Image generation requires no fact checking whatsoever

Sure it does. Let’s say IKEA wants to use midjourney to generate images for its furniture assembly instructions. The instructions are already written, so the prompt is something like “step 3 of assembling the BorkBork kitchen table”.

Would you just auto-insert whatever it generated and send it straight to the printer for 20000 copies?

Or would you look at the image and make sure that it didn’t show a couch instead?

If you choose the latter, that’s fact checking.

That said, LLMs will always have limitations and true AI is still a ways away.

I can’t agree more strongly with this point!

Some problems lend themselves to “guess-and-check” approaches. This calculator is great at guessing, and it’s usually “close enough”.

The other calculator can check efficiently, but it can’t solve the original problem.

Essentially this is the entire motivation for numerical methods.