# The importance of commuting differential operators

Consider the $\mathbb{C}$-algebra $A$ consisting of ordinary differential operators $$\displaystyle\sum_{i \geq 0} p_i(x) \frac{d^i}{dx^i}, \ \ p_i(x) \in \mathbb{C}[x].$$

It's been known for a long time that the subalgebra of all elements of $A$ which commute with a non-constant element of $A$ is a commutative algebra.
What is the importance of this fact in the theory of differential equations?

Thank you

-