The nucleus becomes visible during prophase, the first stage of mitosis.

Here's why:

* Before prophase: The nucleus is a diffuse structure with the genetic material (chromatin) dispersed throughout.

* During prophase: The chromatin condenses into visible chromosomes. The nuclear envelope breaks down, and the nucleolus disappears. This makes the nucleus, now containing the condensed chromosomes, distinct and visible.

So, while the nucleus itself doesn't *appear* during prophase, it becomes clearly visible due to the structural changes that occur.