Secretary General B.R. Sen attempted to answer this question in 1964 while writing for a weekly series in the New Scientist about how the world might differ in 20 years. He touched on many of the same issues that FAO is dealing with today, in particular how technical knowledge would affect agricultural production and the difficulties in estimating whether or not this knowledge would be sufficient to put an end to world hunger. Take a look at Food and Agriculture in 1984: the race has not yet been won.
If you would like to read more on the subject come into the library and you can read the articles by other contributors about the same topic in this issue.