  Inspired by the idea of viewing amplitudes in ${\cal N}=4$ SYM as
differential forms on momentum twistor space, we introduce differential forms
on the space of spinor variables, which combine helicity amplitudes in any
four-dimensional gauge theory as a single object. In this note we focus on such
differential forms in ${\cal N}=4$ SYM, which can also be thought of as
"bosonizing" superamplitudes in non-chiral superspace. Remarkably all
tree-level amplitudes in ${\cal N}=4$ SYM combine to a $d\log$ form in spinor
variables, which is given by pushforward of canonical forms of Grassmannian
cells, the tree forms can also be obtained using BCFW or inverse-soft
construction, and we present all-multiplicity expression for MHV and NMHV forms
to illustrate their simplicity. Similarly all-loop planar integrands can be
naturally written as $d\log$ forms in the Grassmannian/on-shell-diagram
picture, and we expect the same to hold beyond the planar limit. Just as the
form in momentum twistor space reveals underlying positive geometry of the
amplituhedron, the form in terms of spinor variables strongly suggests an
"amplituhedron in momentum space". We initiate the study of its geometry by
connecting it to the moduli space of Witten's twistor-string theory, which
provides a pushforward formula for tree forms in ${\cal N}=4$ SYM.
