Yes another one of these AI posts, this is a big one. OpenAI Claims the ETH is false.

OpenAI states "This work will be verified and shepherded by a group led by Russell Impagliazzo (UC San Diego), Ramamohan Paturi (UC San Diego), and Ryan Williams (MIT). All three are experts in algorithm design and complexity theory."

The k-server problem is known as the "Holy Grail" of online algorithms and competitive analysis, and is/was a long standing major problem.

This preprint by Coester et al. claims to show that the Work Function Algorithm is indeed k-competitive on every metric space.

OpenAI just released this on Github. It seems like the rumors of the Unique Games Conjecture and RL = L were indeed true. There's also a lot of other stuff in there which i haven't looked at yet.

Regardless of one's views on AI, it's safe to say TCS is truly facing a watershed moment...

A new preprint claims to have proven the Komlós conjecture, a major problem in discrepancy theory and algorithms research, with the proof reportedly discovered by an AI research agent called Odin. The proof appears to be existential rather than constructive.

The problem is quite easy to explain. Quanta wrote an article about other recent progress on it very recently.

 
Obviously it is not peer-reviewed yet, but if results like this become routine what do we think is the fate of TCS and algorithms research(ers)?

From Scott's blog: Jeffrey Ketchersid has used Claude Code agents to show that BusyBeaver(10) exceeds Graham’s number, beating the previous best result that BB(13) does so.

[I do not think this is independently verified yet]

https://arxiv.org/abs/2609.20979

This preprint by Lovett (well known in TCS) and Karingula claims to present a simpler proof of the Komlós conjecture than the one in Guo et al.