Hacker News Reader

Comment by tptacek | Hacker News Reader

How does that work in this case? What do those proofs do to help find this counterexample?

In my view, it's theoretically possible for a combination of the author's iterative prompts + evaluation with Wolfram Alpha to activate the weights that encode the language that describes the constraints on these polynomials (from the faulty proofs) in such a way that the author eventually arrives at this:

> ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3

How is that not like claiming that a "combination of iterative prompts and evaluation with Wolfram Alpha" would produce my Google Mail password? I also have to note that this response abandons the original claim, that the counterexample was found by exhaustively searching prior failed attempts.

I've seen a lot of people claiming that these recent examples are just trivial combinations of existing prior work.

I'm yet to see anyone cite the prior work. If it's true I think some credit is due for the authors Fable/Sol are branching from.

I haven't seen these claims, but all of the open problems that have been solved so far have been in the category of "humans could have solved them, but didn't". This doesn't diminish the significance of the results, but it does mean there's still work for mathematicians to do other than glorified prompt engineers.

This specific counterexample really is trivial. There's nothing to cite. People have wasted hours and hours on a question whose answer you could give as a homework problem in Calc II.

Checking the counterexample is a Calc II problem. Finding it was beyond the efforts of the best algebraic geometers for almost a century.

https://xcancel.com/nihilunbounded/status/207910986973986045...

> You’re unable to view this Post because this account owner limits who can view their Posts.

It's absolutely not a trivial combination of prior work, or mathematicians would've found it already. This was not an obscure conjecture.

I can write a program right now that will print your password. It will just take a while.

Reply on news.ycombinator.com