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Trusting your own judgement on 'AI' is a huge risk
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It is a bunch of stochastic parrots. It just happens frequently that the words they are parroting were orginally written by a bunch of intelligent people which were knowledgeable in their fields.
Note this doesn't makes the parrots intelligent - in the same way that a book written by Einstein to explain special relativity has any own intelligence. Einstein was intelligent, his words transport his intelligent ideas, but the book conveying them to other people (as, the printed pages with cardboard cover) is as dumb as a stone. You would not ask a piece of cardboard so solve a math problem, would you?
Your comment doesn't account for the fact that LLMs can generalise. Often not very well but they can produce outputs for inputs not seen in their training sets. Otherwise what would be the point?
Uhhh you know LLMs can solve quite complex maths problems? Including novel ones.