Is colonization of Mars in this century realistic?

Some individuals and organizations aim to establish human colonies on Mars, our nearest neighbor and the planet most similar to Earth in the Solar System. Is human colonization in the 21st century realistic or possible? In less ambiguous terms, is human settlement possible on Mars in the 21st century? The question is still a little ambiguous, and a more narrow question, one not asked here, could be: will a human lay foot on Mars before 2100?

Other formulations: Feasibility of colonizing Mars, Feasibility of living on Mars, Practicability of colonizing Mars, Practicability of living on Mars, Will humans ever live on Mars.

A summary of key relevant facts from Wikipedia and other sources:
 * Mars has an unbreathable atmosphere: 95% carbon dioxide, 3% nitrogen, 1.6% argon, and less than 0.4% of other gases, including oxygen.
 * Mars atmospheric pressure is less than 1% that of the Earth.
 * Mars temperature on average fluctuates between −70 and 0 °C (−94 and 32 °F).
 * Mars landscape is exposed to intense ionizing radiation from solar particle events and cosmic rays, due to no magnetosphere.
 * Mars surface gravity is 38% that of the Earth, slightly above 1/3.
 * Mars has planet-wide dust storms.
 * Mars landscape is covered by fine dust.
 * Mars surface gets less than 1/2 of the sunlight received by the Earth surface.
 * Water on Mars is scarce, with rovers Spirit and Opportunity finding less than there is in Earth's driest desert.
 * Mars has in-situ resources, such as underground water, Martian soil, and ore, which could be leveraged by colonists.
 * Opportunities to generate electricity via wind, solar and nuclear power using resources on Mars are poor.
 * A trip to Mars will take about 7-9 months; it takes about 3 days to get to the Moon . During the trip, astronauts are exposed to high energy radiation unless shielding is provided.
 * A radio message from Mars to Earth travels for about 5 to 20 minutes, depending on planet positions.

Pro

 * It could be possible if water is found on Mars and robots can be used to process water and obtain hydrogen from it as fuel.
 * NASA and Elon Musk are making serious effort in that direction. With enough spirit and effort, it should be doable.
 * That is very inconclusive. Spirit and effort are far from sufficient to make something feasible.
 * If they did not believe it was feasible, they would not spend the effort.
 * They may spend the effort anyway: perhaps they think aiming at an extremely ambitious if unrealistic aim can bring about technology useful for other purposes. Indeed, previous space research contributed to useful technologies ; see also NASA spinoff technologies.
 * They may spend the effort anyway: perhaps they think the aspirational effort will attract people into STEM fields (science, technology, engineering, math).
 * Given they are not running a new analog of Biosphere 2, their effort seems to be not really serious. See also the arguments against.

Con

 * The low gravity and exposure to ionizing radiation are intractable problems, and whether a healthy human population can live with such problems is unknown. That is so even if some aspects of Martian human-habitation-hostility can be terraformed away with present day technology or plausible developments this century.
 * There is no economically viable reason justifying an effort to colonize Mars, and without one, any colonization effort will run on a finite supply of political will and will fail once that is exhausted.
 * A fifth of the 21st Century has already passed and humanity hasn't gone 1000 km from Earth since the 1970s. There are no rotating wheel space stations with artificial gravity. After 60 years of space travel, you still can't have a decent shower in space. There are no permanent Lunar bases. There are no spacecraft that landed on Venus with instruments that lasted an Earth-day. Humanity has yet to go 0.1% the speed of light (over 299 km/s or 1.08 million kph).
 * Most of that does not appear directly relevant to colonization of Mars; it merely bemoans general lack of progress.
 * Martian terraforming is unrealistic in this time frame.
 * Closing the biological material loop is hard. The feasibility should be demonstrable on the Earth. It was tried as part of Biosphere 2 project, where a biologically closed system was set up for a crew to live in. The first Biosphere 2 experiment lasted 2 years, and required injections of oxygen. The second Biosphere 2 experiment was ended prematurely. (Biosphere 2 hosted about 3,000 species of plants and animals, and it is unclear how to get those to Mars either.) If a perfectly closed mini-biosphere with a crew lasting, say, 5 years cannot be demonstrated on the Earth with its sunlight, gravity, lack of radiation, and no dust storms, one should hardly believe it is feasible to do on Mars.
 * Biosphere 2 aimed at oxygen closure. By contrast, oxygen on Mars could be produced from CO2 by the likes of Mars Oxygen ISRU Experiment
 * People genuinely serious about colonizing Mars could set up a semi-closed experiment to show closure for water, food, urine and feces but not oxygen; it would be much easier and cheaper to do on Earth than on Mars.
 * We are investigating feasibility, not whether someone is actually putting resources in a particular direction.
 * By putting resources in the direction of Biosphere 2 on Earth where it does not require transport of material from the Earth to Mars, perhaps not requiring oxygen closure, one would demonstrate part of feasibility and gain task-specific knowledge very useful for an actual Mars colonization. No one's putting resources there suggests no one is genuinely serious about colonizing Mars. (If you do not prepare for X where meaningful and relatively cheap, you do not really aim at X. And if no one is really serious about colonizing Mars, it is very likely to be impossible to do so.)