I have collaborated with Dr. Nambu at two occasions. The first was in 1948–50 when I was a special research student of Tokyo University and the second was in 1952–54 when both Nambu and I were visiting fellow at the Institute for Advanced Study in Princeton.
Nambu mechanics equipped with Nambu bracket is a new formalism proposed by Nambu in 1973 as a possible extension of Hamilton mechanics. We review its essential content and significance for readers who have not been familiar with this development. We also briefly discuss its connection and influence on string/M theory.
Questing for the source of Nambu's fruitful inspirations, the discussion by the author with Nambu in August 1st, 2002 is introduced. In this discussion appears a bud of guiding Nambu towards hydrodynamics. Explaining Nambu's hydrodynamics, a guess is given on what Nambu is going to do afterwards, by the author's limited knowledge and insight.