True, but it's almost always faster than the flow of electrons...well, if it goes at all.

They're both quite different from the US, but saying they're about the same is both weird and wrong. The Chinese are rebuilding the imperium, which was sometimes good and sometimes quite bad. The Russians...they seem to be in the process of destroying their country. The reports I have heard are now a couple of decades old, but they indicated that they country was largely run by non-government-based gangs.

No. But Cornish, however...

Well, Apple *appears* to be doing the right things. This may be accurate, but don't feel too certain.

So your mistake is thinking they're all alike. (Unless that was sarcasm or other humor.)

That's not really true. Consider the ABC proof. It is probably valid, but it uses math that almost nobody who is an English speaker can check. The author is currently translating it into a form that can be read by LEAN (an automated proof-checker). If it passes LEAN, there still won't be many mathematicians who can understand it.

I *think* a lot of those claims are unverified PR announcements by Chinese companies. They *MAY* be correct, but I tend to doubt PR announcements.

So far the evidence seems to indicate that they're still using as many high-level NVidia chips as they can get. I suspect research is being reported as developed systems. If the reports (understood in that light) are accurate, your estimate is correct, but your timeline is off by perhaps 5 years.

IIUC, the proof is verified by Lean, which is NOT an AI, but is rather a deterministic proof checker, and highly trusted.

Sorry, but that's not what reasoning models are doing. Don't trust the logs as accurate traces of their thinking.

OTOH, since the output is a proof, you don't need to even consider the log. Just check the proof, and (if properly formulated) there are deterministic methods of doing that.

Saying 1,0 *is* an integer is false. It converts to an integer. Whether it equals an integer depends on how you represent floats...though in every implemented system I'm aware of 1.0 does convert to 1. However saying 1.0 is within epsilon of 1 is true for every floating point system using a normal meaning of epsilon.

OTOH, they didn't use up the AI in solving the problem, so it's still there to be used for something else. So you can't really count all the cost of building an training it against a problem that it solved as a test of its capabilities.

Actually you've got a pretty good guess that the problems are quire hard, and a reasonable chance that they are indeterminate (unless they involve a finite subsection of math).

Yeah, but what is it competing against?

Not many silent movies made anymore.

If copyright law weren't so bad you might have a point.
Copyright is really too broad a term to have a good law, but basically any time period longer than 20 years is too long. There *are* exceptions, in unitary things with a high initial development costs, but those are edge cases, and rare.