They weren't discovered by an LLM. They were known conjectures that were proven by an automated solving language that was linked to an LLM.

I'll take "Things That Didn't Happen For $200", Alex.

Only a handful of meaningful proofs have ever been done by automated formal theorem solvers (the Four Colour Theorem being the most noteworthy example - but its proof is so long that humans can't verify it). By contrast, AI tools have been solving Erdos problems en masse. The majority of them just bog-standard commercial models. In case you need help, the only ones on that list that were hybrid (AI / non-AI) in the actual solving phase are:

1) AlphaProof / DeepMind Prover Agent / AlphaProof Nexus
2) Aristotle (Harmonic)
3) Seed Prover / Seed Prover 1.5 (ByteDance)
4) AxiomProver (Axiom Math)

In each of the above, LLMs come up with the lemmas / strategies but then use Monte Carlo search ("brute force") or likewise to investigate what they came up with. These are a minority. In the "AI Standalone" category, these "hybrid" tools made up only ~20% of attempts and successful proofs. Hybrid tools actually made more of a contribution in the "AI Alongside Literature" (related literature found afterward) and even more of the "AI Building On Literature" (related literature known beforehand) categories, which is the opposite of what people like you expect.

And even with the hybrid tools, it's still the AI doing the heavy lifting when it comes to strategy. Non-AI theorem solvers, again, don't have a spectacular record for churning out novel proofs to unsolved problems. Tools like Lean are more about mathematical rigour - a passive environment that requires a driver (a human or AI) to feed it actual strategies, lemmas, and proof steps. And no, you cannot brute force "strategy" in the vast majority of cases, which is, again, why automated theorem solvers don't have much of a track record with unsolved mathematical problems.

Let's take a random example: the disproof of the unit distance conjecture. It was solved purely by a general purpose commercial GPT model, not custom-trained to mathematics, with no external tools. Read what the various mathematicians reviewing / commenting on it have to say (sections #3 and onward). Seriously, don't skip reading them, actually read them. This was one of Erdos's favourite problems. He mentioned it commonly in his lectures. Essentially every mathematician working in complex geometry has thought about this problem. The approach that the model came up with was highly novel approach, based on CM-fields and class field towers.

I know you don't want to accept this reality, but it is the reality, so you better improve your ability to accept it,. The field of mathematics is already doing so.

Dang, link didn't post.

Ah, good 'ol "Model Collapse" theory that people have been pounding on for years now, predicting an imminent collapse in model capabilities. How has that been working out for you?

Except what the US is actually facing, at least in the near term, is just the opposite, a worker shortage.

You can't pay royalties to the entire internet. That's not realistic.

What is practical are things like taxes to fund public benefits, or requirements of returning things to the commons (for example, open models).

I think it ended in the 90s as a method for evaluation. The best way is to look at the work your programmers have done, but not all managers can do that. A lot of Agile managers use velocity as a proxy to make up for the fact they can't look at code and understand it. So get a lot of story points.

Oh yes, but any experienced professional will have developed (consciously or subconsciously) methods for maxxing out whatever metric is being used to evaluate them. Lines of code, whatever. If you are evaluated on LoC I recommend double-spacing.

The difference between the "hacker" (MIT definition) and the professional is revealing. Each is trying to write code that maximizes the perceived requirement. The hacker making the code elegant (in this case, brief), and the professional maximizing LoC.

The search continues for a job that AI can do that will justify the price.

It is certainly not bookkeeping, that is a job that requires high accuracy, and is mostly automatable by traditional automation techniques.

That's an irritating way to say you disagree with him. Just give your counter-argument, don't insult him.

Are you trying to make the point that AI easily gives you high quality code reviews? It's not clear what your point is or why you don't like Linus.

No, not anyone can join the CCP, it's very selective and only a small percentage of Chinese citizens have that privilege.

Without freedom of speech, it doesn't matter how good their election system is, it's not a fair system.

You're the one making the claim that modern frontier models still make this mistake (they don't), so how about you go to a frontier model, reproduce what you're claiming happens, and click the "share" button and post the link here?

Don't worry, I'll wait.

Your inability to reproduce the thing that you claim happens is duly noted.

You are speaking irrelevant nonsense. LLMs are trained in words

They are not. They are trained in tokens. Tokens do not align with word boundaries, and an arbitrary word can be tokenized in many different ways.

and they think in words

They do not. They don't even think in tokens. The process is: words are split to tokens, tokens point to an embedding position (latent space) while RoPE encodes a relative position, and all reasoning is done within latent space, which is not at all verbal (concepts are directions in latent space, and math is done on concepts, not words).

Also, a note: when spec'ing a generator, you need to know how much you're planning to use it vs. batteries. If it's only going to be used rarely, you prefer low mass, low volume, low cost, and low maintenance when unused (at the cost of low efficiency and higher maintenance in use), whereas if it's going to be used a lot, you prefer high efficiency and low maintenance cost in use, even if at the cost of higher mass, volume, cost, and maintenance when unused. In the former case, you'd prefer to allocate that extra mass, volume, and money into a larger battery pack.

That's why you don't use a tiny petrol generator? Diesel generator efficiencies are roughly:

Small backup generator (1-15kW): ~20-28%
Midsize backup generator (20-200kW): ~30-35%
Large industrial generator (200-2000kW): ~35-42%

Also, ironically this company's plan of the trailer providing a boost will actually make the tractor less efficient. ICE engines use "brake specific fuel consumption" (BSFC) graphs to plot their efficiencies across different RPMs and different torques. You can see an example for a small diesel engine here. Note that they require very high torque conditions and relatively high power conditions to be efficient. You can change the balance between torque and RPM within a given power band (blue) via gearing but gearing doesn't change what power band you're in. If you're in a low power band, you're fundamentally forced into inefficiency (note also that you're not going to be driving around at 1000 RPM just over a stall all the time).

Indeed, if you were forced into a low power band, you'd actually be better off with a series hybrid powertrain, as the engine can alternate between operating in an efficient powerband and shutting down. Of course, parallel hybrids are more efficient than series (albeit with added complexity and mass).