The critical temperature of the Bose-Einstein condensate is

$$T=\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\frac{2\pi \hbar^2}{mk_B}$$

where $\zeta(s)$ is the Riemann zeta function.

Particularly after the work of Ketterle, this seems as "real" and non-speculative as it gets.