The story was set in a mid-future Earth (at least 20 years from now, but probably less than 100) with AI and nanotechnology. The most striking element (and the one I thought I could find with Google search) is a massive black octahedral building that houses a major AI. I believe it is described as standing "arrogantly" on one vertex. (It is not held up by antigravity or any advanced technology; the AI is powerful enough, and fast enough, to simply maintain its balance despite winds, etc.)
The narrator of the story has a friend who is obsessively tuning the programming of a suite of nanobots, effectively a nanovirus, that he manages to get injected into one of the feed-lines of the aforementioned AI. There is a brief data-blip, and narrator relates that this is the first time in a long time that anyone has managed to cause even the most minor of observable effects on the AI. He may even have seen the octahedron rock ever so slightly (he's not sure).
The narrator is initially fearful for his friend, but comes to the realization that the AI (collectively; this one and others like it) permit, and may even subtly encourage, such people as a way of constantly testing and improving their defences.
I likely read this between 1995 and 2005. It feels like something by Greg Bear, but I couldn't come up with a match.