Gauss's class-number conjecture for imaginary quadratic fields

For an imaginary quadratic field $K$, let $D_K$ and $h(K)$ denote its discriminant and class number, respectively. Gauss's class-number conjecture. Then

$$h(K)\rightarrow\infty \quad\text{when}\quad D_K\rightarrow\infty.$$

This conjecture asserts that the class numbers of imaginary quadratic fields are unbounded as the absolute value of the discriminant grows. It was proved by Hecke, Deuring, Mordell and Heilbronn.