  The analysis of the demographic transition of the past century and a half,
using both empirical data and mathematical models, has rendered a wealth of
well-established facts, including the dramatic increases in life expectancy.
Despite these insights, such analyses have also occasionally triggered debates
which spill over many disciplines, from genetics, to biology, or demography.
Perhaps the hottest discussion is happening around the question of maximum
human lifespan, which --besides its fascinating historical and philosophical
interest-- poses urgent pragmatic warnings on a number of issues in public and
private decision-making. In this paper, we add to the controversy some results
which, based on purely statistical grounds, suggest that the maximum human
lifespan is not fixed, or has not reached yet a plateau. Quite the contrary,
analysis on reliable data for over 150 years in more than 20 industrialized
countries point at a sustained increase in the maximum age at death.
Furthermore, were this trend to continue, a limitless lifespan could be
achieved by 2102. Finally, we quantify the dependence of increases in the
maximum lifespan on socio-economic factors. Our analysis indicates that in some
countries the observed rising patterns can only be sustained by progressively
larger increases in GDP, setting the problem of longevity in a context of
diminishing returns.
