Probably be realist to say it could be done in 200 years, give the rate our technology is improving

I better start packing then!

I think you overestermated a little. here is what Robert Zurbin (a former Martin-Marietta aerospace engineer, prolific author and founder of the non-profit Mars Society) has to say;

If one considers the problem of terraforming Mars from the point of view of current technology, the scenario looks like this:

1. A century to settle Mars and create a substantial local industrial capability and population.

2. A half century producing fluorocarbon gases (like CF4) to warm the planet by ~10 C.

3. A half century for CO2 to outgas from the soil under the impetus of the fluorocarbon gases, thickening the atmosphere to 0.2 to 0.3 bar, and raising the planetary temperature a further 40 C.

This will cause water to melt out of the permafrost, and rivers to flow and rain to fall. Radiation doses on the surface will also be greatly reduced.

Under these conditions, with active human help, first photosynthetic microbes and then ever more complex plants could be spread over the planet, as they would be able to grow in the open.

Humans on Mars in this stage would no longer need pressure suits, just oxygen masks, and very large domed cities could be built, as the domes would no longer need to contain pressure greater than the outside environment.

4. Over a period of about a thousand years, human-disseminated and harvested plants would be able to put ~150 mbar (millibars) of oxygen in the Martian atmosphere. Once this occurs, humans and other animals will be able to live on Mars in the open, and the world will become fully alive.

tl:dr. using current technology it would take around 1,150 years to make Mars habitable

I'll start loading the space ark.

A century is 100 years bro

ye, but shouldnt that mean this would take 200 years?

Mfw We were born too early

made my day

And then you have to consider the progress of technology. It is estimated that our technology doubles every 18 months. If scientists had such a ultimatum as making Mars habitable they could probably even do it even quicker.

Another problem: the low gravity on Mars is not able to hold an atmosphere. Most (all?) gasses on Mars will just float into space.

Not all of it though. The gasses would slowly escape its atmosphere, but it is possible! We would have to bring new water and greenhouse gasses to Mars from elsewhere though, which kinda sucks because Mars won't be able to sustain life entirely by its own resources

That's 1146 years too long for politicians.

It doesn't have to be done through politics.

why isnt this top comment

I'm sorry, but I have to ask if that theory factors in the solar wind at all.
Mars no longer produces a magnetic field strong enough to prtect it from solar wind that would irradiate the planet as well as (gradually) sweap away its atmosphere.
To properly terraform Mars we need a massive shield to protect it from solar winds, the most simple way the comes to mind is giveing Mars a massive molten Iron/nickel core (and that's very unlikely).
When they solve the solar wind problem terraforming will be completely possible, until then I'll settle for just having some small colonies.

best answer I (google) can come up with. make an artifical moon in orbit around mars to "tug" on the planets core to get it moving again. I guess we could always try to move one of the larger asteroids from the belt and put it in orbit but i think that will have to wait for our technology to advance a little!