the Exponential Time Hypothesis and resolving major mathematical conjectures; independent researchers are assessing the results and their implications. Animal Science: A study of jumping spiders found a regulated sleep cycle with eye movements and muscle twitches resembling human REM sleep, offering clues to how sleep evolved. Medical Imaging: Georgia Tech researchers developed a framework to reduce trial and error in mass spectrometry imaging, which maps molecules in tissue and can help investigate disease. Ancient Life: Fossils from China reveal a fully marine amphibian that lived about 237 million years ago, an unexpected find among ancient sea creatures. Climate: Scientists and environmentalists welcomed Lula’s reelection in Brazil, hoping it will sustain efforts to curb Amazon deforestation, though a hostile Congress could complicate forest protection. Infection Research: Honey from Australia’s native stingless bees stopped the growth of all bacteria tested, including hard-to-treat hospital pathogens; researchers are now investigating the compounds behind its effects.