  Vertically thickened bars, observed in the form of boxy/peanut (B/P) bulges,
are found in the majority of massive barred disc galaxies in the local
Universe, including our own. B/P bulges indicate that their host bars have
suffered violent bending instabilities driven by anisotropic velocity
distributions. We investigate for the first time how the frequency of B/P
bulges in barred galaxies evolves from $z = 1$ to $z\approx 0$, using a large
sample of non-edge-on galaxies with masses $M_{\star} > 10^{10}\:M_{\odot}$,
selected from the HST COSMOS survey. We find the observed fraction increases
from $0^{+3.6}_{-0.0}\%$ at $z = 1$ to $37.8^{+5.4}_{-5.1}\%$ at $z = 0.2$. We
account for problems identifying B/P bulges in galaxies with low inclinations
and unfavourable bar orientations, and due to redshift-dependent observational
biases with the help of a sample from the Sloan Digital Sky Survey, matched in
resolution, rest-frame band, signal-to-noise ratio and stellar mass and
analysed in the same fashion. From this, we estimate that the true fraction of
barred galaxies with B/P bulges increases from $\sim 10\%$ at $z \approx 1$ to
$\sim 70\%$ at $z = 0$. In agreement with previous results for nearby galaxies,
we find a strong dependence of the presence of a B/P bulge on galaxy stellar
mass. This trend is observed in both local and high-redshift galaxies,
indicating that it is an important indicator of vertical instabilities across a
large fraction of the age of the Universe. We propose that galaxy formation
processes regulate the thickness of galaxy discs, which in turn affect which
galaxies experience violent bending instabilities of the bar.
