The paradox of youth concerns the presence of massive stars very close to the galactic black hole (approx 3 pc radius). These stars could not have formed there, because such stars form in a molecular cloud, and the cloud could not have withstood the tidal forces. Assuming a density of  n = 10^4 cm^{-3} and black hole mass of of  M_{\bullet} = 4 \cdot 10^6 M_{\odot}, a cloud can only survive at a radius greater than

 r > \left( \frac{M_{\bullet}}{m_p n} \right)^{1/3} \approx 25 pc

(the substitution can be found here). The other option is that they formed elsewhere, and migrated to their current location. The problem with this option is that massive stars are short lived, so they might not have had enough time to get there.