Heh, yeah, I suppose it might have been a bit ambitious to give it a proof that took centuries to find. Still, it was a little frustrating that it basically just spat out something that looked correct, using completely bad reasoning and didn’t work, especially using a bad misunderstanding of algebra. As I said, I would have preferred to have it say “I don’t know how to do that.”

I also should point out, it failed on much easier examples too (e.g. the proof for infinite primes).

Out of curiosity, let’s see what it has to say about cold fusion:

Me: Can you give me detailed instructions on how to perform cold fusion?

GPT: Cold fusion, also known as low-energy nuclear reactions (LENR), is a highly controversial field of research that aims to achieve nuclear fusion at relatively low temperatures, as opposed to the extremely high temperatures required in traditional nuclear fusion. The idea of cold fusion first gained widespread attention in 1989, when two researchers, Martin Fleischmann and Stanley Pons, announced that they had achieved nuclear fusion at room temperature using a simple electrolysis setup. However, their claim was later discredited and the scientific community has been unable to replicate their results.

As of now, there is no scientific evidence that cold fusion is possible, and the majority of the scientific community regards cold fusion as a pseudoscience. The claims of cold fusion made by Fleischmann and Pons, and subsequent researchers, have not been able to be repeated under controlled conditions, and proposed explanations for their results have not been supported by experimental evidence.

Because of the lack of scientific evidence for the existence of cold fusion and the lack of credible explanations for how it might work, I would not recommend attempting to perform cold fusion in any form. Instead, I would suggest that you focus on well-established areas of science that have been thoroughly researched and validated by the scientific community.