This is completely tangential, but I want to share my latest GPT4 story somewhere.
I've tried before to gaslight GPT4 into saying things which are mathematically untrue, I lie to it, I tell it it's malfunctioning, I tell it to just do it, it wouldn't do it.
I was recently studying linear algebra which can be a very tricky subject. In linear algebra the column space of a matrix is the same as the column space of the product with itself transposed: C(A) = C(AA^T). If you ask GPT4 if "C(A) = C(AA^T)" is true, it will understand what you're asking, it knows it's about linear algebra, but it will get it wrong (at the time of this writing, I've tried several times).
I couldn't get GPT4 to agree it was a true statement until I told it the steps of the proof. Once it saw the proof it agreed it was a true statement. However, if you try to apply the same proof to C(A) = C((A^T)A), GPT4 cannot be tricked, and indeed, the proof is not applicable to this latter case.
So GPT4 was incorrect yet able to be persuaded with a correct proof, but a very similar proof with a subtle mistake cannot trick it.
I've tried before to gaslight GPT4 into saying things which are mathematically untrue, I lie to it, I tell it it's malfunctioning, I tell it to just do it, it wouldn't do it.
I was recently studying linear algebra which can be a very tricky subject. In linear algebra the column space of a matrix is the same as the column space of the product with itself transposed: C(A) = C(AA^T). If you ask GPT4 if "C(A) = C(AA^T)" is true, it will understand what you're asking, it knows it's about linear algebra, but it will get it wrong (at the time of this writing, I've tried several times).
I couldn't get GPT4 to agree it was a true statement until I told it the steps of the proof. Once it saw the proof it agreed it was a true statement. However, if you try to apply the same proof to C(A) = C((A^T)A), GPT4 cannot be tricked, and indeed, the proof is not applicable to this latter case.
So GPT4 was incorrect yet able to be persuaded with a correct proof, but a very similar proof with a subtle mistake cannot trick it.