How the robot proves these statement is by writing LEAN code that represents the math. If the lean compiles, the math was valid. If it doesn't, it tries again.

It will do this forever until it finds a solution.

Goedel predicted this in 1933, btw. From his work on formal systems, he ascertained that since every mathematical statement is trivially true following from the rigorous application of the axioms of mathematics or entirely false, theorems could be checked and proven automatically.

These systems are able to prove statements at a scale beyond humans, because they have effectively infinite time to exhaustively explore applying every rule.

Unfortunately, this isn't all that helpful for the various fields of math as a whole. Effectively they have a list of statements and a second column with 'true' or 'false', but the actual route taken by the models to get that answer is often incredibly indirect and therefore difficult to gain insight from and apply to new areas. The approach taken to produce an answer is often more valuable to the field than the answer itself.

The field moves forward when the people in it understand the new results and techniques sufficiently to begin asking new questions, simply giving the answer isn't all that useful. The robots cannot (yet) do this. Someone has to, at a minimum, pose the question in formal mathematical language. There are an infinite number of true statements in mathematics ( trivial example 1=1, 2=2, ...) asking the interesting questions is the important part. The field will still only advance as fast as the people in it are able to digest results.

Further, results in pure math do not generalize to the more applied fields that directly affect our ability to do things. Most engineering formulae are NOT rigorously true - they are weak approximations with envelopes of applicability. The same is true even in base physics. So while a robot can crank through ten million lines of lean to prove an obscure theorem, it cannot think about physics for a week and come up with a theory of quantum gravity.

I am more skeptical. Even with Navier Stokes, I never heard anyone actually internalize the result and have trust in it. I just heard vague lean-dih waving.

Supposedly it's 26000 subtheorems of goobledigook, feels untameable.

Mathematicians seemingly: Axioms are correct, we trust lean => Result correct.

As a physics, CS thinker: AI probably found a bug in our axioms. And/or usual self-referential math issue. And/or connected to Goedel's incompleteness. Also I wonder why I even trust lean as much, havent even read its code. Most software works great until somebody starts poking at its limits.

Ok but actual practical real world use case exists for this? So we know that in theory an imaginary thing that doesn't exist could create a singularity event?

Honestly seems like it's not useful but I'm not a mathematician so I don't really know.

Because the AI contribution was so huge was surely the reason openAI did not want to give any credit to the researches that worked on the foundation for that breakthrough.

Assume all that is true, AI can really do well in these fields, but there are some other fields it can't do well in.

Now who is going to work on those fields? Who is going to take the risk of studying for it, practicing for years, being an expert in the field that takes maybe a decade, and the AI can suddenly solve your field too, and you don't get anything.

I learned it as 80/20 rule where the first 80% of progress is made with 20% of effort, and the last 20% of progress takes 80% of the effort.

It's true im many layers deep in it help

I hate AI, but I'd much rather work for an AI over the idiot higher leadership at my company. They use AI for everything anyway, including literally answering emails.

I know people always say that, but there still needs to be executives so there's still humans to be held accountable.

The vast amount of middle management are useless, but there has to be a human sitting in a chair above the chatbot for legal liability. Otherwise the board will just blame the chatbot for everything.

That also doesn't mean they should be paid so much, just that a human needs to be above the chatbot as far as final authority

Super fucking sorry that my finding a way around the paywall wasn't good enough for you.

But of course, you couldn't even link it either for some reason.

So here's what I say we do:

You block me so you never see me putting effort in, you'd have came here, not seen my link or any discussion.

And then maybe you'd actually provide your paywall removed link for everyone instead of bitching.

Now I'm doing something to, don't worry.

I'm going to block you, because obviously it's hard for me to put up stupid shit like this.

And I just never want to see anything from you again.

Everyone wins champ.

If you really thought that, you could have just typed what you thought I was wrong about instead of a literally useless comment...