Eclipse 🌖

I love AI, it’s pure LLMs I hate. Pure LLMs *are* basically just autocomplete. Recent progress (e.g. Claude Code) doesn’t show otherwise Rather, lot of the progress in the last two years has come from *introducing* other things – mainly classic symbolic techniques and tools, to offset the weaknesses of pure LLMs. Shame to see the tweet below muddle all of this. If we want to make further progress we need to understand where the progress is coming from; mostly it is coming from leaving pure LLMs behind.

We love seeing all of the worlds you’ve been creating with Genie. SO much so, that we’re excited to announce Project Genie is now fully available to all Google AI Ultra subscribers globally (18+).

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

My definition of model intelligence has been very clear over the past two years. For me the sign of an intelligent model was always good results with as few resources as possible, which is why I was a big fan of Sonnet 3.5/3.6 and Opus models. These models would just get things and one-shot problems "without thinking". On the other hand I really disliked reasoning models from o1-preview up until o3, because it just wasn't worth it back then and felt like inelegant brute-force slop. You would get slightly better results for 10x the cost. Later from GPT-5 up to GPT-5.2 the reasoning budgets exploded from a few thousand tokens to 50-100k tokens. Since then reasoning efficiency has only improved, and we are now living in a world where GPT-5.5 and Mythos get insane results with very low reasoning budgets and where higher token budgets feel worth it. I think part of this is also that models nowadays know how much reasoning to spend on each problem. So when you set reasoning effort to xhigh it doesn't think for 100k tokens on a very easy problem just for the sake of the xhigh setting. (but personally I still use medium thinking budget like 90% of the time and will only go up to xhigh when the tasks have a high enough skill ceiling. it's overkill to use xhigh for everything)

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.