The first European to find the source was the British Speke, in 1858. A monument was raised at the exact spot where Speke was standing when he discovered the source.
A statue of Gandhi also graces the place. It was sponsored by the huge Indian community living in Jinja. The reason of this statue is that the ashes of the "no violence" prophet were sprayed all over the Nile waters.
Once you reach the island, you'll find some fishermen eager to show you the "real source of the nile", meaning that the actual source of the Nile is not only the lake's waters but also coming from underground springs that keep on pouring a clean water into the river. This, they say, explain the difference between the Lake's and the River's waters.
Hoax or fact? This is part of Africa charms, we never really know on what ground to stand. But definitely, if you ever come to Uganda, you cannot afford to miss the Source of the Nile, it is just less than 2 hours from Kampala. Enjoy...