  The running of the top quark mass ($m_\mathrm{t}$) is probed at the
next-to-next-to-leading order (NNLO) in quantum chromodynamics (QCD) for the
first time. The result is obtained by comparing calculations in the modified
minimal subtraction ($\mathrm{\bar{MS}}$) renormalisation scheme to a
differential measurement of the top quark-antiquark ($\mathrm{t\bar{t}}$)
production cross section at $\sqrt{s} = 13~\mathrm{TeV}$. The scale dependence
of $m_\mathrm{t}$ is extracted as a function of the invariant mass of the
$\mathrm{t\bar{t}}$ system, up to an energy scale of about $0.5~\mathrm{TeV}$.
The observed running is found to be in good agreement with the three-loop
solution of the QCD renormalisation group equations.
