  Stars move away from their birthplaces over time via a process known as
radial migration, which blurs chemo-kinematic relations used for reconstructing
the Milky Way (MW) formation history. To understand the true time evolution of
the MW, one needs to take into account the effects of this process. We show
that stellar birth radii can be derived directly from the data with minimum
prior assumptions on the Galactic enrichment history. This is done by first
recovering the time evolution of the stellar birth metallicity gradient,
$d\mathrm{[Fe/H]}(R, \tau)/dR$, through its inverse relation to the metallicity
range as a function of age today, allowing us to place any star with age and
metallicity measurements back to its birthplace, $R_b$. Applying our method to
a large, high-precision data set of MW disk subgiant stars, we find a
steepening of the birth metallicity gradient from 11 to 8 Gyr ago, which
coincides with the time of the last massive merger, Gaia-Sausage-Enceladus
(GSE). This transition appears to play a major role in shaping both the
age-metallicity relation and the bimodality in the [$\alpha$/Fe]-[Fe/H] plane.
By dissecting the disk into mono-$R_b$ populations, clumps in the
low-[$\alpha$/Fe] sequence appear, which are not seen in the total sample and
coincide in time with known star-formation bursts, possibly associated with the
Sagittarius Dwarf Galaxy. We estimated that the Sun was born at $4.5\pm
0.4$~kpc from the Galactic center. Our $R_b$ estimates provide the missing
piece needed to recover the Milky Way formation history.
