3 ms·

I doubt it. I've tried to trick GPT4 into accepting invalid proofs, it wouldn't accept them. I told it a textbook said so, it said "sorry, the text book must be

I doubt it. I've tried to trick GPT4 into accepting invalid proofs, it wouldn't accept them. I told it a textbook said so, it said "sorry, the text book must be wrong". I finally gave it the correct proof and it accepted it. This was a proof that C(A) = C(AA^T) in linear algebra. The proof was not too hard, but depends on solid logical reasoning. GPT did well here, able to discriminate valid and invalid proofs.

moritzwarhier 3y ago
I feel like it hurts ChatGPT when the training set contains many variations of explaining the same logical fact and/or proof. Which might be wrong, it sounds paradoxical at least. Levels of abstraction differ, and terminology too. And of course there's content on the web that's just wrong, often in some subtle detail. Example: I had a lengthy discussion with it about a school mathematics question and probabilities. The question was clearly defined and every time the answer was ambiguous or not a valid proof, I tried to point out the inconsistencies to the best of my limited knowledge. The question was What is the **expected** number of rolls needed to roll the first six using a fair 6-sided dice? Prove your answer. I know this is a simple and innocent question, but it can trap one up when mathematical knowledge is limited (I include myself here, my education is just too rusted). In this case, it came up with lots of hand-wavey answers on why the answer is 6. The answer was correct but the explanations were not. Altering the question, for example by asking for at least two times the number six made things worse. It took a lot of follow-up questions, then the model explained to me why the terms of the expansion of the recurrence equation it came up are bounded by a geometric series. The correct answers were very good, precise and understable, but interspersed with misleading inconsistent, and wrong answers. I wonder if it will break completely at some point for this kind of conversation, when it keeps ingesting content of unpredictable quality.

moritzwarhier 3y ago

I feel like it hurts ChatGPT when the training set contains many variations of explaining the same logical fact and/or proof. Which might be wrong, it sounds paradoxical at least. Levels of abstraction differ, and terminology too. And of course there's content on the web that's just wrong, often in some subtle detail. Example: I had a lengthy discussion with it about a school mathematics question and probabilities. The question was clearly defined and every time the answer was ambiguous or not a valid proof, I tried to point out the inconsistencies to the best of my limited knowledge. The question was What is the **expected** number of rolls needed to roll the first six using a fair 6-sided dice? Prove your answer. I know this is a simple and innocent question, but it can trap one up when mathematical knowledge is limited (I include myself here, my education is just too rusted). In this case, it came up with lots of hand-wavey answers on why the answer is 6. The answer was correct but the explanations were not. Altering the question, for example by asking for at least two times the number six made things worse. It took a lot of follow-up questions, then the model explained to me why the terms of the expansion of the recurrence equation it came up are bounded by a geometric series. The correct answers were very good, precise and understable, but interspersed with misleading inconsistent, and wrong answers. I wonder if it will break completely at some point for this kind of conversation, when it keeps ingesting content of unpredictable quality.