I've decided to write a theory that's more of an outline of their lives and why they are so important to the show. This information is based on data we already know and also some possible conclusions I've come to.
1930s:
Eloise Hawking is born under unknown circumstances. I think she is Charles Widmore's sister, but with a different father therefore the different last name.
1930s-1950s:
Eloise is living on the island with Charles, Richard, and the Others, protecting the island from outside forces. They came into contact with the U.S. army during this time, who had planned on detonating a hydrogen bomb called "Jughead" until Richard and his people were forced to kill them all.
1954:
Eloise runs into Daniel, Miles, and Charlotte, and think they are part of the U.S. army so she takes them captive and brings them to Richard. Daniel tells Richard that he can help with the bomb situation, so Eloise takes Daniel out to see Jughead. Daniel feels that Eloise looks familiar to him. He tells her to bury it and says he's from the future. Sawyer and Juliet show up just before Eloise is about to kill Daniel and force her to drop her gun. Very soon afterwards, they disappear in front of her eyes.
1950-1970:
Eloise is still presumably living on the island and protecting it, eventually dealing with the DHARMA people and the truce.
1974-1977:
Eloise runs into the time-travelers again. This time when Daniel sees her, he immediately recognizes Eloise as his mother, but Eloise notices this as an opportunity to capture him and possibly kill him before he can disappear again. Daniel will probably spill his guts to Eloise about her being his mother, sounding like a complete schizophrenic. He tells her that she will eventually be off the island and meet an American man with the last name Faraday. Eloise either doesn't believe Daniel or is too scared to believe so she kills him during the interrogation. "The incident" happens during this time so Faraday's death might be somehow involved in that, but I have no theories at this time.
1977-1980:
Eloise leaves the island under unknown circumstances and goes back to England. She meets an American man with the last name Faraday and realizes that Daniel was telling the truth the entire time. She has a child with the man and names the baby Daniel. She raises him in England, knowing that he will eventually go back to the island to see her in the past.
1980-1990:
Daniel grows up a child genius and skips many grades because of his incredible mind. Eloise probably tells Daniel that he is a special person, and even gives him the notebook he had when he died, but this confuses him to no end. I believe his Mr. Faraday eventually divorces Eloise because of her strange attitude, and moves back to America with Daniel.
1990-1996:
Daniel moves back to England and graduates from Oxford many years before his classmates. He is given the opportunity to work at Oxford to focus more on his electromagnetism studies, but keeps some of his work a secret to avoid ridicule. Eloise soon runs into Desmond at the jewelry store and tells him his destiny is to be on the island and that he does not take the ring to marry Penny. Desmond doesn't believe her, but after a series of events he comes to believe that she was right.
1996:
Daniel is working at Oxford when time-traveling Desmond finds him and asks him to help figure out his problems. Daniel eventually believes him and shows his experiment with Eloise to Desmond, but Des is not convinced and thinks he's going to die. Faraday tells Desmond that he needs to have a constant. Desmond leaves in confusion.
1996-2000:
Daniel continues his work on time-travel, funded by his uncle Charles Widmore, and later tests his experiments on his willing wife Theresa. The experiments turn out to be a disaster which puts Theresa in a time-traveling coma. Daniel moves to the US to escape the pain he's caused.
2000-2004:
Daniel goes crazy and realizes that his destiny is indeed to be on the island just like his mother told him. Since the island gets found by Penny's crew in Antarctica, Daniel is contacted by one of Widmore's men, Abbadon, who gives him the opportunity to go back to the island with a small crew of pre-determined people. The small crew travel by freighter from Fiji to the island and then by helicopter. Faraday jumps from the helicopter and lands in the jungle right as Jack and Kate arrive. Faraday probably noticed Jack because as soon as he landed, his mind jumped into the future when he knew Jack.
2004:
All the on-island events in season 4 happen until Ben turns the wheel and sends island skipping through time.
2007-2008:
Off-island, Eloise Hawking meets with half of the Oceanic 6, Ben, and Desmond, and tells them how to get back to the island.
2008:
The island briefly skips to a time after flight 316 landed. They get attacked by unknown people on a boat and travel back in time again.
Unknown - Locke turns the wheel and the island stops one more time in the 1970s. Time loop starts over again. Daniel recognizes his young mother on the island, tries to convince her that he's her son, but she murders him just like she is supposed to.Theory by Xenization
1930s:
Eloise Hawking is born under unknown circumstances. I think she is Charles Widmore's sister, but with a different father therefore the different last name.
1930s-1950s:
Eloise is living on the island with Charles, Richard, and the Others, protecting the island from outside forces. They came into contact with the U.S. army during this time, who had planned on detonating a hydrogen bomb called "Jughead" until Richard and his people were forced to kill them all.
1954:
Eloise runs into Daniel, Miles, and Charlotte, and think they are part of the U.S. army so she takes them captive and brings them to Richard. Daniel tells Richard that he can help with the bomb situation, so Eloise takes Daniel out to see Jughead. Daniel feels that Eloise looks familiar to him. He tells her to bury it and says he's from the future. Sawyer and Juliet show up just before Eloise is about to kill Daniel and force her to drop her gun. Very soon afterwards, they disappear in front of her eyes.
1950-1970:
Eloise is still presumably living on the island and protecting it, eventually dealing with the DHARMA people and the truce.
1974-1977:
Eloise runs into the time-travelers again. This time when Daniel sees her, he immediately recognizes Eloise as his mother, but Eloise notices this as an opportunity to capture him and possibly kill him before he can disappear again. Daniel will probably spill his guts to Eloise about her being his mother, sounding like a complete schizophrenic. He tells her that she will eventually be off the island and meet an American man with the last name Faraday. Eloise either doesn't believe Daniel or is too scared to believe so she kills him during the interrogation. "The incident" happens during this time so Faraday's death might be somehow involved in that, but I have no theories at this time.
1977-1980:
Eloise leaves the island under unknown circumstances and goes back to England. She meets an American man with the last name Faraday and realizes that Daniel was telling the truth the entire time. She has a child with the man and names the baby Daniel. She raises him in England, knowing that he will eventually go back to the island to see her in the past.
1980-1990:
Daniel grows up a child genius and skips many grades because of his incredible mind. Eloise probably tells Daniel that he is a special person, and even gives him the notebook he had when he died, but this confuses him to no end. I believe his Mr. Faraday eventually divorces Eloise because of her strange attitude, and moves back to America with Daniel.
1990-1996:
Daniel moves back to England and graduates from Oxford many years before his classmates. He is given the opportunity to work at Oxford to focus more on his electromagnetism studies, but keeps some of his work a secret to avoid ridicule. Eloise soon runs into Desmond at the jewelry store and tells him his destiny is to be on the island and that he does not take the ring to marry Penny. Desmond doesn't believe her, but after a series of events he comes to believe that she was right.
1996:
Daniel is working at Oxford when time-traveling Desmond finds him and asks him to help figure out his problems. Daniel eventually believes him and shows his experiment with Eloise to Desmond, but Des is not convinced and thinks he's going to die. Faraday tells Desmond that he needs to have a constant. Desmond leaves in confusion.
1996-2000:
Daniel continues his work on time-travel, funded by his uncle Charles Widmore, and later tests his experiments on his willing wife Theresa. The experiments turn out to be a disaster which puts Theresa in a time-traveling coma. Daniel moves to the US to escape the pain he's caused.
2000-2004:
Daniel goes crazy and realizes that his destiny is indeed to be on the island just like his mother told him. Since the island gets found by Penny's crew in Antarctica, Daniel is contacted by one of Widmore's men, Abbadon, who gives him the opportunity to go back to the island with a small crew of pre-determined people. The small crew travel by freighter from Fiji to the island and then by helicopter. Faraday jumps from the helicopter and lands in the jungle right as Jack and Kate arrive. Faraday probably noticed Jack because as soon as he landed, his mind jumped into the future when he knew Jack.
2004:
All the on-island events in season 4 happen until Ben turns the wheel and sends island skipping through time.
2007-2008:
Off-island, Eloise Hawking meets with half of the Oceanic 6, Ben, and Desmond, and tells them how to get back to the island.
2008:
The island briefly skips to a time after flight 316 landed. They get attacked by unknown people on a boat and travel back in time again.
Unknown - Locke turns the wheel and the island stops one more time in the 1970s. Time loop starts over again. Daniel recognizes his young mother on the island, tries to convince her that he's her son, but she murders him just like she is supposed to.Theory by Xenization
