Problems with ChatGPT

I've been an occasional user of ChatGPT for about a year. It occasionally is truly impressive but today I had an interaction with it that, in many ways was both weirdly human and stubbornly wrong. I had been investigating a geometrical question:

What is the condition that the midpoints of a quadrilateral form a square?

I began by telling ChatGPT that I knew that the midpoints of a quadrilateral always formed a parallelogram. It agreed and gave me the proof that requires two applications of the midpoint theorem. Then came this dialogue

Me: For what type of quadrilateral is this parallelogram a square?

ChatGPT: The parallelogram formed by the midpoints of the sides of a quadrilateral is a square if and only if the original quadrilateral is a rectangle.

This was followed by several lines of proof which included the claim that the diagonals of a rectangle intersect at right angles. ChatGPT's claim is false and I pointed this out saying that it could not be true for long thin rectangles. So then....

ChatGPT: You are correct, and I apologize for the confusion. Let's revisit the conditions under which the parallelogram formed by the midpoints of a quadrilateral's sides is a square.

Then came...

ChatGPT: For the parallelogram formed by the midpoints of a quadrilateral's sides to be a square, the original quadrilateral must be an isosceles trapezoid.

More dialogue in which I again refuted this claim with long thin isosceles trapezoids to which I got:

ChatGPT: I apologize for the confusion earlier. You are right; neither rectangles nor isosceles trapezoids in general guarantee that the midpoints of their sides will form a square under all circumstances. Let's clarify the exact condition needed for the parallelogram formed by the midpoints to be a square.

ChatGPT: For the parallelogram formed by the midpoints of a quadrilateral to be a square, the quadrilateral must be a rhombus.

Another refutation by me and then ChatGPT returned to its original declaration that the quadrilateral had to be a rectangle. And finally...

ChatGPT: I appreciate your patience and the opportunity to clarify this correctly.

At that point I could not get much change in ChatGPT's replies. Its geometrical reasoning was superficially plausible in that it set out its arguments in a logical progression of steps. I have to confess I would have been hugely impressed had it got its logic correct. But the weirdly human aspect of it was its insistence, despite all the evidence, that it was right all along.

And I guess the moral of this interaction is that, despite its answers being couched in the most plausible of clothes, it was entirely wrong. And so, be careful, perhaps it is wrong lots of times.