Madison Li was born in 2229. She was a young, idealistic scientist when she met James and fully bought into the notion of Project Purity. Madison hid her growing romantic feelings for James while respecting his marriage to Catherine. The project was going smoothly, and even had the support and help of the Brotherhood of Steel, but soon it all went downhill. Super mutant attacks were more frequent and purifying water on a large scale was much harder than first thought. After James and Catherine had a child, things couldn't get any worse for Project Purity when Catherine died and James decided to abandon the project to keep his child safe. The Brotherhood and the other scientists also left, and Project Purity was put on hold.
Dr. Li is the first distinct face that the player sees, during the birthing scene, as she carries the newborn Lone Wanderer away while Catherine is going into cardiac arrest.
Although Madison Li was filled with remorse upon Catherine's death, her sadness was replaced with a powerful sense of betrayal after James abandoned Project Purity. She headed to Rivet City, hearing about its thriving scientific community set up by Horace Pinkerton. Soon after she arrived, she began to argue with Pinkerton, as they often had different views on the matters at hand. One day, having enough of it all, Pinkerton left Rivet City and began to live in the bow of the ship. Doctor Li soon became head scientist of the group and began to grow healthy, radiation-free produce like fresh apples and fresh pears.
Nineteen years after abandoning Project Purity, she is older, wiser, and much more cynical. Her life was going smoothly, but things drastically changed when she got an unexpected visit from James, who had escaped from Vault 101 and returned to Rivet City. He tried to recruit Dr. Li in his efforts to revive Project Purity, but she refused, thinking too much time had passed. Soon after her talk with James, she meets the now-adult Lone Wanderer. With Dr. Li's directions, the Lone Wanderer locates James, who returns to Rivet City and is finally able to recruit Madison to help him. Along with several other scientists, they head for the Jefferson Memorial, the location of Project Purity.
Once there, the scientists begin repairs to make things operational again. All is going smoothly, but suddenly the Enclave arrives and quickly overruns Project Purity. A squad of troopers led by Augustus Autumn occupies the project control room, demanding that the project be handed over to them at once. James, not trusting the Enclave, refuses to hand over the project. When Autumn, losing his patience, kills Janice Kaplinski, a fellow scientist working on the project, James sabotages the project, resulting in his death. Madison hesitates for a moment, in shock over the death of James and Janice, but then tells the Lone Wanderer that they can escape through the Taft Tunnel. Madison, the Lone Wanderer, and possibly some other scientists, escape and eventually make it to the Citadel. She speaks to Elder Lyons personally and demands that the Brotherhood of Steel take back the purifier.
After the Brotherhood defeats the Enclave at Project Purity, she tells the Lone Wanderer and Sarah Lyons that the equipment has been damaged, whether unintentionally or by sabotage. She further tells the two that the project control room is lethally irradiated, but it still needs to be activated quickly or the facility would explode.
After the purifier was activated, Madison left the Capital Wasteland and traveled to the Commonwealth to pursue other scientific endeavors, after the events of Fallout 3. The Brotherhood stayed in the Capital Wasteland with a large military presence, Dr. Li disagreed with the Brotherhood, believing now that with Project Purity running and the Enclave destroyed, the Brotherhood no longer need to stay. 
By 2287, Madison Li joined the Institute and became director of its advanced systems division. However, unlike everyone else in the Institute, Li wants to help the people of the Commonwealth, and she thinks that the Institute could greatly improve the Wasteland.
During the quest From Within, she can be convinced by the Sole Survivor to rejoin the Brotherhood of Steel by either persuading her via speech checks or collecting evidence of Doctor Brian Virgil's fate. Afterwards, she leaves the Institute for the Brotherhood, where she contributes to rebuilding Liberty Prime. Initially, she refuses to help the Brotherhood rebuild Liberty Prime both because it was a weapon of war, and because the Brotherhood previously wanted to control Project Purity, deciding who would and would not be allowed to benefit from it. She says this in response to selecting the dialogue option "Reluctance to help" while discussing the possibility of her joining the Brotherhood. After Prime is rebuilt and the Brotherhood wins the war against the Institute, she will express anger at the Sole Survivor for misleading her; believing that the Brotherhood would only use Prime as a show of force, and not to destroy the Institute. No matter what you say, Dr Li will be furious and will mockingly say, ""Ad Victoriam", Sentinel" and refuse to talk to the Survivor ever again.
Doctor Li has a unique hairstyle that is unused by any other NPC, as does Cherry.
Unlike Cherry, however, her hairstyle, "The Sophisticate," can be selected for the player character if they are female.
After the escape from Project Purity, Doctor Li no longer has any dialogue available with the Lone Wanderer; she just wants the player to leave her alone.
The door to her quarters is always locked and must be picked to gain entry.
Unlike most beds in the personal quarters of Rivet City residents, Dr. Li's bed is classified as unowned. This sometimes results in NPCs appearing at her door fruitlessly attempting to gain access to the open bed, or spawning in her room during their assigned sleeping hours (trapping them inside).
It is possible to kill Li in Fallout 4. But killing her will turn Brotherhood hostile towards the player even if they sided with the Brotherhood at the end.
"You know, I never understood why the Institute was so damn selfish. All those innocent people up there...dying. And here I am surrounded by technology that could make their lives better. Yet we hide down here and insulate ourselves from everything and everyone. It's not right."
"I knew it was just a matter of time before your people would track me down. I've been looking over my shoulder for almost a decade, waiting for them to send someone like you to kill me."
"You'd think being surrounded by cutting edge laboratory equipment and some of the greatest minds the world's ever known would be enough. Only problem is the transparency. I don't think we get the full story on everything that occurs down here."
If the player chooses to have Doctor Li join the Brotherhood of Steel in Fallout 4, but then has the Prydwen and airport destroyed, Doctor Li will survive, but will remain in a section of the Boston Airport ruins that is only accessible via Console commands. She cannot be interacted with. [verification needed]
pc Similarly to above, if the player convinces Li to join the Brotherhood but then destroys both the Institute and the Brotherhood along with the Prydwen and the airport, Li can be found standing in the Prydwen's burnt-out carcass, wearing her BOS attire and acting like she never left the Institute and the Sole Survivor was made its director [verification needed]