In a crackling sharp movie about brilliant people solving very tough problems, it is endearing that the first and most important involves one of the earliest skills developed by mankind. Indeed, it is the skill that made it both possible and necessary to develop the very first communities. It is the skill that turned nomads and hunters into complex societies: the cultivation of crops.

Mark Watney, played by Matt Damon as an endlessly resourceful Eagle Scout-type who would run over from next door to help carry your groceries, is part of a US astronaut team on a mission to Mars. When a storm comes up, they have to make an emergency evacuation weeks before the mission is completed. He is separated from the group and they believe he is dead. So, like ET, he is left behind on an alien planet. But no Reeses Pieces here, and no Elliot to befriend him. The first thing he has to do is figure out how to feed himself. “Fortunately,” he explains to us via his video log, “I am a botanist!” {Hmmm, just like ET, who came to earth to collect plant specimens.) That credential has never been announced with such deserved satisfaction. What if the one left behind was the expert in telemetry or navigation?

As he explains in an unnecessary coda, one of the tightly constructed film’s few excesses, he knew he was probably going to die. But his attitude was, “Not today.” He understands that any hope of rescue is 140 million miles away. Even if NASA could figure out that he was still alive and could figure out a way to rescue him, it would take years before they could reach him. He counts out the meals left behind by the crew to figure out how long he has before he has to have some sustainable source of nourishment. Of course there are no seeds. There is no water (Mark would be very happy with the latest reports that in fact there might be water on Mars, but for this movie, there is none.) The ground (I guess you can’t call it “earth”) does not have the necessary nutrients. But there’s a bag marked “Do not open before Thanksgiving,” and inside, there are potatoes. And Mark is a botanist. He rigs up a machine to create water and empties out the lav for fertilizer. He plants the potatoes and sure enough, little shoots appear.

Meanwhile, the crew is still on its way back to earth. On earth, there is a state funeral for Watney. And then an analyst looking at transmissions from Mars sees something that could be a person. NASA realizes that Watney is alive. Can they mount a rescue mission before it is too late? Given the risks to the crew, should they?

Director Ridley Scott and the nicely space-named screenwriter Drew Goddard (based on the book by first-time author Andy Weir) have created a completely believable and utterly immersive world, and Damon’s Watney is an idea hero for the story. He is smart, self-deprecating, optimistic, and inventive. “I’m going to science the s*** out of it!” he says, understanding that the odds are against him but also understanding that the only way to stay sane and focused is to work each problem, one at a time. He genuinely enjoys the challenge (well, most of the challenges) and that makes it fun to watch.

Watching the way he thinks through problems is endlessly enthralling. He even rigs together a version of ET’s Speak and Spell to phone home. On earth, we see characters debate the politics and practicality of a rescue operation, ranging from who should know what when to whether the US should work with the Chinese on a launch mission. Jeff Daniels as the head of NASA, Kristen Wiig as the media liaison, and the various people in charge of crew and equipment all have different perspectives and priorities. The political and personality puzzles are as tricky as the scientific ones.

Production designer Arthur Max and cinematographer Dariusz Wolski (who worked with Scott on “Prometheus”) provide striking images of stunning beauty that are both strange and familiar. At times, it almost looks like the red rocks of the American Southwest but we are also aware of the peril constantly surrounding Watney, where a crack in the helmet can mean death. The scenes on the spacecraft, with the captain (Jessica Chastain) and crew matter-of-factly floating through corridors, are brilliantly realized.

This is an exciting, absorbing story, an adventure with a genuine hero whose courage, fortitude, and intelligence will spark the hero inside anyone who see it.

Parents should know that this film includes intense and prolonged peril with injuries, some disturbing images, brief nudity, some strong language

Family discussion: What was Mark’s most difficult challenge? What were the differing priorities of the people at NASA and when there are conflicts, who should decide?

If you like this, try: “Gravity” and “Apollo 13” and the miniseries “From the Earth to the Moon” — and the book by Andy Weir