The Vallenzetti Equation: It predicts the exact number of years and months until humanity extinguishes itself, and it is likely to have something to do with “the numbers”. Hanso explains this in the video and then in one of the subsequent fragments says that “it’s results are chilling” which I believe means that the equation predicts the human race will come to an end much sooner than anyone had expected.

The Dharma Initiative was formed expressly to find a way to save the human race by discovering a way to change one of the factors of the equation. The facilities on the island were built to research possible solutions to this problem and were built in secrecy so the research could go on with out scrutiny or question, or perhaps becasue the research required was inhumane or illegal.

We don’t know exactly what happened to the Dharma Initiative (we can make some assumptions having to do with “incidents” from the show), but we do find out in this video that, according to Mittelwerk, it failed. Currenly the Hanso Foundation is still working hard to find a way to change the equation and find a better outcome, but their methods are highly questionable. It has something to do with a virus that they have designed, a virus that is not yet perfected and is now being tested on unknowing people disguised as a vaccine.