This list is really shady. Irrationality of 2 is a candidate for No 1, but Green's theorem at 21? Doesn't belong on the list, considering that it's only the 2 dimensional version of Stokes's theorem, which is much more powerful. And why has the fundamental theorem of calculus fallen to 15? And Taylor's theorem at 35? I feel like the authors of this list don't really know that much about analysis, but like number theory and algebra a lot more.
In my opinion, number one theorem is Archimedes principle for ordered fields, otherwise stated as 'you can empty a large bathtub with a small spoon.'