Maybe we could colonize Mars with a relatively small community of pioneers. Not so another solar system. In that case, the mass would be critical. From Sarah Fecht at Popular Mechanics:

“Back in 2002, John Moore, an anthropologist at the University of Florida, calculated that a starship could leave Earth with 150 passengers on a 2000-year pilgrimage to another solar system, and upon arrival, the descendants of the original crew could colonize a new world there—as long as everyone was careful not to inbreed along the way.

It was a valiant attempt to solve a thorny question about the future of humans in space. The nearest star systems—such as our nearest neighbor, Proxima Centauri, which is 4.2 light-years from home—are so far that reaching them would require a generational starship. Entire generations of people would be born, live, and die before the ship reached its destination. This brings up the question of how many people you need to send on a hypothetical interstellar mission to sustain sufficient genetic diversity. And a new study sets the bar much higher than Moore’s 150 people.

According to Portland State University anthropologist Cameron Smith, any such starship would have to carry a minimum of 10,000 people to secure the success of the endeavor. And a starting population of 40,000 would be even better, in case a large percentage of the population died during during the journey.” (Thanks Browser.)