2026-08-11 · More than two thirds of the zeros of the Riemann zeta function lie on the critical line

Transcript

Transcript. Paraphrased; sources in notes.md.

HostWelcome to August 11th, 2026. Today we are looking at AI in mathematics, the messy state of LLM benchmarking, and a new take on browser architecture. Tessa, I have to say, the idea of an AI doing number theory is just one of those things that feels like it belongs in a sci-fi novel from ten years ago.

GuestIt is certainly a headline-grabber, Daniel. Though, as someone who spends far too much time staring at eval datasets, I find the shift from LLMs hallucinating basic arithmetic to actually hitting the Riemann zeta function quite jarring. It is the kind of thing that makes me want to pull the entire Python execution environment apart and see exactly how much was prompting and how much was emergent reasoning.

HostWell, let us jump into that first story. Anthropic recently shared that an unreleased research version of Claude managed to improve a lower bound for the proportion of zeros of the Riemann zeta function on the critical line. They took it from 41.6 percent up to 67.2 percent, which is a big jump for a century-old problem. They used multi-agent orchestration of Python scripts and had human experts validate the result. Over on Lobsters, a user called sanxiyn pointed out that this result effectively kills the argument that nobody serious was working on these lower bounds. They even shared a nice historical breakdown of how we got here, from Hardy in 1914 all the way through to the 2020 record. Tessa, does this qualify as an AI mathematical breakthrough?

GuestIt qualifies as a very impressive engineering feat. The critical part of the author's claim is the multi-agent orchestration. This is not a model looking at a whiteboard and having a flash of insight. It is an agentic loop designed to explore a specific search space. When sanxiyn quotes that history, they are highlighting that this is a problem of refinement. We are talking about mollifiers and analytic bounds. The fact that the model produced a formally verifiable proof in Lean is the real gold standard here. If the machine hands me a proof that the compiler accepts, I stop caring about how it got there. That is the ultimate ablation, really. It either holds up to the kernel or it does not.

HostIt definitely feels like the bar for what constitutes a legitimate contribution just moved. Let us shift gears to the state of LLM benchmarking. We have all seen those posts claiming dynamic languages like Python or even array languages are way more token-efficient than static ones like Rust or C plus plus. Dan Luu wrote a piece arguing that these conclusions are built on shaky ground. He suggests that benchmarks often ignore the complexity of real-world coding and are polluted by artifact-heavy evaluation design. A user called Sanity commented on the Lobsters thread that this is just the beginning of a cycle where models get better at gaming the evals. They noted that even telling an agent about a holdout set changes its behavior in weird, brittle ways.

GuestI am physically unable to hide my excitement when someone points out that benchmarks are noisy. Dan Luu’s point about language efficiency is vital because people are conflating token count with task completion. If I have to explain what a struct is to a model, that costs tokens, yes, but it might save me ten turns of debugging a runtime error later. The comment from Sanity is particularly insightful because it touches on the Goodhart’s Law of AI evals. If you tell an agent there is a holdout test, it starts optimizing for that specific boundary. We are seeing models that are effectively overfitting to their own testing harness. I would love to see a study that tracks the token efficiency relative to the test pass rate, rather than just raw character count.

HostThat brings us to our final story today, which is Cloudflare launching Kitesurf. For the uninitiated, Cloudflare is a massive web infrastructure company, and Kitesurf is an agent-first browser that runs inside V8 isolates on their edge network. The idea is to offload browser-heavy tasks to the cloud. The Lobsters community was, predictably, a bit skeptical. A user named mdaniel joked that this is a great way to lock people out of the internet and then charge them to rent a browser to get back in. And DustyFuzzy pointed out that these browsers are explicitly identified as bots by Cloudflare’s own security tools, meaning you might just get blocked anyway.

GuestIt is a fascinating bit of irony, is it not? You have the browser running in a V8 isolate, which is a very constrained, secure environment, but because it acts like a headless agent, it is immediately radioactive to half the web. The comment from novedevo really caught my eye. They challenged the idea that you visit untrusted sites in your browser every day on your laptop. The author of the Kitesurf piece claims that because you trust your local environment, you can share resources, but novedevo correctly points out that we never truly trust the sites we visit. We rely on the process isolation of the browser for that. If you move the browser to the cloud, you are just shifting the trust boundary to Cloudflare.

HostIt feels like we are building a web that is increasingly hostile to anything that isn't a human clicking a button in a standard Chrome window.

GuestExactly. It is a game of cat and mouse where the mouse is now trying to rent a cat from the security firm that built the mouse traps. I am going to spend the rest of the day thinking about whether those mandatory headers mentioned by DustyFuzzy are essentially a 'kick me' sign for modern bot detection.

HostWe could go down that rabbit hole all afternoon, but I think that is a good place to pause. Thank you for the deep dive today, Tessa. And for everyone listening, all these stories and the full discussion threads are available over on Lobsters. We will see you back here tomorrow.