Thursday, September 10, 2026

OpenAI claims its AI has solved the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems worth $1 million, by producing a proof showing that the equations for fluid motion can develop a singularity in finite time. The result was formally verified using the Lean programming language, though some mathematicians have raised concerns about potential conflicts with unpublished research.^[1]

Paleontologists have identified a giant new dinosaur species from Brazil that reached about 20 meters long and lived 120 million years ago. The fossils were found at a road-rail terminal construction site, and the animal's evolutionary ties to a Spanish dinosaur suggest its ancestors crossed ancient land connections between Europe, Africa, and South America.^[2]

The ESA-JAXA BepiColombo spacecraft has begun its arrival phase at Mercury after an eight-year journey, successfully separating its propulsion module from the two science orbiters on September 3. The spacecraft is on track to enter Mercury orbit in November 2026, with scientific operations scheduled to begin in April 2027.^[3]

New observations from the ALMA radio telescope show that interstellar comet 3I/ATLAS contains unusually high levels of methanol, exceeding amounts seen in almost all known comets from our solar system. The findings suggest the comet formed under conditions very different from those in our solar neighborhood.^[4]

Researchers at the University of Leipzig found that an experimental compound called AP503 significantly strengthened bones in mice by activating GPR133, a receptor that boosts bone formation while slowing bone loss. The same treatment has also been linked to stronger muscles, suggesting potential applications for age-related decline and osteoporosis.^[5]

Hungary expelled 10 Russian diplomats for activities deemed incompatible with their diplomatic status, marking a significant shift under Prime Minister Peter Magyar's government. Russia's foreign ministry said it would retaliate, calling the expulsion an 'extremely unfriendly step.'^[6]

Record rainfall of 104 millimeters in an hour forced hundreds of Asian Games athletes to evacuate their accommodations in Nagoya, Japan. Municipal officials issued evacuation orders for parts of the city, with rainwater also leaking into some competition venues.^[7]

The United Kingdom, France, and Canada joined nine other European countries in banning trade with Israeli settlements in the occupied West Bank, which are considered illegal under international law. Israel responded by ordering Britain to close its East Jerusalem consulate within 30 days.^[8]

Spain experienced its hottest summer on record, with average temperatures of 24.5°C—0.3°C above the previous record and 2.4°C higher than the 1991-2020 reference period. The country recorded 44 heatwave days, surpassing the previous high of 41 from 2022.^[9]

A study published in Nature found that phone-based tutoring produced large, cost-effective learning gains for children during school closures across five countries. The research suggests that remote phone tutoring can keep children learning when schooling is disrupted by disease or climate events.^[10]