Quanta’s write-ups of math discoveries are always enjoyable to read. In this case an undergraduate (!) figured out something new about hash tables and how fast they can be. Not sure yet when this will be shipped in code, but still it’s a pretty amazing discovery.

LLMs are fundamentally matching the patterns they’ve seen, and their abilities are constrained by mathematical boundaries. Embedding tricks and chain-of-thought prompting simply extends their ability to do more sophisticated pattern matching. The mathematical results imply that you can always find compositional tasks whose complexity lies beyond a given system’s abilities.

The Agents chapter from Chip Huyen’s book “AI Engineering” is clear and enjoyable to read. She’s right that “the concept of an agent is fairly simple” but building something functional still looks like a massive lift.