If $n$ is a nonnegative integer, a partition of $n$ is a sequence of weakly decreasing positive integers which sum to $n$. Partitions arise in the study of the symmetric group of permutations of the set $\{1, 2, \ldots, n\}$, the geometry of the Grassmannian of $k$-dimensional subspaces of an $n$-dimensional vector space, and in numerous combinatorial areas such as finite field theory. I will show how a visualization of partitions obtained by shoving boxes into a corner can be used to define a polynomial refinement of the binomial coefficients called the Gaussian polynomials and will discuss various properties of this polynomial refinement (and present at least one open problem).