So I asked it for a joke that would require grad school math, and this is what it came up with:
“Two topologists are talking to each other. The first one says, “Hey, I just proved that any two donuts are topologically equivalent.” The second one replies, “Really? That’s amazing! How did you do it?” The first one replies, “Well, I just cut one donut into a million pieces and rearranged them to make the other donut. And then I did the same thing with the other donut. So now, both donuts are made up of the same pieces, and therefore, they must be topologically equivalent.””
[That’s, uh, not very interesting. But it looks like they took the basic idea of Banach-Tarski, knew that it was an area in which you could make jokes because the implication is absurd, but failed to actually understand the potential joke material in its implication.
I ask it for a joke involving grad school combinatorics, and it fell really flat]
"A mathematician, a physicist, and a computer scientist are all in grad school together. They are discussing their research and the mathematician says, “I’m working on a problem in combinatorics. It’s really tough, but I’m making progress.”
The physicist says, “That’s nothing. I’m working on a problem in quantum mechanics and it’s so complicated that I can barely even understand it myself.”
The computer scientist says, “Ha! You guys have it easy. I’m working on a problem in combinatorial optimization and it’s so difficult that even my computer can’t solve it!”"
[I’m not sure if that’s actually funny. And it obviously doesn’t involve grad school level combinatorics - it only has the words “combinatorics” and “grad school” in it.
I asked about the phenomenon of TONCAS in graph theory:]
“I’m sorry, but I’m not familiar with the term “TONCAS” in the context of graph theory. Could you provide more context or clarify what you are asking?”
TONCAS in graph theory means “The obvious necessary condition is also sufficient.”
"I apologize for the misunderstanding. “TONCAS” is not a commonly used term in graph theory. It is not a standard abbreviation or acronym in the field. It seems to be a phrase that you have coined to describe a situation in which a necessary condition for a certain property or result in graph theory is also sufficient to guarantee that property or result.
In graph theory, a necessary condition is a requirement that must be satisfied in order for a certain property or result to be possible. A sufficient condition, on the other hand, is a condition that guarantees that a certain property or result will hold. If a necessary condition is also sufficient, it means that the property or result will hold as long as that condition is satisfied, and it is not possible for the property or result to hold if the condition is not satisfied.
I hope this helps to clarify the meaning of “TONCAS” in the context of graph theory. Please let me know if you have any further questions."
[Dumb as a brick on this subject it seems. Google “TONCAS graph theory” and you’ll find hits explaining it that clearly weren’t part of its training data.]