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We show that the mass-weighted age of a galaxy correlates strongly with stellar velocity dispersion (<jats:italic>\u03c3<\/jats:italic>\n                  <jats:sub>*<\/jats:sub>) and ongoing star formation (SF) activity, with the stellar content in higher-<jats:italic>\u03c3<\/jats:italic>\n                  <jats:sub>*<\/jats:sub> galaxies having formed earlier and faster. The SFHs of quiescent galaxies are generally consistent with passive evolution since their main SF epoch, but a minority show clear evidence of a rejuvenation event in their recent past. The mean age of stars in galaxies that are star-forming is generally significantly younger, with SF peaking after <jats:italic>z<\/jats:italic>\u00a0&lt;\u00a01.5 for almost all star-forming galaxies in the sample: many of these still have either constant or rising SFRs on timescales &gt;100 Myr. This indicates that <jats:italic>z<\/jats:italic>\u00a0&gt;\u00a02 progenitors of <jats:italic>z<\/jats:italic>\u00a0\u223c\u00a01 star-forming galaxies are generally far less massive. Finally, despite considerable variance in the individual SFHs, we show that the current SF activity of massive galaxies (&gt;<jats:italic>L<\/jats:italic>\n                  <jats:sub>*<\/jats:sub>) at <jats:italic>z<\/jats:italic>\u00a0\u223c\u00a01 correlates with SF levels at least 3 Gyr prior: SFHs retain \u201cmemory\u201d on a large fraction of the Hubble time. Our results illustrate a novel approach to resolve the formation phase of galaxies, and, by identifying their individual evolutionary paths, one can connect progenitors and descendants across cosmic time. 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