/ɛpɪˈmiːθiəs/; Greek: Ἐπιμηθεύς, meaning “hindsight” or “afterthought” was the brother of Prometheus, he is depicted as foolish compared to his brother who is characterized as ingenious and clever.
The myth of Prometheus and Epimetheus tells the story of the creation of mankind, the twin Titans were tasked with the distribution of traits amongst the creatures dwelling the Earth. Epimetheus gave positive traits to every animal, but by the time they reached mankind, he had nothing left to give them.
Prometheus feeling sorry for them, took it upon himself to give them the gift of fire and with that the tools in which to create using it. Unfortunately, the Gods Athena and Hephaestus didn’t take this act of kindness too well and punished him.
Epimetheus, the being in whom thought follows production, represents nature in the sense of materialism, according to which thought comes later than thoughtless bodies and their thoughtless motions.Plato
Epimetheus was the one who accepted the gift of Pandora from the gods, it was only inferred that they married. But in later myths, Pyrrha the daughter of Epimetheus and Pandora was married Deucalion, Prometheus’ descendant. They are the only two humans who survived the flood which wiped out the planet.
David, calling Walter “Brother” in the Engineer’s Cathedral, draws parallels to this myth. As well as Walter, in a deleted scene, as a metaphor to this myth, hands Daniels a lighter to create a fire with. David is like Epimetheus, in the sense he uses his time on Planet 4 to gift special traits to his Xenomorphic creations, using his knowledge of genetic manipulation paired with the ‘fire’ from the gods, the pathogen. Walter is also like Epimetheus, in the sense he doesn’t realise what a dangerous threat David is until it is too late.