SpaceX states in each of its job ads that it has "the ultimate goal of enabling human life on Mars".
To this end, his website houses a picture of a rust-red planet turning into an earth-like world. The illustration is an allusion to a hypothetical and speculative process called terraforming.
Terraforming is a type of climate change, but deliberate and faster than the process that is currently happening on Earth.
The idea is that Mars could be turned into a warm, humid world – one that is better suited for permanent human colonization – if we can melt the planet's carbon dioxide-rich ice caps.
In its current state, Mars has less than 1
It is not known if terraforming could be done in a sustainable time on Mars. NASA doubts that this is possible at all, as there may not be enough gas trapped in the poles to create a comfortable planetary atmosphere.
In addition, the effort could require a kind of powerful satellite that could produce a magnetic shield to protect against solar radiation that would otherwise blow away any human-made atmosphere.
On the other hand, the scenarios the researchers have studied do not really consider water or methane (a potent greenhouse gas) that could be trapped in the Martian soil. Nor do they investigate whether chemically rich comets and asteroids could be rerouted to hit Mars. Musk even said that Mars could help.
Experimenting with terraforming can only be one way to tell if it's possible. Musk, or perhaps his memory and legacy, could only be the drive that makes it possible in the distant future.