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Three Mathematicians Prove Long-Standing 2004 Graph Sandwich Conjecture

A team of three mathematicians has finally proven the 2004 'sandwich conjecture,' which claims that any sufficiently large graph of interest can be mathematically bounded above and below by two simpler, well-understood random graphs. The proof, completed in 2025, resolves a two-decade-old open problem in graph theory by pushing existing mathematical techniques to their limits.

AI memory boom triggers price surge for NOR flash and SLC NAND chips

Analysts at Morgan Stanley, JPMorgan, and TrendForce report that legacy memory types like NOR flash and SLC NAND are facing severe supply shortages as manufacturers redirect production capacity toward more profitable HBM and DRAM chips driven by AI demand. Contract prices for both chip types have already more than doubled in the first half of 2026, with SLC NAND expected to rise another 120-170% in the second half.

Independent researcher claims AI-assisted Lean proof of Conway's 50-year-old refinement conjecture

An amateur mathematician spent a month using a frontier AI model to attempt a formal Lean proof of John Conway's refinement conjecture about omnific integers in surreal number theory, a problem posed 50 years ago. The proof reportedly passed mechanical verification through the Palomar registry, and some Lean and field experts said the statement appears correct, though full independent mathematical verification is still pending.

Twilio's Jeff Lawson to discuss fusion startup Inertia at TechCrunch Disrupt 2026

Jeff Lawson, who co-founded and scaled Twilio to over $4 billion in revenue, is now leading Inertia, a fusion energy startup. He will speak about this career shift at TechCrunch Disrupt 2026 in a fireside chat on the Smart Systems Stage, discussing how his software background applies to a capital-intensive deep tech venture involving lasers and manufacturing.

ICE Stopped Tracking Miscarriages in Detention After Recording 18 Cases

A Guardian investigation found ICE documented 18 miscarriages among detained women in the first nine months of Trump's second term, but stopped keeping records after October 2025, leaving an unknown number of subsequent losses uncounted. One detainee, an asylum seeker named Anabell, described being denied prenatal care and a doctor's visit for weeks despite bleeding, before finally being taken to an emergency room shackled to a bed, where she learned she had lost her pregnancy.

Virginia Gov. Spanberger signs order restricting data center NDAs, creates AI task force

Virginia Governor Abigail Spanberger issued Executive Order 22, barring executive branch officials from signing NDAs on data center projects, mandating faster noise regulations, and reviewing backup power operations. The order also launches an AI task force to study risks like job losses and privacy harms, alongside a new state framework aimed at ending automatic zoning approvals and rolling back subsidies for data center developers.

Google Messages extends chat themes to standard SMS conversations

Google is quietly expanding its chat themes feature in Google Messages beyond RCS conversations to include standard SMS texts, according to a Reddit user's discovery confirmed on a Pixel 6a. Users can access the feature through the three-dot menu or contact info page, though Google hasn't published official documentation about the rollout.

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