WARNING: This article contains spoilers from Stranger Things 2
With the arrival of Stranger Things 2, the Duffer Brothers have revealed more details about Eleven's origins. Season 1 seemed to hint that the young telepath could be either the daughter of Jim Hopper or Terry Ives, and the new season soon makes it clear that the latter is true.
Terry was a participant in one of the CIA's Project MKUltra experiments during college, which in the TV series were run by Dr. Brenner out of his lab in Hawkins. Terry didn't know she was pregnant when they made her take psychedelic drugs and kept her in sensory-deprived confinement, and when she gave birth, Brenner was there to snatch the baby away and implement a cover-up that declared the child dead in a third-trimester miscarriage.
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With no birth certificate or evidence, Terry faced a tough struggle to get people to believe the child, which she had named Jane, was snatched away and failed in her attempt to sue Brenner. In Season 1, we learn through Hopper's investigation that she had tried to sue and that she's now in a semi-comatose state due to the latent effects of the drugs she was administered during Project MKUltra. We now know that was not the case.
Eleven tracks down Terry after discovering files about her in the cabin Hopper is hiding her in. Frustrated that she's spent nearly a year in confinement, El heads off to find Terry having connected with her using astral projection. She arrives at Terry's house and introduces herself to Becky as Jane before once again using her powers to communicate with her "Mama".
The Truth About Terry Ives and Her Daughter
It's at this point we learn the truth about Terry's catatonic state and why she repeats the same phrases over and over again. Projecting memories into Eleven's mind, Terry reveals that after several years of trying to get back her daughter, she eventually broke into the Hawkins Laboratory with a gun. After shooting a guard, Terry raced around the facility before finding a room with a rainbow picture on the outside. Inside, she finds her daughter as well as another older child playing together but is captured by guards before she is able to escape with Jane. Brenner and his team then perform a lobotomy on Terry - the real cause for her catatonic state.
The confirmation of Terry as Eleven's mother isn't the only thing we discover from this interaction as we also see her "sister". The young Indian girl Jane is playing with in Terry's memory was introduced grown up in the cold open of Season 2. The eighth child to be involved in Brenner's experiments, Kali is a few years older than Eleven and has slightly different telepathic abilities; she's able to make people see or not see whatever she wants.
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El believes that Terry wants her to find Kali and she does so in Chapter 7: The Lost Sister. Their reunion is shortlived, although the introduction of another telepath and child of Brenner's experiments could lead to more of them appearing in future series; if El is 011 and Kali 008, that means there are potentially nine other children of varying ages with powers at large. Of course, just because Eleven and Kali escaped it doesn't mean that the children were quite so fortunate. Brenner may have already successfully trained up his other "children" and have them on missions for the CIA. Whatever the case, numbers 1-7 and 9-10 would certainly be an obvious addition to future seasons.
What About Eleven's Father?
Sadly though, we are no closer to learning who Eleven's father is. Obviously Brenner manipulated her into seeing him as a father-figure - that's why she continues to call him "Papa" - but we're still clueless as to who her biological father really is. If Terry knew who he was she would surely have relayed that information to El; however, when she fell pregnant it was under mysterious circumstances and during her time being experimented on.
That leaves several possibilities as to who Eleven's father is. It could be Brenner - he certainly seems like the egotistical kind of a guy who would want to be the father to a superhuman race of telepaths and has already positioned himself as a father to his test subjects. However, he's clearly not the biological father of Kali so that complicates things. Given the other experiments, it's possible that Terry was impregnated via artificial insemination but was too hopped up on psychedelics to realize; evidently, Brenner and his team had no ethical qualms about what they were doing to them or their offspring. We haven't heard much about men taking part in his experiments, but maybe they used one of their male test subjects to impregnate female captives in order to see what a child would turn out like with parents who were both tested on.
Interestingly, Kali was kidnapped in London, which could mean that her mother escaped the facility and left the country in order to hide her daughter away. That said, it's possible there was another facility out there, making things more complicated.
For now, thanks to a fake birth certificate made by Dr. Owens, Eleven's "real" father is Hopper. But the Duffer Brothers will surely be exploring her origins and family ties even further in future seasons of Stranger Things.