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

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.

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.

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.

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.

Compared to what OpenAI is claiming its word machine has solved (without any human verification for the claims so far, not even in OAI), the scribbles kinda are (just highschool math).

The proofs are written in Lean so, like in all mathematics, you don't have to trust the person because you can independently verify the proof.

Spot on, this is the thing people often miss out.

These problems aren't actual problems in the way most people think about. They are problems in the way that they are exercises. Like the Navier Stokes problem is reporting in the news like one of the biggest problems in maths ever. Leading people to think we are stuck on it and can't progress in some way without a solution. But in reality the limitations of the equation are well known and don't impact normal every day use. And in cases where they would, we have other tools at our disposal.

The goal of these problems is to challenge mathematical people and push boundaries. Having a proof pop out of nowhere is like having someone tell you the answer to a question, where the whole goal was to formulate the answer yourself. The answer itself is meaningless, that's why you get 0 points on the exam unless you show the workings out. It's like having a movie spoiled for you, the goal wasn't to know the outcome, the goal was the experience the story yourself.

Working backwards from some proof might lead to insights, but it also might not and be harder than working forwards. It also might pick a certain path, where there were multiple and we would be blind to the other paths. Those other paths might lead to more insights, if we had explored them.

The way OpenAI specifically has approached this is also very weird and awful in my opinion. Like they set their sights on yet again ruining some aspect of the world with AI and then throwing billions of dollars at it to make sure it's properly ruined. For what purpose exactly? Not to make any money, that's for sure, they are 2 trillion in the hole and counting.