here's something that i'm really surprised that i only just realized: it's slightly nontrivial that a ring spectrum whose underlying spectrum is discrete (i.e. in the heart) is equivalent data to an ordinary ring. given a discrete ring spectrum $R$, in its multiplication map $R \otimes R \to R$ the source need not be discrete. but due to the adjunction $\pi_0 : Sp^{\geq 0} \rightleftarrows Ab : H$, that map is equivalent data to a map $Tor_0(R,R) := \pi_0 (R \otimes R) \to R$.