Gaal Dornick

On Synnax, Gaal grows up among priests who see math as heresy. She solves a problem no one had cracked and wins a place studying with Hari Seldon on Trantor. Soon after she reaches the capital, she's arrested with him: Hari's psychohistory predicts the end of the Empire, and Brother Day doesn't want to hear it. After the trial and the attack that brings down the Star Bridge, Hari and his followers are exiled to Terminus.

On the voyage, Gaal grows close to Raych, Hari's adopted son, and finds flaws in her mentor's math. Hari is murdered on board, and Gaal is ejected into space in a pod. She wakes on a ship and meets Hari again, now a digital consciousness, who explains his death was part of the plan. Gaal decides to head home in cryosleep. She reaches Synnax 138 years later and finds it in ruins. At the bottom of the sea, in a pod, is Salvor Hardin, who has learned she is Gaal and Raych's daughter.

Gaal, Salvor and Hari follow a signal to Ignis, home to a community of Mentalics led by Tellem Bond. Gaal discovers she has the gift of prescience: she can see possible futures. And she starts having visions of a future ruled by someone called the Mule. Tellem drives a wedge between Gaal and Hari and has dark plans for her. In the end, Salvor dies protecting her mother. The Mentalics now follow Gaal, who goes into cryosleep with Hari, set to wake when the Mule rises.

Gaal and Hari wake on Ignis 152 years later, with the Mule already on the move. She forms an alliance with Brother Dawn and meets him in person, but clashes with Demerzel. After the Mule destroys New Terminus, Gaal takes the fight to him. In the final battle she shields her mind and kills the man who seemed to be the Mule, but senses another mind still probing hers. Bayta and Pritcher arrive right after, but Gaal turns Magnifico's music to her advantage and escapes. The Vault's copy of Hari asks to come with her, and she says no.

In Isaac Asimov's books, Gaal Dornick is a young male mathematician who only appears in the first part of Foundation, as the newcomer's eyes on Trantor. The show turned Gaal into a woman and the lead.