I wonder which city can claim the title nowadays. At some point many would say San-Francisco but IMO it was a different kind of center, and that seems to be gone too anyhow.
I think when it's about an intellectually and culturally rich capital/world city, SF would not make the cut even among such cities of the USA, let alone the world. Unless one completely equates diverse intellectual and cultural heritage and tradition to something like hippie movement or money-making alone.
