0909 | Proofs, Parameters, and the Pushback

Mia: Welcome back to the show, everyone. I'm Mia.

Milo: And I'm Milo. It's been one of those days where the feed reads like three different podcasts stitched together — a formal math proof that turned into a credit war, models getting faster and bigger and smaller all at once, and a bunch of stories about who you can actually trust with your data.

Mia: Yeah, the thread running through everything today, honestly, is trust in systems. Whether that system is a math proof, a model quantized down to almost nothing, a Border Patrol database, or a feed algorithm. So let's just dive in, because the Navier-Stokes story is the one everyone's arguing about.

Milo: Okay, so set it up for people who haven't been following. Navier-Stokes is one of the Clay Millennium Prize problems — describing how fluids move, and specifically whether smooth solutions always exist or whether they can blow up. It's been open for decades. And OpenAI announced they have a solution: a proof, formalized in Lean, of existence and smoothness.

Mia: Which, if it holds up, is enormous. This isn't a benchmark or a competition problem. This is a centuries-scale open problem, and the claim isn't "we have a sketch" — it's "we have a machine-checkable formal proof." The Lean part matters because Lean doesn't take your word for anything. Either the proof compiles or it doesn't. So in principle the validity question is answerable, not a matter of taste.

Milo: Right, and that's exactly why the drama around it is so weird. Because on the same day, essentially, two mathematicians — Buckmaster and Alpöge, who are at NYU — announced a counterexample. Which is the opposite claim, right? If they have a genuine counterexample, smoothness fails, and OpenAI's proof can't be right as stated.

Mia: And they didn't just announce the counterexample. They accused OpenAI of rushing a parallel result — of hurrying their own announcement out the door. So you've got a priority fight layered on top of a technical dispute.

Milo: And it goes further. There's a separate NYU mathematician who accused OpenAI of aggressive conduct for pre-empting his Navier-Stokes test. So this isn't one disgruntled person — the complaint pattern repeats. OpenAI apparently moved on a problem that other people were actively working on, and at least two groups feel they got scooped or steamrolled.

Mia: The part that commenters kept circling back to is the accusation about chats. Buckmaster and Alpöge's dispute isn't only about credit for the result — it's about the use of their chats. Which raises a question nobody's really answered yet: if mathematicians discussed their partial work with an AI assistant, and the lab behind that assistant then announces a result on the same problem, what happens to the informal norms the math community runs on?

Milo: That's the uncomfortable one. Math has always run on a kind of honor system around seminars, preprints, and "I mentioned this to someone at a workshop." If conversations with AI tools become a channel that the tool's owner can build on, people will just stop having those conversations openly. And that would be a real loss, because informal sharing is how a lot of progress happens.

Mia: Though — and this was a genuine disagreement in the discussion — some people pushed back and said, look, OpenAI is under no obligation to wait. Companies announce results when they announce them. If your proof strategy leaked through a chat with a commercial product, that's a risk you took. Others found that too cold, arguing that the power asymmetry makes "caveat emptor" a pretty thin defense.

Milo: Terence Tao weighed into the broader question, and his point reframes the whole thing. He said the good open problems in mathematics are being "mined" by AI in a way that's non-renewable. And that's a striking image, because math problems aren't like data you can generate more of. There's a finite stock of genuinely great open problems — Navier-Stokes, Riemann, the rest — and once an AI system cracks one, that's it. That problem is spent.

Mia: And the incentive structure makes it worse. If labs are racing to claim Millennium Prize problems for the prestige, the best problems get consumed fastest, not the ones where the techniques would teach us the most. Commenters were split on how serious this is. One camp said, honestly, we've waited decades on these problems — if they get solved, even by a machine, that's a win, and there are more problems being generated all the time.

Milo: But the other camp said that's missing Tao's point. The problems being solved aren't necessarily the ones that open new fields. A proof of existence and smoothness, checked in Lean, might close a question without opening anything — and the finite shelf of iconic open problems is part of what gives the field its shared ambition.

Mia: So where does this actually stand? The unknowns are real. Nobody independent has verified the counterexample yet. We don't know the details of how the chats were used, or whether anything from them actually fed into OpenAI's work. And for all the certainty of the Lean announcement, formal verification is only as good as the formalization — the definitions have to be right too.

Milo: What to watch next is exactly that: who verifies what, and in Lean. If Buckmaster and Alpöge's counterexample gets formalized and it compiles, that's a direct refutation and the whole thing gets very interesting. If OpenAI's proof compiles and the counterexample doesn't, the credit war might quiet down but the norms question won't go away.

Mia: Okay, let's shift gears — from mathematics to the sheer physics of running these models. There were a few posts today that, put side by side, tell you where LLMs are actually heading, and they point in opposite directions.

Milo: So the headline-grabber: Inception announced Mercury 2.5, which is a diffusion LLM. And the number that jumped off the page is 1,107 tokens per second. For context, that's not a little faster than typical autoregressive models — that's a different order of magnitude. It also handles 260K context, and they claim it's 40% more intelligent than Mercury 2, so it's not just fast, it's better than its predecessor.

Mia: And the reason a diffusion LLM can do that is structural. Instead of generating one token at a time, left to right, it refines chunks of text in parallel. So the speed isn't coming from cleverer hardware tricks, it's coming from a different generation paradigm. People in the discussion who'd tried earlier Mercury versions said the historical weakness was quality — you got speed but you paid for it — so the 40% intelligence claim is really the thing to watch, not the token count.

Milo: Because 1,107 tokens per second of mediocre text is a demo. Fast and good is a product.

Mia: Exactly. Now contrast that with the other end of the spectrum. Somebody got Kimi K3 running on a MacBook — an M5 Max — and Kimi K3 is a 2.78 trillion parameter mixture-of-experts model. And it runs at about one token per second. One. By streaming the expert weights off four SSDs.

Milo: Which is, in its own way, as impressive as the Mercury number. The model doesn't fit in any reasonable amount of RAM, so the trick is: only the active experts are needed at any moment, so you keep the rest on disk and stream them in as the router picks them. You're trading latency for the ability to run a frontier-ish model entirely locally, no datacenter, no API.

Mia: And commenters who've done this kind of offloading said the experience is exactly what one token per second sounds like — you type, you go make coffee, you come back. It's a proof of capability, not a usable assistant. But the interesting debate was about whether that matters. One side said this is a dead end — SSD bandwidth improves slowly, and by the time it catches up, models will be bigger again.

Mia: The other side said no, look at the trajectory: mixture-of-experts means you only touch a small fraction of parameters per token, and SSDs keep getting cheaper. The gap between what fits on disk and what fits in RAM is exactly the gap this trick lives in.

Milo: The third piece of the triangle is quantization. Someone ran benchmarks on quantized versions of Qwen3.8 27B, and the results have a sharp cliff in them. At Q4 — four-bit quantization — performance matches the full BF16 model. Which is remarkable: you cut the memory footprint by roughly four times and lose basically nothing.

Mia: But at 1-bit, on GPQA — which is a hard graduate-level science benchmark — the model collapses to chance. To random guessing. Not degraded, not noticeably worse — random. All the intelligence is gone.

Milo: And that cliff shape is what people found most interesting. The intuition a lot of people carried was that quantization is a smooth dial: less precision, somewhat worse output. The data says no — there's a regime where the model is genuinely robust, and then a threshold where it falls off a cliff entirely. So the practical advice from the discussion was basically: Q4 is free, don't go near the extremes if you care about the answers.

Mia: There was also a neat tool posted alongside all this: a web visualizer that shows attention inside an LLM, using the opacity of each token based on the magnitude of its value vector and the QK interaction. So instead of reading a wall of numbers, you literally watch which tokens the model is "paying attention to" light up as it processes.

Milo: People liked it as an intuition pump, and there was the usual healthy skepticism — attention visualizations can be suggestive without being explanatory. Seeing that a token is bright doesn't tell you why it matters causally. But as a teaching tool, several people said it finally made attention click for them in a way diagrams in papers never did.

Mia: So the through-line of all of this: one lab is making generation massively faster by changing the paradigm, someone else is making trillion-parameter models run on a laptop by hiding the latency, and quantization research is mapping out exactly where the precision cliff is. And there was one more data point — ChatGPT Images 2.5, which brought more precise editing, consistency across multi-turn editing sessions, and latency down by up to 50%.

Mia: Same story in a different domain: the frontier of these products is speed and reliability, not just raw capability.

Milo: Which connects, uncomfortably, to our next topic. Because if open-weight models keep getting cheaper to run — and they are — the question of what people can do with them stops being technical and starts being political.

Mia: So, Mistral. They raised €3,000 million — three billion euros — in a Series D, at a valuation north of €21,000 million. And that's the largest round in Europe, led by Samsung. Their bet is sovereign, open-weight AI — European AI infrastructure that anyone can inspect and run.

Milo: Three billion euros is real money, and commenters read the Samsung lead as significant. It suggests Asian hardware and industry interests see value in a non-American, open-weight champion — sovereign AI isn't just a European talking point, it's a market someone will fund at scale.

Mia: Now hold that in one hand. In the other hand: an essay arguing that we have roughly one year to fix global security, and the reason is GLM 5.3-flash — an open-weight model that's cheap enough and capable enough that anyone can execute attacks at scale.

Milo: And that's the tension in a single sentence, right? The exact property that makes Mistral's pitch attractive — open weights, cheap inference, no gatekeeper — is the property that essay says is lowering the cost of doing harm to nearly zero.

Mia: The discussion on this was pretty polarized. One camp took the essay seriously: capability is being commoditized faster than defenses are being built, "one year" might be rhetorically sharp but the direction is right, and once cheap open models enable scaled attacks — phishing, disinformation, automated exploitation — the asymmetry between attackers and defenders gets worse, not better.

Milo: The other camp said this is the same warning we've heard in different clothes for years, and that openness is also what makes defense scalable. Open weights mean defenders get the same tools attackers do; closed models concentrate capability in a few companies who become single points of failure. If only three labs can run capable models, attacking them means attacking three targets — but so does defending everything.

Mia: And there's a middle position that came up: the question isn't open versus closed, it's whether policy moves in the window before capability grows. That's genuinely unknown. Europe just funded a sovereign open-weight champion at record scale. Whether governments build real safety infrastructure in the same window — nobody knows, and nobody in the discussion claimed to.

Milo: Let's go from billions of euros to billions of base pairs. DeepMind launched AlphaGenome Atlas, and it predicts the molecular effects of 9 billion single-nucleotide variants across the human genome. The dataset is a petabyte, and it comes with these AVI scores for each variant.

Mia: To unpack that: a single-nucleotide variant is one letter changed in your DNA. Most of them do nothing, some of them change how genes are regulated, and a tiny fraction matter for disease. There are roughly that many possible single-letter changes across the genome, and Atlas has scored essentially all of them — 9 billion predictions of what each one does molecularly.

Milo: What made this land for a lot of people is the coverage. Previously, if you got your genome sequenced and it showed a variant of unknown significance, that variant stayed unknown. Now there's at least a computational prediction attached to all of them. Whether those predictions are trustworthy enough to act on is the big open question — commenters were emphatic that clinical validation is the bottleneck. A petabyte of predictions is not the same as a diagnosis.

Mia: And there was a bit of healthy grumbling noting that this is essentially the same 9-billion-variant claim from the earlier AlphaGenome announcement, now packaged as an atlas — so part of the discussion was about what's actually new here versus a repackaging. The petabyte dataset and the scores being publicly available seem to be the substance.

Milo: The companion piece in the same conversation was AlphaGeo, which ranked the climate resilience of 72 megacities — and Chicago came out among the best adapted. Different domain, same move: take an enormous raw dataset, model it, and turn it into a ranking that a planner or an investor can actually use.

Mia: Some people found that framing inspiring — prediction is moving from the lab into practice, whether it's a clinician holding a variant score or a city government looking at its resilience rank. Others were wary: rankings create their own reality. If a city scores badly on climate resilience, does that redirect investment away from the places that need it most? A score is only as good as its validation, whether the subject is a genome or a city.

Milo: Okay. From foresight to agents that actually do things. Three posts today, and they share a pattern that I think is the real story.

Mia: The most technically ambitious is Copperhead — an open-source agent that designs PCBs, circuit boards, in KiCad. And the design is what people wanted to talk about: it works in eight stages, each stage has verification gates — ERC and DRC checks, which are electrical rule and design rule checks — and it makes exactly one commit per stage.

Milo: That structure is doing a lot of work. Instead of letting the agent free-run and hope the final board is right, each stage has to pass an objective, machine-checkable gate before the next one starts. And the one-commit-per-stage discipline means a human can review the diff at every step and roll back any single stage without losing the rest.

Mia: Commenters with hardware experience said this mirrors how human engineers actually work, and that's probably why it works. Board design has natural checkpoints — schematic, layout, routing — and existing tools like KiCad already ship with the rule checkers. So the agent isn't inventing verification, it's plugging into verification that already exists. The open question was how far it generalizes: ERC/DRC are objective gates, and plenty of domains don't have equivalents.

Milo: A smaller but revealing post: a skill called "i-have-adhd" that forces coding agents to produce action-first, numbered output, using ten rules. So instead of the agent giving you a rambling explanation with the command buried in paragraph four, it leads with what to do, numbered, in order.

Mia: And people with ADHD in the thread said this genuinely changes the experience of using these tools — the default chatty output style is a real accessibility barrier, not a preference. But plenty of others said the deeper point applies to everyone: agents ramble, and forcing a structured, action-first format is just better interface design. The interesting sub-debate was whether this should be a skill you opt into or the default behavior.

Milo: And then DaVinci Resolve 21.1 added integration with AI assistants — Claude, Codex — so they can analyze your project, organize your media, and render based on natural-language instructions. Which is the same pattern in a creative tool: the agent doesn't do the editing, it operates the software.

Mia: Right — and that's the pattern across all three. Agents are becoming workflow-aware. Copperhead respects the gates of its domain, the ADHD skill respects the cognitive constraints of its user, and Resolve's integration respects the structure of an editing project. Nobody's talking about agents that think freely; they're talking about agents that fit into existing verification structures and output formats.

Mia: The prediction from the discussion was simply: more gated agents, in more specialized domains, next.

Milo: Alright, the big one. Trust under pressure — and this cluster of stories, honestly, reads like a single article about shrinking choice.

Mia: Start with 404 Media's reporting on Border Patrol's PITT units. These units analyze the financial data of Americans and coordinate detentions without specific cause. So this isn't targeted surveillance of suspects — it's mass analysis of ordinary people's financial lives, feeding into detention decisions that don't rest on individualized cause.

Milo: Commenters who work in data or finance pointed out that financial data is uniquely invasive — it maps your associations, your movements, your habits — and that the "no specific cause" part is the constitutional problem, not just a privacy quibble. The revealed capability matters as much as the current use, because once the pipeline exists, its scope tends to grow.

Mia: Then the UK, where police are worried that Meta's smart glasses could secretly record officers and inside detention facilities. Which is a strange inversion — law enforcement concerned about being recorded by consumer hardware — and the discussion noted that the glasses look more or less like ordinary glasses, so there's no reliable way to know you're being recorded.

Milo: And Meta appears again in a softer register: they launched Muse, a personal AI agent, and the dominant reaction was doubt — people questioning whether you should hand your personal data to Meta of all companies. The skepticism wasn't about capability; it was about the custodian.

Mia: Then Paramount, which used an astroturf group called "Neighbors for Strong Communities" to manufacture the appearance of public support for its merger. Fake grassroots. So when the regulatory record says "the community supports this," part of that record was staged.

Milo: Which connects directly to Australia, where the response to manufactured feeds is legislative: a proposed law called "My Feed, My Way" would let users over 16 opt into a chronological feed with no algorithmic recommendations. The right to turn the algorithm off.

Mia: And there was real debate about whether that's enough. Supporters said it's a meaningful first crack — it establishes the principle that the feed belongs to the user, and it creates a natural experiment: if millions switch to chronological feeds, we finally get data on what algorithmic curation actually does to us. Skeptics said an opt-in buried in settings changes little, because defaults rule everything, and the platforms have every incentive to keep the default algorithmic.

Milo: And the last piece makes the whole cluster cohere: nearly 9 in 10 European companies that use a CDN depend on Cloudflare. Bunny.net was cited as the main alternative, but that's the state of the market — one company sits under a huge fraction of the web's traffic.

Milo: So when people in the discussion connected the dots, the argument was: surveillance narrows your privacy, astroturfing narrows your voice, the feed narrows your information diet, and infrastructure concentration means even the choice of plumbing is mostly illusory.

Mia: The counterpoint, to be fair, was that concentration isn't automatic evil — Cloudflare got big partly by being good and cheap, and a CDN is a commodity you can switch. The rebuttal was that "you can switch" is exactly what everyone said about social feeds, and here we are with Australia writing a law about it. What happens next, most people agreed, is that regulation like Australia's probably expands — the question is whether it arrives while choice still exists in practice, not just on paper.

Milo: Let's close the loop with the quieter stories, because they actually belong with everything we've just talked about. A study found that LLMs develop new social biases about fictitious demographic groups — groups with no inherent differences at all. The model invents the differences from statistics alone.

Mia: That's a strong result, because it rules out the defense that bias only comes from biased training data reflecting real-world differences. Here there were no real-world differences — the groups were fictitious — and the model constructed social bias anyway, just from the statistical structure of how the groups appeared in text. Bias as an emergent property of pattern-matching, not a mirror.

Milo: And people connected that to a wonderful piece of cultural history: the Christian saints Barlaam and Josaphat, who turn out to derive from the story of the Buddha — passed through successive translations and retellings until a Buddhist figure ended up canonized as a Christian saint. Cultural transmission does the same thing the model did: it takes material, passes it through channels, and the structure of the transmission itself generates new content that nobody intended.

Mia: Which is a good frame for the last two items. LibreOffice 26.8 passed a million downloads per week right after announcing it will include no generative AI, explicitly for privacy reasons. And FreeBSD 14.5-RELEASE shipped as the sixth release of the stable/14 branch, purely maintenance-focused.

Milo: The LibreOffice number is the interesting one, because it suggests "no AI" is becoming a market position rather than just an omission. After a whole episode about surveillance, astroturfing, and trust in custodians, a million people a week downloading a word processor because it doesn't phone home with your documents starts to look like a signal, not a coincidence.

Milo: And FreeBSD quietly maintaining its stable branch, plus an article cataloguing obsolete HTML relics — X-UA-Compatible, IE conditional comments, the old meta ICBM tag from the browser wars — it all points the same direction: software inherits things, deliberately or not, and sometimes the most valuable choice is what you refuse to inherit.

Mia: And there was even a small, joyful post in that register — someone running 1-bit sound experiments on an original ZX Spectrum, squeezing PCM, PWM, and multichannel chords out of the stock beeper. Constraints as craft. And in the same spirit, a very practical one: someone turned a Xteink X3 e-reader into a real IPP printer for macOS, driver-free, using penguin — a nice bit of "the manual never imagined this" engineering.

Milo: That's the show for today. From a fluid dynamics proof that broke out into a fight over credit and chats, to diffusion models at a thousand tokens a second, to a genome fully scored and a city ranked, to agents that check their own work, to the slow accumulation of things we can no longer opt out of — and a million people a week opting out anyway.

Mia: Thanks for listening, everyone. We'll be back tomorrow with whatever the feed — chronological or otherwise — throws at us.