4 ideas
Ryland Grace, a science teacher and former biologist, wakes with amnesia aboard the Hail Mary at Tau Ceti. As his memory returns, he learns he refused the suicide mission out of fear and was forcibly sent by project head Eva Stratt, a fact he had forgotten.
Stripped of memory, Grace re-derives what he needs from cheap experiments instead of trusting recollection. He times falling objects to measure the ship's gravity, deduces his location from observation, and tests Astrophage's properties empirically. The method is to form a hypothesis, design the smallest test that could falsify it, and build each conclusion only on what has actually been measured.
Rocky's species are superb engineers who build xenonite and fix machines by touch. But they have no concept of radiation or relativity, and that ignorance killed the rest of his crew. Grace brings theoretical science but little building skill. The partnership works because each supplies exactly the knowledge the other's culture never developed, so a mixed team can see failure modes that neither member could see alone.
The same selection process also produces strains that can pass through xenonite, the material holding them in. Applying selection pressure to solve one problem does not produce a narrowly targeted change. It produces an organism that adapts in ways nobody designed for, including ways that defeat its containment.