Associate
Th Numbers = The valenzetti equation, a group of numbers which predict the end of the world (like the real life doomsday formula)
Dharma = A company looking for ways to change these numbers, thus changing the date of the end of the world. They were brought to the island by Jacob, but they came to experiment with the island unusual magnetic properties and exotic matter
Polar Bears = Part of the Dharma Experiments. Also used to move the island through time and space once trained (hence finding skeletons in the Tunisian desert)
Michael = Died on the freighter, but stuck on the island as he is a sinner and needs to repent before moving on.
It really does make me wonder why some people can't understand why the polar bears were on the island. People don't ask about the Dharma branded sharks though, it's the same deal, Dharma brought them there for experiments. I pretty much figured this out as soon as we found out about Dharma, and when I saw the bear cages I knew for certain.