You vastly overestimate the amount of human intelligence that can be gathered from looking at search queries. Working for search quality, two things I quickly

You vastly overestimate the amount of human intelligence that can be gathered from looking at search queries. Working for search quality, two things I quickly learned from watching a lot of random sample queries are: (1) People like porn. (2) People can't spell. In other words, if you are working for algorithm "X", and if you gather one hundred random queries mentioning X, a lot of them will be along the lines of: "python library X", "CLR ch 12 X solution", "knuth X 1985", "given figure 12 what is the amortized time complexity of X" (or some other exact copy-paste of a homework problem). People don't type "Amortized time complexity of X can be improved when f and g are monotonically increasing" into a search box. Besides, exactly who's going to use the result? Imagine you meet a Googler who has PhD in Algorithm X, working for a super secret project, and tell them "You know, I found random guys on the internet searching for X and I thought their disjointed query terms might teach you a thing or two about how to use Algorithm X." (Not to mention that almost everyone will view it as a gross breach of ethics.)