John Carmack discusses BSP trees, or binary space partitioning trees, in several segments of the conversation:

- At 02:43:26, Carmack talks about starting to use BSP trees when he was working on a project with limited processing power. He mentions that although it was ugly visually, it was fast enough to play and still fun, marking his initial use of BSP trees.

- At 02:43:30-02:43:56, he elaborates on how BSP trees were a stepping stone that was easy to understand in the grid world of Wolfenstein, with all its 90-degree angles, and how this experience was a big success that he later brought into his work on Doom, despite the challenges with arbitrary angles.

- At 02:47:30-02:47:58, Carmack reflects on his further exploration of BSP trees, how he learned about them, and how he used them in a two-dimensional fashion while working on Quake. He also mentions meeting Bruce Naylor, one of the original researchers on BSP trees.

- At 02:46:00-02:46:27, he discusses the technical challenges associated with BSP trees, such as dealing with floating-point issues and how BSP trees work by carving walls and providing a consistent ordering of all elements in the world from any point.

- Additionally, at 02:48:30-02:48:56, while BSP trees are mentioned, Carmack points out that after Doom, there were other technologies used by competitors like Ken Silverman's Build Engine for Duke Nukem 3D, which did not involve BSP trees, highlighting that there is not just one true way of doing things in game development.

These segments provide insights into how Carmack used and understood BSP trees in his programming work for various games.