Agile, as a concept, is old, it is very old. In my research trying to answer your question, I saw a quote from 1977 defining Agile, although not calling it by its current name.
However, I don't think we can say that Agile is 34 years old. Agile, in my opinion, has the same age of the Agile manifesto.
But when was the Agile manifesto published? It was published in early (February, some say) 2001, which means that Agile is slightly over 10 years old!