Manned Mars exploration is technically feasible - I have no doubt we could send someone there by 2020 if we put in the effort. But we would eventually abandon it for the same reason we abandoned manned exploration of the Moon. It's just too difficult to safely transport living human cargo to and from other worlds for anything beyond small exploration expeditions.
If trasnshumanism eventually becomes "a thing", if we manage to shed our biological shells and take on forms that are more at home in hostile environments, THEN we might see a blossoming of space exploration and ultimately colonization. Space is too vast, other worlds are too alien and we are just fragile bags of meat that need lots of external systems to maintain life (pesky things like "breathable atmosphere" and "food"). We fairly regularly and cheaply send robots in our stead. If we eventually "become" the robots, then yes, we will have manned space exploration of a sort.