How could the same person be existing and then dying on different planets in apparently different time zones? He named her the 'impossible girl' and resolved to find her, eventually tracking down the 'real' Clara to modern day England where she worked as a nanny for the Matelands.
Although there were parallels between Oswin and Clara Oswin, it was their similar deaths that sparked the Eleventh Doctor to begin his investigation into her identities - coining the "Impossible Girl" term after realizing that it shouldn't have been possible for him to run into the same woman when she had died twice.
Clara is the future child of the Doctor and River who's had her memory erased. The two Time Lords must be up to something on their nights away from River's prison cell.
The Doctor initially wanted to wipe Clara's memory because the Time Lords could track her through them. Since Gallifrey probably wouldn't want an undead Clara rampaging through the universe with Ashildr, it can perhaps be assumed that wiping The Doctor's memories of Clara has the same effect.
She died in the process but on Clara's urging, the Twelfth Doctor used a Mire repair kit to bring her back to life. The side effect was that she effectively became immortal.
Clara Oswald is the Impossible Girl | The Name of the Doctor | Doctor Who
Why does Clara keep dying?
Clara Oswald is one of the Doctor's most extraordinary companions. In order to help the Doctor she allowed the time winds to tear her into countless different iterations of herself, or as River phrased it, 'A million versions of you, living and dying all over time and space, like echoes.
Both of them had ties to each other since their childhoods — thanks to time travel — and their relationship blossomed as she was the companion of his eleventh and twelfth incarnations. Soon enough, it became clear that Clara and the Doctor were most definitely in love with each other, despite not becoming lovers.
In Victorian London, there's “sweet little Clara” from the Rose & Crown, who's also an upright children's governess. In the far-flung future, Oswin Oswald, the shipwrecked Junior Entertainments Manager from Starship Alaska, in reality a human-Dalek conversion refusing to accept her fate.
Clara would have wanted nothing more than for the Doctor to be the Doctor again. Her final message to him even is "Run you clever boy, and be a Doctor".
Asked in the new issue of DWM about the reason behind the TARDIS's treatment of Clara, Doctor Who showrunner Steven Moffat responded: “The TARDIS, being aware of all time simultaneously, was also aware that Clara was the precise motivator that would drive the Doctor to an extreme that was dangerous for all time and ...
River, who is a professor of archaeology and carries a TARDIS-colour/pattern diary of her adventures, is able to convince the Doctor of his future trust in her by whispering his real name into his ear, which he explains he would only divulge under rare circumstances.
The Doctor loved River Song enough that he suppressed the urge to roam for over two decades. This is something he was never able to do before River, and has never done again since. This proves, definitively, that River Song was not, and never will be, just another companion.
Companions like Katarina, Adric, and Kamelion have sacrificed themselves for the Doctor, and their deaths have had a lasting impact on him. Clara, Bill, Astrid, Adelaide, and River have all faced tragic ends but have returned or found ways to continue their adventures in different forms.
Oswin is revealed to have been captured by Daleks after the Alaska crashed on the Asylum and, to preserve her genius-level intellect for Dalek use, was turned into a Dalek. Unable to cope with her conversion, her mind retreated into a fantasy of survival as a human.
Behind the scenes. Clara's headstone in 1892 states that she was born on 23 November 1866 and died 24 December 1892, meaning she not only shared the same birth date as Doctor Who itself but that she was also 26 years old when she died.
The Eleventh Doctor has exceptional luck when it comes to meeting women who kiss him out of nowhere. It happened to him with Clara, with River... and also with his mother-in-law, Amy. At least it was before she actually became his mother-in-law.
The Doctor eventually reveals that the patch did not work on him; instead, he had used it on Clara to learn why she was upset and to see how far she was willing to go. He offers—as a friend, despite her betrayal of him—to see if they can locate Danny in the afterlife.
Danny Pink worked as a Maths teacher at Coal Hill School where he met Clara Oswald and the pair became romantically involved. Previously, he had been a Sergeant in the army, serving both in the UK and Afghanistan, until he accidentally shot and killed a young boy while on a mission.
After being shot through the stomach on a Mondasian colony ship, Bill was taken to meet the mischievous Razor, a man who turned out to be an earlier incarnation of The Master. Sadly, Bill was subjected to Cyber-conversion and in her final moments carried the dying Twelfth Doctor to the TARDIS.
While they may not have been in love with each other, there's no denying that the Doctor and Amy shared a huge amount of affection for each other. The Doctor loved Rory too, but Amy was the first person who he travelled with for a while, and that meant something.
Spoliers for the episode Darkwater. So, in the episode Darkwater, Danny dies and Clara plans to take the doctor into a volcano and threatens him to save Danny and if not she will destroy all the TARDIS keys, but can't the Doctor just snap to open the TARDIS doors.
Eleven of course fell in love with Clara Oswin Oswald in “The Snowmen” (and was strangely drawn to unlucky Oswin Oswald before that) and luckily for him the original Clara - though perhaps a bit more world-weary than her counterparts - turned out to be just as amazing.
