> On the other hand, none of the proofs so far seem to contain “alien ideas,” a move-37, or completely novel arguments or new concepts that were not present in the literature in some form or another.
I have the same optimism as Prof Tao. That said, I can understand why so many mathematicians have been so upset or stressed out. It turned out much of the mathematical work is about clever combination of existing methods - this already requires enormous amount human ingenuity and years of dedicated learning. Unfortunately, or maybe fortunately, AI can be very good at knowledge transfer and finding combination of existing ideas to solve seemingly impossible problems. Even though mathematicians are extremely smart and capable, only a small number of them are capable of truly inventing "alien ideas", discovering new ground-breaking mathematical structures, or coming up with new problem-solving techniques. That is, AI can eat many mathematicians' cake. That said, I'm still hopeful. Mathematicians still understand mathematics deeply. If someone can prompt AI to solve an important problem, that person is more likely a good mathematician than an average joe like me. So, I think mathematicians do have a bright future: leverage AI, and make more and bigger math discoveries. It's still the same north star: we must know, and we shall know. It's just that with AI, we will know sooner and more.
I was recently working on a project where I had to come up with a novel solution to a problem the company was facing. The problem has been solved before, but in suboptimal ways that wouldn’t work for this specific company. I came up with a pretty interesting solution, one that combines different statistical methods, and was a little more complicated, but gave better results.
I asked Claude what it thought about the technique. It hated it. It loathed the idea that I was not sticking with traditional methods that were pointed to in papers and pre-existing open source packages. Even after talking through the idea and how it was better and showing it the results, it was weirdly hesitant to admit it was a valid method, simply because it seemed nervous that the idea was novel.
I don’t have a real moral to the story, I just thought I would add my anecdote here.
I had a similar experience with not being able to convince Claude of a different approach to a problem. Then I shared the idea with Codex and it liked it. As another commenter said, you can have the same thing happen with humans.
Interesting! My experience is that Claude has a tendency to always suggest the true and tried, but likes off-center ideas when I present them. Fable especially has a "yes, and!" attitude where it understands and plusses the idea.
It's pretty much the same story with software development. There are two camps and the bigger camp got hit hard. Nowadays I feel entitled to use the "software engineer" title. Essentially, all the decisions-making and nuanced trade-offs which AI is not capable of making; that's engineering. AI can only do programming and code analysis... At least so far.
That said, in the past couple of month, AI has gained a lot of ground on the 'project management' front in terms of planning capability for a lot of simple to medium-complexity projects. It still needs a lot of help for more complex projects. Just today, it almost fooled me into making a major structural mistake but thankfully I asked the right question and saved myself a lot of future problems; it was essentially dancing around a critical point and giving me the illusion that the critical point had been addressed but only when I phrased my question in a particular way, I understood the core issue was not addressed.
It's quite amusing that this mistake gets made on every single one of these guest posts when the first words on the page are "This is a guest post by Álvaro Lozano-Robledo" and the first paragraph starts with "I would like to give Terry my heartfelt thanks for giving me the opportunity to contribute a post to his blog." It's pretty clear that everyone is skimming these at best. Maybe he should put the disclaimer in a bigger font or something.
Though it’s very funny to imagine Tao suddenly acquiring a massive ego:
> At any given time in the history of mathematics, there have been mathematicians … whose mental capacity for mathematics seems completely super human (e.g., the owner of this blog, among many others).
It's interesting, what would be Tao's views on the creativity question. Like, I don't find the empirical observation of LLMs now, the notion these proofs are mostly "just" sophisticated grinding, to be a strong indicator of what could/couldn't happen.
I'm actually more optimistic. Math will still be fun and challenging and rewarding. It's just that we need to adapt how we choose which problems to solve.
Previously, due to the cognitive limitations of our brains, it was difficult to tell whether resolving a conjecture genuinely required years of dedicated effort, or if the answer was already hidden within existing human knowledge. Or whether a problem is just waiting to be searched out through ingenious or even brute-force means. With AI, we can now offload this search, especially across different areas of math, allowing us humans to focus our minds on discovering new mathematical structures and techniques.
Indeed, if one believes what Hilbert believed: we must know and we shall know, he should feel happy, as the belief has never been about who solves a problem, but about whether can advance our understanding of the universe. With the help of AI, we have a lot more possibilities.
You'd be surprised how VPs love to insert PMs. A famous game platform company, for instance, had two PMs for their storage team, one PM for their data team, one PM for the compute team, one PM for their dev tools team, if I remember correctly (the numbers could be larger, but won't be smaller)
It may appear so, but if you you talk to the Anthropic employees and management, especially those researchers, you'll see that they truly believe that the AGI is coming, if not has been here already.
> Google, a search engine which does not have human emotions, assumed that I had been spurned by a man in my life named Dario and decided what I wanted was an empathetic digital friend.
I'm not sure why this is a surprise. Google most likely uses an efficient yet limited language model to give us search answers. When a search query does not have strong or specific enough context, the model will sample and find what most of the training material will cover. That is, the most likely average behavior covered in the training data. In this case, "hes never coming over dario" is such a generic sentence, so unless Google happens to have indexed what the author mentioned and ranked it high, the answer would appear natural to the AI. Or using the AI jargon, the answer appears to be properly aligned.
> I'm not sure why this is a surprise. Google most likely uses an efficient yet limited language model to give us search answers.
The surprise is that Google decided such an "efficient yet limited language model" is suitable to be shown before actual search results on every search, even though it gets things so wrong, so often. It's not about the technical limitation or design. You really don't understand why that business decision is surprising to users?
If you further type "its an NBA meme", Google AI correctly responds: "The origin of the phrase "Dario is never coming over" dates back to a classic Joel Embiid meme from the peak "Trust the Process" era of the Philadelphia 76ers."
> so they’re using LLMs to build native applications for every platform they support.
People say LLMs will let us build native apps instead of Electron, but is that missing the point? I thought people turned to Electron for a reason: building a fast, rich, collaborative Markdown editor on macOS is notoriously hard. Neither SwiftUI nor AppKit makes handling those rich interactions easy. AI can do wonders, but can it really overcome the inherent limitations of macOS's native UI frameworks?
I thought the difference is that clearly written rules or SLAs are acceptable and can even be negotiated before signing a contract, but having a person, in this case Amodei himself, manually approve DOJ's usage case by case with his own moral judgement after a contract is signed is not okay.
No one wanted case-by-case veto ability at Anthropic. The red lines were made clear ahead of time: No use of Anthropic models for autonomous weapons (Skynet) or mass-domestic surveillance, negotiated in the agreement.
OpenAI, xAI, and Google happily agreed to DoW contracts which allow both of those use cases.
> Ability to use the plan outside of the official harness. Codex wins. Anthropic does shit like bills requests as extra usage if it sees a hermes.md in a commit.
I'm quite puzzled about why Anthropic is so hellbent on blocking other coding agents. It's not like Claude Code has any secret sauce, right? And doesn't Anthropic make monkey off API usage, and their magic is on the model side anyway?
It's for lock-in - same reason why it took them so long to finally support AGENTS.md.
But to be fair, they don't really enforce the harness rule that much anymore. I guess if your harness doesn't do a lot of weird things like a lot of cache misses, or triggers some distillation attacks, or some broader Chinese fingerprints, they're tongue-in-cheek okay with you using a third party harness.
Not natively, as it's still a ToS violation and adding that in pi would go against pi principles, but there are many plugins/proxies that make it work.
oh-my-pi supports it natively (again, still a ToS violation), by impersonating claude code's fingerprints.
I have been using oh-my-pi with 3 claude subs for the past few months without any issues. Even native server-side OAI/ANT compaction works out of the box.
It's pretty unclear because they have two somewhat competing sets of documentation but I believe using the agent sdk with a harness like pi is not against the ToS if it's for yourself.
> Unless previously approved, Anthropic does not allow third party developers to offer claude.ai login or rate limits for their products, including agents built on the Claude Agent SDK.
This feels like a horrible precedent. Billing based on data like commits feels like it opens the door to tech stack based billing in general - could we see different prices for people who use other devtools Anthropic doesn't like? Makes me feel grateful for open models
Originally it was because Anthropic was so compute constrained they relied on the extra care the Claude harness took with caching (heavy use of cache breakpoints etc) that other harnesses didn't.
I think that is less of a factor now, and I think Anthropic have backed off some on being as strict (eg, AFAIK they never implemented the two-tier "claude -p" pricing model they were planning)
Very true. Or further, access to capital is the moat. It is the very reason that we don't have a real open-source community that trains frontier models - individuals simply can't afford the training infrastructure, nor sufficient high-quality training data.
None of those are frontier models, nor could they have been. E.g. DeepSeek's "$5 million" included piggybacking off OpenAI/Anthropic's hundreds of millions/billions by using distillation.
1) I don't think "frontier model" is a term of art, it is a marketing term. I have an M1 MacBook Pro. What do you have? Always the "frontier model" laptop? Do you always order the most expensive "frontier menu item" at the bar and grill?
2) I do not believe the "billions" number is OpenAI/Anthropic's training costs. I suspect it includes business expenses (including the big $$ to the guy who came up with "frontier model") and infrastructure, etc. That includes the data-center costs for running the cloud. And the "R&D" expenses which includes who-knows-what. And the settlement payment for data access. Etc. Why are the cost breakdowns not available to the public? Not because of thoughtfulness, altruism, care for the human race, but because of business plans.
3) "Piggybacking off OpenAI/Anthropic" - Scraping the web is "piggybacking" too, and so is buying existing data or even paying for new data. The "L" in LLM stands for "language" which is our common heritage.
But what does this have to do with anything anyway? People argue that truly Free (FOSS) LLMs couldn't be be developed because of costs, but I do not think that that is obvious. This used to be the argument against Linux and Wikipedia.
Just regarding "frontier model", it is most definitely not just a marketing term. It was borrowed from the financial concept of "efficient frontier", i.e. the best performance at a particular cost, though in the context of things like "pacing the frontier" it refers to the highest capability models. ECI (Epoch Capability Index) is probably the most commonly used metric of overall capability: https://epoch.ai/eci?view=graph&tab=release-date
"What this has to do with anything anyway" is that pushing the boundaries on AI capabilities has required tons of compute (and money). Open weight models exist and are useful but they always trail in capabilities and they can't be used as evidence to think somehow you can push the boundaries of LLMs without a shit ton of money.
"can't be used as evidence" << the whole field is only a few yrs old and is based on academic maths from decades ago.
A lot of progress is in harnesses and distillation and weird research that requires creativity. The "Frontier" always tries to frame things in terms of "the frontier" in order to limit how we look at things.
We don't know the true costs of pre- and post- training, running data-centers, hiring people, making business deals, etc., so even the (maybe) quantifiable question of cost vs capabilities is not at all clear. The efficiency of businesses ultimately gets measured by their ability to maximize a commercial return; but this is NOT a good metric for other important things, including maybe "how good is this"? (Where "good" is open to debate but maybe not quantifiable.)
It had been true that the "best" operating systems required a lot of business money. And encyclopedias. And ... (list some other good historical examples here!) ... Are Linux and Wikipedia the "efficient frontier"? In a sense they are both infinite performance at zero cost. Hard cash outlays sometimes stop being the determinant for high-effort endeavors.
I remember in the 1990s Encyclopedia Britannica's CDs and MSN (Microsoft Network(tm)) among many others argued that the web would never be able to match the curated, bespoke, expensive products they offered. It was IMPOSSIBLE for that crap to be matched!
I have the same optimism as Prof Tao. That said, I can understand why so many mathematicians have been so upset or stressed out. It turned out much of the mathematical work is about clever combination of existing methods - this already requires enormous amount human ingenuity and years of dedicated learning. Unfortunately, or maybe fortunately, AI can be very good at knowledge transfer and finding combination of existing ideas to solve seemingly impossible problems. Even though mathematicians are extremely smart and capable, only a small number of them are capable of truly inventing "alien ideas", discovering new ground-breaking mathematical structures, or coming up with new problem-solving techniques. That is, AI can eat many mathematicians' cake. That said, I'm still hopeful. Mathematicians still understand mathematics deeply. If someone can prompt AI to solve an important problem, that person is more likely a good mathematician than an average joe like me. So, I think mathematicians do have a bright future: leverage AI, and make more and bigger math discoveries. It's still the same north star: we must know, and we shall know. It's just that with AI, we will know sooner and more.
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