Mathematician here specializing in number theory with a side-order of graph theory. I've only had time to start looking at two of them. First, is the Hadwiger-Nelson/chromatic number of the plane https://ancillary-proxy.atarimworker.io?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FHadwiger%25E2%2580%2593Nelson_problem proof. As far as I'm aware (and I could be wrong) the technique it uses here is not in the literature, so this is a genuine construction of a new technique. Second is the Erdos Egyptian fraction bound, and for that one it looks like the techniques are about what I'd expect, but I'm definitely still digesting both of these.

For the quasi-Riemann Hypothesis the striking thing is almost the opposite direction. It looks like the AI used standard complex analytic techniques to get the result. But many mathematicians have often thought for years that those techniques would not likely be strong enough to get this sort of result.

I know less about the Unique Games Conjecture https://ancillary-proxy.atarimworker.io?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FUnique_games_conjecture but having talked with some of the people there it looks like it took a somewhat standard set of ideas and then combined them with multiple just weird stuff and sort of took a hard left turn at one point for no clear reason and ended up at the result.

It is also worth noting that while many of these have Lean code confirming their correctness (quasi-RH for example) others do not. The three I mentioned above have all also been looked at at this point by human mathematicians who have not found issues; that's likely true for others, but those three I'm aware at least of people doing so. Not all the claims have Lean code though; a bit under half. One of the non-formalized problems also has been withdrawn due to what essentially amounts to a sign error https://ancillary-proxy.atarimworker.io?url=https%3A%2F%2Fgithub.com%2Fopenai%2Fmath%2Fblob%2Fmain%2Fpreprints%2FAlgebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026%2Fpaper.pdf. It is likely others will be withdrawn also by the end, but I'd be surprised if more than 10 are. And even if everything single one without Lean code turned out to be wrong (which seems very unlikely), this would still be an amazing set of math. I commented elsewhere that if a human mathematician had made the quasi-RH result they'd be likely a shoe-in for the Fields Medal, and another mathematician replied saying "delete likely."

Now a more editorial comment: There are legitimate concerns about what this is doing to mathematics. This sort of thing is very cool. But it also is part of a trend that may make it much harder to train young mathematicians or get them to exist at all. If the AIs are limited in how genuinely novel their ideas can be, then we may end up in a situation where we get a massive burst in math over the next few years, and then math stalls out because we don't have enough good really high caliber mathematicians (Not the mathematicians like me, but people like Serre, Tao, Scholze, Clausen,etc.) to come up with deeply new ideas that the AIs can build on.

"Guarantee" isn't what matters here. Likelihood is what matters. They provide predictions better than random chance. That's the central point.

Let's modify your analogy a bit. If someone has a recording a person starting to eat spaghetti, is it more or less likely that the recording will show them then having a drink of water? And if we instead had a series of comics of a person, and the first one says "I'm hungry," and the second shows the person ordering spaghetti., is it likely that they will then eat the spaghetti? Yes, even though they are fictional. Because apparently using fictional being's mental states is useful for modeling what they will do. In the same way, if the AI is modeling based on human emotional states, then recognizing that those are useful predictors for what will happen helps us predict more, whether or not they genuinely have those emotions.

If the chain of thought resembles a human emotion, it is trained on human emotions, and it acts like a human would when they have those emotions, how is that not a useful framework? But also putting aside, whether or not one wants to insist on describing the AI as "frustrated," there's a worrying trend that this is part of, which is when the AI is given a specific set of goals, they will engage in behavior which is clearly unwanted in order to achieve those goals. That's the classic sort of alignment failure that was predicted by those concerned about AI safety years before any LLMs even existed. Some of these events are minor things like this Starcraft situation, or an LLM slipping a "sorry" command into Lean code that won't compile, and others is more serious like the HuggingFace attack. But reward-hacking and alignment failure are now very real.

Let me be perfectly clear about this: I am insulting you. I am calling you out as either being such a plonk that you keep old copies of People magazine around just in case ... or you are such a plonk that you google and select the answer you want.

Either way, you are a plonk. Your memory is reliable and truthful, mine is full of lies.

Yah, right, like I keep sources of everything I remember from 30 years ago. Uh huh. You of course, being perfect, do keep such sources, instead of just googling and reporting the results which confirm your own bias.

Yes, but the authorized version of Pluto had extremely high performance without those elements.

The headline makes it sounds like the AI has just managed to play the game. But that's not what TFS and TFA are talking about. This is about the system beating the best human player at the game. In the meantime, in a very different game direction, there's a new Starcraft AI which learned the game playing against itself (similar to how AlphaZero self-trained) and is apparently beating almost all the humans even as it does some really weird stuff, some of which looks decidedly suboptimal https://ancillary-proxy.atarimworker.io?url=https%3A%2F%2Frelog.gg%2Frazno%2Fvesti%2FAI-Bot-Pluto-Invades-StarCraft-Ladder-and-Defeats-Professional-Players%2F1695%3Flang%3D2 .

Lots of inventions were unasked-for until they were invented.

No we have not. That's another cherry picked date comparison. Corals have been bleaching and repopulating themselves for several hundred million years.

That's not how it was reported at the time, and I have no reason to trust People magazine.

If you were an anti-alarmist, you'd be crowing this shows sea levels dropping.

For another indication of how sloppy sea level rise claims are, the alarmists published a list of sea level changes along the US Atlantic coast, and funny thing, they differed considerably, as if the ocean were rising more in some places than others. The alternative explanation of sinking land levels was pooh poohed as climate denialism. But another funny thing: California's central valley was once reported as having sunk 22 feet since the gold rush days 150 years earlier, due to pumping out so much underground water. Gosh, could the same thing be happening along the Atlantic coast?

They made those loans because the government promised to bail them out if the loans soured, and the government said there would be consequences for not making enough subprime loans.

Oh yes it did, starting back in the Clinton era. I forget what they called it, other than subprime lending. Banks were specifically told the government (taxpayers) would back their risky loans, and if they did not cooperate, there would be consequences.

The claims were "extinction" and "disappearance" by now, not "lower from some cherry picked date". People don't resort to shenanigans like that when they have truth on their side. You, sir, act as if you do not have truth on your side.

There was a world record high temperature reported in Algeria a few years back. Turns out the weather station was situated at an airport, on or close to the tarmac where jet airplanes shot their hot exhaust at the area.

There are standards for weather stations, such as fresh white paint, size and shape of the containing box, louvers, situated with grass around it, no artificial heat sources nearby, etc etc etc. Something like 90-95% of Britain's weather stations violate those standards, some so badly that they are rated as only being within 5 degrees of correct. Britain was also reporting record high temperatures for weather stations that haven't existed for decades; they average other weather stations within 50 miles to create fake weather station data.

These same patterns show up in the US and other countries. The reported "record high temperatures" are nothing of the sort.

Again: people don't lie like this when they have truth on their side. They not only don't need to, they know that lies ruin their reputations. These alarmists don't seem to mind being caught in such egregious lies. Apparently they don't mind having shit reputations.