It is a feature of $\mathbb{A}^{1}$-homotopy theory that analogous results over the complex and real numbers may indicate the presence of a common generalization valid over a general field $k$. For example, there are $15\langle 1\rangle+12\langle-1\rangle$ lines on a cubic surface, and $\langle1\rangle+\langle-1\rangle$ lines through four lines in space. The counts now take values in the Grothendieck-Witt group of stable isomorphism classes of non-degenerate, symmetric bilinear forms. $\langle a\rangle$ represents the class of the bilinear form $k \times k \mapsto k$ mapping $(x,y)$ to $axy$. The above examples are from joint work with Jesse Kass and Padma Srinivasan. Results over $\mathbb{R}$ and $\mathbb{C}$ can be recovered by taking the rank and the signature. This talk will introduce $\mathbb{A}^{1}$-enumerative geometry and present a wall-crossing formula for $\mathbb{A}^{1}$ Gromov-Witten invariants joint with Erwan Brugallé.