Why is it wasteful to solve one of the most famous problems in modern mathematics? And why would one particular company have no business solving it in the first place?
I guess by their own account they were doing competitive analysis on the product and incidentally solved NS. Probably the two companies should agree to benchmark on random diophantine systems, which are harder and more applicable anyway. It wasn't "brute force" but they did spend $10-20M over the course of a few days based on a rumor, which is ... something. The fact they're not actually taking credit, and published no insights other than "it's a vortex" shows the company really has no business in mathematics. They're not interested (the guy said as much) and it obviously won't pay the bill - rather, they were able to pre-empt an announcement they thought Anthropic may have been preparing to make.
> That theorem statement is correctly encoded (FLT has a very short 1 liner description really)
As someone not very familiar with Lean, does it really just depend on the entry point / theorem being correctly encoded? Can intermediate statements ever be mis encoded or misinterpreted, or is this what would count as a “bug in the Lean compiler”?
It is the latter. If you are certain your theorem is stated correctly, and you believe that the Lean kernel against which you validate is correct, your proof is correct.
This is how the theorem for FLT looks in the particular proof we discuss here:
theorem fermat_last_theorem (n : ℕ) (hn : 3 ≤ n) (a b c : ℕ)
(ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a ^ n + b ^ n ≠ c ^ n
As long as this statement is correct, and the kernel is correct, the proof could be trillion lines of code, and if the kernel says it is correct, it is correct.
This proof was checked against TWO independently built kernels. So you would need TWO kernels to have the same bug to mistakenly accept an incorrect proof.
(Not impossible: such a bug indeed was recently discovered (and patched))
If you just "translate" an existing proof step by step to Lean, then of course you could mis-encode the intermediate statements too. But if you mis-encode the steps and still pass Lean check, it means you found a new proof! (Or you found a bug in Lean)
There's no guarantee that the intermediate statements match the informal mathematical intermediate statements, but if there is a mismatch, then this has to be repaired elsewhere to yield a proof that passes the Comparator tool. Running this tool indeed reduces the correctness question to what the parent comment mentioned.
I don't think we can selectively reject them, it's not anything I've looked into though so not certain about that.
Although we are a B2B business, most of our card transactions are from business owners personal cards so it's not really an issue. We occasionally monitor the split and if it became significant we'd need to look at addressing it, probably by increasing prices for those customers.
I’ve been using codex more recently, like others here.
But one thing I’ve noticed which I find a bit of a red flag: by default you only archive chats. If you go online, it says there’s a location in settings where can delete your archive. But it’s not that obvious where to find, and when I finally find some link, it was literally broken. It said it can’t find any archived chats, even though I archive them all the time.
Bit of a red flag for me. Both Anthropic and OpenAI claim that when you delete a chat, it’s gone after some retention period. They’re just words but if they’re secretly training on your traces and you delete your chats, then they would need to break two terms/conditions: ignoring your “train on my data” preference and ignoring your orders to delete chats. So it is an extra barrier.
But OpenAI, as far as I can tell, doesn’t let you delete your chats. Convenient then if they change their mind about training sometime in the future.
His fund didn’t fold btw. They sold / were forced to sell a position that was several hundred percent up at a very very bad price relative to peak. AFAIK the fund is still up on the year though.
AIUI they were forced to sell all their positions in public companies at a net loss. The fund is still up for the year only because of a prior investment in Anthropic.
That is called folding the fund. It did in fact fold. "My fund would not fold if I made different hypothetical decisions" argument means your fund did in fact fold.
Yes, being unable to pay margin call means your fund is folding.
It's not part of the strategy or operating agreement of a GP/LP structure to sell a specific fund to another investment firm at a discount. The fund may buy and sell assets to create returns for LPs but selling the fund itself at a discount is not a successful exit, e.g. they folded.
I feel like I’m arguing against the grain here, and it seems to me like there’s a lot of emotion around this topic. I’m not even a defender of AI billionaires. I just posted because I see this type of discussion around SA recently and it’s mistaken. So I’ll just leave this comment, and it goes for the other replies too.
What happened to SA is not what anyone would call “a fund folding”. Normally you’d assume folding means the fund went bankrupt, or closed at a loss.
This fund is not closing and not on a loss. It’s not bankrupt, and apparently it is opening up new positions and continuing to invest in its main theme last I saw it in the news.
It is on a major drawdown from its peak a few months ago, but it’s still up for the year, most of its investors are likely well in the positive. If you make a huge investment and it goes up 5x before trimming its gains and ending up 100%, you’ll be annoyed, you’ll wish you sold at the top, but you’ve still doubled your money.
Getting margin called and closed this way is not the same as going bankrupt.
> Getting margin called and closed this way is not the same as going bankrupt.
Technically we don't actually know the details here since no one here is privy to the specific fund structure - which is very likely WAY more complex than reported.
So, realistically we're arguing semantics. I said it folded and for intents and purposes if you're getting margin called and have to sell, then that's folding.
Just like in poker I can fold and not play anymore and still have a stack of chips.
it's in the article, around 2030 the device should be able to write and "make changes to the brain: hear audio, or tell the brain to use more calories" ...and later she envisions chatGPT becoming an extension of the brain like a sixth sense.
I don’t think users (as in the general population) have a good track record of being judicious with how they share data. In the past with social media etc it was consistently the opposite, if the price is lower or free people tick any box and hand of all their personal data. Might turn out the same here too no?
Not arguing against on-device LLMs, I also wish it were so.
Surprised so few are pushing back against some of the claims in this article.
Eg that the entire surface of the earth gets replaced in a million years by tectonics.
Many of the large plates are more than 1000km across, they’d need to be moving meters per year for that to happen. In reality it’s cm per year. Also typically it’s oceanic plates that get subducted and take material under the crust, not continental plates. If it were true, then how do we see dinosaur fossils, and creatures even older than that; how do we find rocks that are over a billion years old.
This doesnt reject the possibility that there was a civilization tens of millions of years ago, but it makes the article hard to take seriously. If you’re gonna spend time writing an article on this you might as well try to research it a bit more. Someone is gonna read this and repeat this nonsense like it’s some fun trivia.
Banks don’t do this because of profit. They do it because of decades of laws pushing in this direction. Anti-money laundering, know your customer, digitalised currency, abandoning cash, preventing tax evasion etc… it’s been getting more extensive over time.
None of the things you mentioned inherently require the user to own (and babysit) an expensive general-purpose computing device produced by tracking-obsessed adtech giants and with software obsolescence built into the product.
