We give very simple proofs of the classical results of Magnus and Hill on the spectral properties of the Hilbert matrix \(\displaystyle H = \left ( {1 \over i+j+ 1 } \right )_{i,j\geq 0} \) which defines a bounded linear operator on the sequence space \(\ell ^2\) . In particular, we use the Mehler-Fock transform to find the spectrum and the latent eigenfunctions of the Hilbert matrix, that is, we show that the spectrum of H is \([0,\pi ]\) with no eigenvalues (Magnus’ result) and describe all complex sequences x such that \(Hx=\mu x\) for some complex number \(\mu \) (Hill’s result).