The Centrality of Galois Groups of Local and Global Fields of Dimension One

Professor Manin's 1990 ICM talk states there is a convincing case to be made that these groups are, in some sense, "more fundamental" in number theory than even the integers. The talk's purpose being a broadest-possible survey of the works of Professor Drinfel'd, Professor Manin does not deem it appropriate to devote so much time to elucidating this perspective. I was hoping someone here could parse what he means.