For those who are not watching ahead here is another warning, THERE ARE SPOILERS AHEAD. The first time we meet The Face of Boe (and presumably the Doctor’s first encounter) is on platform Platform One in the episode The End of the World. In this episode The Face of Boe doesn’t have a single line but it is said that he sponsored the event. The next time The Face of Boe appears is in the hospital during the episode New Earth. The reason the Doctor and the Rose visit the planet in the first place is because the Doctor receives a message on his psychic paper reading “Ward 26, Please Come”. It is explained that The Face of Boe is dying and there is nothing the doctors can do for him. Throughout the episode the face does nothing, however at the end of the episode he is miraculously better and tells the Doctor that there are better things to do and then vanishes. In Gridlock we see The Face of Boe die after using his life to sustain the undercity.
We then get to the episode The Last of the Time Lords at the end of which, Jack Harkness says to the Doctor and Martha that since he was the first from his area (the Boeshane Peninsula) to become a Time Agent. Because of this he became a poster boy and known as The Face of Boe. This means a lot of things that are somewhat confusing and there is limited concrete information on the link between Jack and The Face of Boe. For one Jack is classified as human while The Face of Boe is classified as “Boekind”. If Jack is The Face of Boe then that means for whatever reason the power that Rose gave Jack to restore him in the episode Doomsday either ran out or just stopped. In addition to the because Jack gets teleported back Earth 1869 after the events during Doomsday. It is after this that it is assumed Jack finds out he cannot die and does not age normally. Because of this theoretically The Face of Boe could be Jack Harkness because if he eventually does travel back in time to a point shortly after the beginning of the universe he could age and eventually evolve into a different “species” because evolution is just change over time and Jack would have the time and is slowly changing.
Is Jack Harkness really The Face of Boe or is this merely a large coincidence that the writers decided to throw in just to create a large fan conspiracy theory? We will likely never know but it is definitely something that will keep fans guessing and arguing for seasons to come.