OpenAI just published solutions to three math problems that researchers have been stuck on for years. One of them knocks out the Exponential Time Hypothesis, or ETH, a core assumption in computer science that defines what's hard to compute. If it holds up, that's a big deal.
Why you should care: ETH says the fastest algorithms for a certain class of tricky logic puzzles need exponentially more time as variables grow. OpenAI's models produced algorithms that solve those puzzles in sub-exponential time. Anyone who has cited ETH in a paper, and that's a lot of papers over the past decade, now has homework. The catch? Faster algorithms here could also threaten cryptographic systems that depend on certain key sizes. OpenAI says its claims don't break any crypto, which is a relief.
The release process is the messy part. Mathematicians got the work dropped on GitHub. Computer scientists formed a working group and asked for public proofs plus OpenAI funding for a conference. Physicists are still deciding how their result gets published. Spoiler: it's not that simple, and this is a live experiment in how AI-driven discovery gets shared.
OpenAI just shipped dots, a persistent personal assistant that works without being prompted. It lives in the ChatGPT desktop and mobile apps, and it's gated behind the Pro tier, which starts at $100 a month.
If you already use Codex for coding help, dots is the same underlying power repackaged for everyday work. Codex can get you most of the way there, but you'll do more hand-holding. dots connects to your calendar, email, computer, and other tools, so it can flag conflicts, surface upcoming deadlines, and even analyze an outage and suggest a fix. The catch is timing. It warns you about deadlines, just not always in time to act on them.
Privacy controls mirror ChatGPT's, including the option to turn off model training and limit which resources it touches. It won't accept read-only access to cloud drives, though, and it collects data about your family and friends, similar to Muse. OpenAI says it plans much more granular controls and is working with the wider ecosystem on partnerships, including payment companies that could let it spend money. Bottom line: that's a lot of trust for a tool that's still learning when to speak up. Let's dive deeper…
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