This paper questions the perspective of a "world without agriculture" which underpins the economic paradigm of "structural transformation" and "modern growth". It does so by recomposing worldwide land and labour productivity trends in caloric terms from 1961 to 2007 and by providing an heuristic model showing that the "Lewis Path" to prosperity is only one out of four possible pathways. It shows that more than half of the world population is rather embarked in a "Lewis Trap" where farmers are increasingly numerous and relatively poorer. It highlights how land scarcity and insufficient job opportunities outside agriculture prevent them to increase their labour productivity and incomes with motorized machineries. The emerging paradigm of "ecological intensification" might contribute to overcome the current deadlocks by redirecting worldwide R&D towards small-scale knowledge-intensive and context-specific agricultures overlapping the manufacture and service sectors.