  In this paper we define a new object, the momentum amplituhedron, which is
the long sought-after positive geometry for tree-level scattering amplitudes in
$\mathcal{N}=4$ super Yang-Mills theory in spinor helicity space. Inspired by
the construction of the ordinary amplituhedron, we introduce bosonized spinor
helicity variables to represent our external kinematical data, and restrict
them to a particular positive region. The momentum amplituhedron
$\mathcal{M}_{n,k}$ is then the image of the positive Grassmannian via a map
determined by such kinematics. The scattering amplitudes are extracted from the
canonical form with logarithmic singularities on the boundaries of this
geometry.
