9x cheaper than Haiku 4.5 and 2 letter grades better. It's also now the fastest model (using the default speeds, not trying any of the other models "Fast" mode) to complete the exam.

Similar ballpark to Luna in price, cost, and accuracy. These are very cheap models: $0.38 to answer 40 in-depth data analytics questions (compared to $15 for Opus 5.5 or $20 for Astra).

Overall very good at data analysis - handling all of the straightforward data analytics questions correctly. It fell short answering some of the questions that required some deeper statistical analysis like looking into other variables. In other words, it's not as persistent as other models in its analysis, which I think we'd expect from how they're positioning the model.

Compared to OpenAI: GPT-6 Luna did a bit better and was about 30% the cost of Haiku 5.5. GPT-6.1 Sol got all answers correct, but was 10x more expensive.

Low messes up the bicycle frame, but medium/high/xhigh/max all get the bicycle frame right.

The max one took 5 minutes 9 seconds and cost 3.3826 cents. The cheapest one (low) cost 0.0936 cents and took 7 seconds.

The most recent release of my llm-anthropic plugin queries the Anthropic model listing API directly, so I didn't have to upgrade the plugin to add support for this model:

  llm install llm-anthropic -U                                
  llm anthropic refresh
  llm -m claude-haiku-5.5 'prompt goes here'

For a while Anthropic has lacked a cost effective “cheap” LLM for summarisation, compacting, RAG helpers, etc.

These ‘ephemeral’ workloads are often under 100k tokens, or can be structured to be under 100k.

In some coding benchmarks, Haiku 5.5 beats Sonnet 5! (Especially implementation; do a well defined Jira ticket; etc), it’s really impressive how much intelligence per dollar has grown in just a few short months.

What's funny about "Intelligent UI" is I said like 2 or more years ago, that these AI companies need to start thinking outside of these basic chat UIs, they do some things here and there, but its really depressing how little they do to innovate in these spaces. Same with the coding harnesses, the UI for all these things could be drastically superior.

Given that OpenAI is making noises about merging work with chat (a horrible idea imo), and Work is very similar to Codex... I dearly hope things like these won't have any meaningful cross-polination into the actual work tools.

Seeing that the chat is based on 6.0 and not 6.1 is disappointing. The "Visual and interactive explanations" seems genuinely useful, but 6.1 is just so much better. I wouldn't truly trust the 6.1 with the explanations, but I'd trust them a fair bit more than 6.0. I understand that compute isn't infinite, but tons of people only interact with the chat and having your "things-explainer" be as good as it can be is important when people increasingly treat AI models as the source of truth, or even use them for academic learning and whatnot.

Still, the models will improve, so the visual explainer seems pretty good as an idea / mvp.

The idea that an AI company is beyond peer review is harmful.

Other than the complexity of its implementation, there is very-little-to-no business nor technical reason not to use it or include it.

It has every right to be "the" image format for the next 20-odd years. Excellent compression, excellent lossless mode, transparency, etc. etc.

And probably my favorite feature- progressive rendering, which means you never have to make thumbnails ever again, you just truncate the output stream at the right proportion of pixel data (!)

iOS also now supports it natively for the photos it takes... but only if you have a newer iPhone than mine (a 15 Pro Max).

  curl https://api.openai.com/v1/decisions \
    -H "Authorization: Bearer $(llm keys get openai)" \
    -H "Content-Type: application/json" \
    --data '
  {
    "model": "gpt-6-luna",
    "input": [{
      "role": "user",
      "content": [
        {"type": "input_text", "text": "I am angry about the new product feature"}
      ]
    }],
    "questions": [{
      "type": "predicate",
      "name": "complaint",
      "instructions": "Is this a complaint?"
    }, {
      "type": "predicate",
      "name": "compliment",
      "instructions": "Is this a compliment?"
    }]
  }'

  {
    "model": "gpt-6-luna",
    "answers": [
      {
        "type": "predicate",
        "name": "complaint",
        "probability": 0.91
      },
      {
        "type": "predicate",
        "name": "compliment",
        "probability": 0.06
      }
    ],
    "usage": {
      "input_tokens": 310,
      "input_tokens_details": {
        "cached_tokens": 0,
        "cache_write_tokens": 0
      },
      "output_tokens": 0,
      "output_tokens_details": {
        "reasoning_tokens": 0
      },
      "total_tokens": 310
    }
  }

(I turned this all into a new llm plugin: https://github.com/simonw/llm-openai-decisions)

Why do you "suspect" this as if it's some hidden motivation when the very first paragraph of the advisory group's statement (linked from the OpenAI post) says:

> At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community. Our recommendations are formulated with this practical context in mind. However, ideally, they would not do so. We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.

Tao and others in that group have been strongly and publicly pro AI from the start. They are not advocating "going back". They're objecting to the strip mining of open problems using proprietary technology.

"it's a matrix-tree cancellation wearing Kasteleyn's planar signs, run as a Witten index over Penrose-lineage states, evaluated as a fugacity-zero loop gas in an infinitesimal magnetic field — and the reason it reads like physics is that every one of those tools was built for partition functions"

I thought this was pure slop when I read it but there are some clear analogues in these other areas of physics, really neat computational tricks, and a very interesting paper by Penrose calculating Tait colorings I never knew about previously (extremely relevant, actually related to a separate approach I had once taken on this problem). The problem is that the paper isn't saying "aha, we were inspired by the related problems of pairing excited states and creating spanning trees out of cancelled coefficients" it just defines the function apropos of nothing. Which is kind of like the Jacobian counterexample in that it works but doesn't really explain how exactly it got there.

I really think the load-bearing concept here is "prior work". If prior work is considered papers on this problem or graph theory, yes this has one huge subjectively unintuitive logical leap. If "prior work" is the entire corpus of neat computational tricks that physicists derived to make their equations spit out something other than zero or infinity, maybe it's not so crazy?

The Unique Games Conjecture (sorry, "Unique Games Theorem" now!) is huge. It was a very significant pillar supporting many of the limits of the polynomial-time approximation algorithms in the graduate-level randomized and approximate algorithms course I took in theoretical computer science. Textbooks will have to be re-written.

Here is an explainer: https://share.gemini.google/nbjIK6X3tOfz

With UGC proved, certain polynomial-time approximation algorithms used in difficult real-life problems are now known to be the best approximations we can achieve in polynomial-time:

> If UGC holds, the elementary algorithm that grabs both ends of an edge is fundamentally the best efficient algorithm that will ever exist. No amount of advanced linear programming or heuristics can achieve a ratio of 1.999.

> Under UGC, the Goemans-Williamson algorithm's 0.87856 ratio is mathematically optimal.

> UGC is considered the "Rosetta Stone" of approximation algorithms. In 2008, Prasad Raghavendra proved that for every single constraint satisfaction problem (CSP), a canonical Semidefinite Programming relaxation paired with the best rounding scheme achieves the optimal approximation ratio if and only if UGC is true. If the conjecture holds, the algorithmic boundary for an entire class of combinatorial problems is completely resolved.

Other hardness of approximation results from this UGC proof:

> [Max acyclic subgraph, a problem encountered in real life]: No polynomial-time algorithm can fundamentally outperform an unthinking coin toss.

> [Relative scheduling, another realistic problem]: As with acyclic subgraphs, the problem is "approximation-resistant": clever algorithms cannot beat random shuffling.

I will never meet that person and I will never hold a real conversation with the "creator" of that proof. They will never tell me how they came up with the cancelling exponential summation that cracked the construction. It's just another enigma but one that is far more unknowable than the original problem.

The "aha" insight for this is actually f**ing wild, it involves a complex valued exponential sum on the edges. I've seen a lot of clever counting arguments before in graph theory but this is the first time I've seen complex roots and annihilating terms like this, the symbolic manipulation tricks in this look like things out of quantum physics. I don't understand where this trick originated, I need to really digest this.

As for Riemann's memoir, it's hard to compare. You could argue that was "just" noticing a connection (between number theory and Fourier analysis) that nobody had noticed before; in fact this is the kind of thing AI is extremely good at. I'm being a little cute here.

I think if a human had proven just these two results in the form of a uniform zero-free region for L(s,chi) from nothing as OpenAI did it would not be unfair to say that it would be the single greatest advance in math (easily dwarfing Wiles' FLT), and it would instantly put them in the ranks of greatest mathematicians of all time. Unlike something like Navier Stokes there wasn't a semblance of a research program, experts basically considered this hopeless and would have said the chance of seeing a proof in our lifetime was near zero.

For some comparison, Yitang Zhang's bounded gaps result might have gotten him a Fields Medal if he was not disqualified by age. When it was floated that he might have proven Siegel zeros don't exist, it was considered (by experts) clearly a much bigger deal. This result blows that out of the water (it's a way better version); at least analytic number theorists I talked to thought it was plausible but unlikely that Siegel zeros would be eliminated in our lifetime but thought RH was basically hopeless.

At least put a disclaimer for the ad for this site, and maybe disclose how you came up with a total ordering for "top" open problems (vibes)?

> How problems are ranked. LLMs compare pairs of problems. A reliability-weighted model combines those judgments into the ranking, with calibration across model families. The model-family weights are OpenAI 1.00, Claude 1.00, GLM 0.95, and DeepSeek 0.90. These are modeling choices, not measured probabilities of correctness.

> A Unique Games instance has a finite vertex set, a finite alphabet K, and a nonempty list of oriented constraints e = (u_e,v_e,π_e), where π_e is a permutation of K. A labeling a satisfies e when a(v_e) = π_e(a(u_e)).

I'm sorry, what? I admit it's been quite a few years since I've thought about the Unique Games Conjecture, and I never dug that deeply, but this part is very, very elementary graph theory and notation. So let's unpack it.

1. e is maybe a name of a list.

2. The elements of that list are tuples, where each tuple is (a vertex, a vertex, a permutation). So e indexes into the list and u_e is the source vertex for the e-th constraint in the list called e. Thanks.

3. a is a labeling. I'm fairly confident that, by "a labeling", they mean that e is a function from vertices to colors, where the colors are the elements of k.

4. That vertex coloring a satisfies the list e, when, for, um, an index e into e, a(v_e) = π_e(a(u_e)). But this isn't for all e, it's for some e, and the goal is to count them.

So maybe e isn't a list? Maybe e is a constraint that is represented as a tuple, so e = (u_e,v_e,π_e) and u, v, and π aren't sequences at all but are, in fact, the trivial unpacking functions that unpack the pieces of the tuple.

Reading this stuff is pointlessly painful, and it's extremely easy to make mistakes when being sloppy like this.

If this were my paper, or if I were trying to train a model to write math, I'd want something like:

A Unique Games instance has a finite vertex set V, a finite edge set E = (V × V), a finite alphabet K of possible vertex colors, and a nonempty list of oriented constraints. Let Π be the set of permutations of V. Each constraint e is a tuple in E × E × Π, where we write u_e ∈ E for the first element, v_e ∈ E for the second element and π_e ∈ Π for the third.

A vertex coloring a : V → K satisfies e when a(v_e) = π_e(a(u_e)).

Like do you see the technology plateauing at the current level, do you expect progress will continue but only in mathematics, I'm interested to know why others are not concerned?

It's like Clippy pops up and goes "It looks like you're trying to maintain a shred of human connection in an online interaction. Would you like a smiling skinwalker to do that for you instead?"

Why would they? The people who use these "loopholes" know exactly what they're doing.

https://www.972mag.com/ellisons-paramount-tiktok-israel-medi...

OK well I couldn't resist this one:

  llm -m claude-opus-5.5 'Generate an SVG of an armadillo in fishnet tights jaywalking on Mars'
  llm -m gpt-6.1-sol 'Generate an SVG of an armadillo in fishnet tights jaywalking on Mars'
  llm -m gemini-3.8-flash 'Generate an SVG of an armadillo in fishnet tights jaywalking on Mars'
  llm -m mistral/mistral-large-4 'Generate an SVG of an armadillo in fishnet tights jaywalking on Mars'

One Piece of Flock Camera Data Put This Innocent Woman in Jail for 13 Days https://news.ycombinator.com/item?id=49852065

And

Anthropic reported diary entry to police, woman faces felony charge https://news.ycombinator.com/item?id=49961057

I dont buy this "europe not free" nonsense.

And as you can probably tell by now, the first amendment in the US is not actually preventing the US government from promoting a specific religion or silencing speech. It's just words on a paper at this point. Look at the actual practice.

Several European countries do a much better job at protecting the rights described in the first amendment to the US constitution.

That setting didn't seem to make any real difference - it added a tiny bit of thinking trace and high actually produced less output tokens than none.

The high bicycle frame is better then the none one though.

Pelicans: https://tools.simonwillison.net/markdown-svg-renderer?url=ht...

(Definitely the best I've seen from any Mistral model: https://simonwillison.net/tags/pelican-riding-a-bicycle+mist... )

I certainly wouldnt have predicted that 10 years ago.

Very glad to see Mistral still in the game even after some big stumbles with Large 3. I deeply hope that this model is 'good enough' that it becomes the European go-to, giving them the resources to keep the pace up.

I'm excited to try this out today.