Closed-form formulas exist for solutions of polynomials up to degree 4, but not more than that.
Only 4 colors are required to color a map of any size, with adjacent areas being distinct colors.
Division rings over the reals have a maximum of 4 dimensions, and cannot have more.
Having more than three regular convex polytypes is a property of dimensions only up to 4.
And more number-4 things by Saharon Shelah (presented in Twitter post by Artem Chernikov).