  In Surveys in Differential Geometry, Volume 7, published in 2002 and
Philosophical Transactions of the Royal Society A, Volume 359, published in
2001, Sir Michael Atiyah introduced what is known as the Atiyah problem on
configurations of points, which can be briefly described as the conjecture that
the $n$ polynomials (each defined up to a phase factor) associated
geometrically to a configuration of $n$ distinct points in $\mathbb{R}^3$ are
always linearly independent. The first ``hard'' case is for $n = 4$ points, for
which the linear independence conjecture was proved by Eastwood and Norbury in
Geometry & Topology (2), in 2001.
  We present a new proof of Atiyah's linear independence conjecture on
configurations of four points, i.e. of Eastwood and Norbury's theorem. Our
proof consists in showing that the Gram matrix of the $4$ polynomials
associated to a configuration of $4$ points in Euclidean $3$-space is always
positive definite. It makes use of $2$-spinor calculus and the theory of
hermitian positive semidefinite matrices.
