  This paper studies how spatial thinking interacts with simplicity in
[informal] proof, by analysing a set of example proofs mainly concerned with
Ferrers diagrams (visual representations of partitions of integers, and
comparing them to proofs that do not use spatial thinking. The analysis shows
that using diagrams and spatial thinking can contribute to simplicity by (for
example) avoiding technical calculations, division into cases, and induction,
and creating a more surveyable and explanatory proof (both of which are
connected to simplicity). In response to one part of Hilbert's 24th Problem,
the area between two proofs is explored in one example, showing that between a
proof that uses spatial reasoning and one that does not, there is a proof that
is less simple than either.
