Mankind was born on Earth. It was never meant to die here.
Why it is hard sci-fi
Set during a slow-motion ecological collapse driven by crop blight. The film treats time as the rare resource. Time dilation on Millers planet is computed correctly. One hour at the surface is seven years for the orbiter. The Endurance assembles in a rotating ring for centripetal gravity. The wormhole and the black hole were rendered using a real general-relativity ray tracer built with Kip Thorne, and the visualisations were published as research papers.
Science inside it
General relativity in two regimes, gravitational time dilation, accretion-disc imaging, slingshot manoeuvres around a Kerr black hole, and a fictional but internally consistent five-dimensional bulk used to send information back through gravity. The blight backstory leans on real plant-pathology fears and the films early act treats farming as the binding constraint on a civilisation in retreat.
Spoiler alert
Cooper falls into Gargantua, is recovered into a constructed five-dimensional space inside the singularity, and uses gravitational coupling to send Murph the data she needs to crack the gravity equation that gets humanity off Earth. The closing of the loop is also the explanation for the ghost in his daughters bedroom in the first act, which was him.