Haha, indeed Göttingen has more bikes then inhabitants. At least thats what it seems like near the university.
Yes you´re right, the importance of an idea is sometimes very hard to evaluate, some may say that topological studies are far less important then
for example achievements in stochastics, but you may never now what kind of knowledge can be "useful" in the future.
And even beyon use, mathematics is like art, and art is always subjective.
I mostly agree with your choices, especially since Gauß is somewhat sacred to me and Hilbert just inspires me everyday when entering the math faculty
(theres a bust in the entrance hall, which is actually called "Hilbert-Raum/Hilbert-Room" among the mathematicians, I guess you get the joke).