The USGS computes the average interval between Yellowstone's eruptions — 725,000 years — calls it meaningless because it rests on two intervals, and notes that even if you trust it, there are about 100,000 years to go.
The rock is phonolite porphyry and the columns are cooling cracks — that much is agreed. How the magma got there is not. The NPS lists four origin hypotheses and says discrepancies remain for all of them.