But your own example implies that you could've achieved the same results by simply using the "and" operator: ring AND mathematics. No reason to give up privacy.
I'm actually surprised that your friends didn't get the Wikipedia entry on "ring" among their top results. When I ran the search on both Google and Bing, it came up second.
I was expecting to get garbage pages about wedding rings, or something like that. As its #1 result, Google sent me where I had wanted to go:
http://en.wikipedia.org/wiki/Ring_(mathematics)
By knowing my interests lie in computer science, technology, and mathematics, Google was able to return this for me as the first result.
Other searches my friends did took them to rings for sale on Overstock.com or Amazon.
I welcome this new technology.