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MugaSofer comments on The flawed Turing test: language, understanding, and partial p-zombies - Less Wrong
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I don't think there are many novel math problems that are easy enough that you don't falsely label people as chatbots when they say they don't know how to do it. If you let people make maybe promising sounding solutions, that opens up a cheating mechanism for the AI to fool you back, by making mushy statements related to the topic.
Math problems are one thing, "problems" expressed in natural language are both easier to invent and (if you're human) solve, I should think.
Also, math problems don't seem GAI complete, yeah, especially if you're dealing with an "average" human player.