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We address the nature and origin of a spiral disk at the center of NGC 1275, the giant elliptical galaxy at the center of the Perseus cluster, that spans a radius of $\sim$$5\,\rm kpc$. By comparing stellar absorption lines measured in long-slit optical spectra with synthetic spectra for single stellar populations, we find that fitting of these lines requires two stellar populations: (i) a very young population that peaks in radial velocity at $\pm 250 {\rm \, km \, s^{-1}}$ of the systemic velocity within a radius of $\sim$$720\,\rm pc$ of the nucleus, a $1\,σ$ velocity dispersion significantly lower than $140 {\rm \, km \, s^{-1}}$, and an age of $0.15 \pm 0.05 \rm\,Gyr$; and (ii) a very old population having a constant radial velocity with a radius corresponding to the systemic velocity, a much broader velocity dispersion of $\sim$$250 {\rm \, km \, s^{-1}}$, and an age of around $10\,\rm Gyr$. We attribute the former to a post-starburst population associated with the spiral disk, and the latter to the main stellar body of NGC 1275 along the same sight line. If the spiral disk is the remnant of a cannibalized galaxy, then its progenitor would have had to retain an enormous amount of gas in the face of intensive ram-pressure stripping so as to form a total initial mass in stars of $\sim 3 \times 10^9 \,M_\odot$. More likely, the central spiral originally comprised a gaseous body accreted over the distant past from a residual cooling flow, before experiencing a starburst $\sim$$0.15\,\rm Gyr$ ago to form its stellar body.