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A newly published online atlas organizes 3,915 known periodic solutions to the three-body problem into a navigable map, grouping similar orbits into families that appear as clustered 'islands.' Each orbit has its own dedicated page where users can watch it animate through one full period, nudge it slightly off its original path, and compare or rank it against other orbits.
OpenAI says it has solved a Millennium Prize-level math problem, extending a string of high-profile claims in mathematics. Researchers including Tristan Buckmaster and Andreas Thom say the company has been vague about whether their own prior work, done through OpenAI's Codex tool, fed into its results. OpenAI denies this, insisting Buckmaster's recent prompts could not have influenced the system's training.
The Clay Mathematics Institute issued a statement noting growing momentum toward solving the Navier-Stokes Millennium Prize Problem, which concerns whether smooth, well-defined solutions always exist for the equations governing 3D fluid motion. CMI pointed to recent breakthroughs in related research, some already honored with its Clay Research Award, as evidence that a resolution could be near.
Employees are increasingly suspicious of coworkers who use AI tools, largely because organizations haven't established clear guidelines on when and how AI use is appropriate. This ambiguity is creating friction and eroding trust among team members who lack a shared understanding of acceptable practices.
A new study found that scent-detection dogs make more false-positive alerts when they have not eaten breakfast before starting work. Researchers observed that dogs on empty stomachs were more prone to signaling a scent that wasn't actually present, compared to dogs that had eaten beforehand.
An Entrepreneur contributor writing from experience scaling a regulated payments company argues that surpassing roughly 100,000 customers does not mark the end of hard problems but the start of new, more dangerous ones. Early shortcuts in engineering, treasury, compliance and onboarding that worked at small scale begin to buckle under volume, often without warning until systems are already strained.
United Launch Alliance remains one of the few major US rocket companies still focused almost entirely on launch services rather than branching into satellites, spacecraft, or other space businesses. Competitors like SpaceX, Blue Origin, Rocket Lab, and Firefly Aerospace have all expanded beyond launch to capture higher-margin revenue streams, leaving ULA increasingly isolated in a low-margin segment of the industry. This has renewed speculation about whether ULA's parent companies, Boeing and Lockheed Martin, will eventually sell the venture.
Tesla has begun distributing a 'Robotaxi interest form' encouraging entrepreneurs to buy fleets of its two-seat Cybercab and share ride revenue with the company as it expands robotaxi operations in Austin. The push follows Elon Musk's long-standing claims that self-driving Tesla vehicles could become passive income machines for owners.
AI training campuses can swing 70% of their electrical load within milliseconds and disconnect just as abruptly to protect expensive compute hardware, a pattern conventional grid infrastructure was never designed to handle. Analysis of the setup shows the standard power stack—medium-voltage feeds, transformers, and uninterruptible power supplies—fails at three points: undersized battery buffers, converters run in bypass mode that let raw swings and grid transients pass unfiltered, and protection logic built for far smaller loads that trips offline at the worst possible moment. The 2024 Virginia grid disturbance was traced largely to this outdated protection logic disconnecting under stress.
The US Commerce Department is distributing $300 million in CHIPS Act funding equally among D-Wave Quantum, Rigetti Computing, and Quantinuum, giving each $100 million while also acquiring minority ownership stakes in the companies. The money targets hardware manufacturing challenges like cryogenics, semiconductor fabrication, ion traps, and photonics rather than quantum software development.
OpenAI announced its AI resolved a long-standing open question about the Navier-Stokes equations, one of the Clay Mathematics Institute's Millennium Prize Problems, claiming it did so within days using roughly 10,000 agents. Mathematician Tristan Buckmaster disputes the credit, saying he and Anthropic researcher Levent Alpöge had already developed the key approach before OpenAI learned of it and rushed to finish the proof over a weekend.
OpenAI published a paper claiming an unreleased model coordinated up to 10,000 AI agents over 88 hours to produce a formal Lean proof addressing the Navier-Stokes existence and smoothness Millennium Prize Problem. The company says the proof identifies conditions under which the equations develop a mathematical singularity, not evidence that real fluids behave impossibly. Outside mathematicians have yet to verify the claim.