Basic computer science problems creep up often enough (about once a month) at my mostly normal job. We had to implement a prefix trie (specifically a modified radix trie with extra caching) to solve an interesting problem.

If you don't know about these data structures or algorithms, you won't even know where to look.

When he works for the company that this whole conversation is stemming from.

Database indexes are very frequently btrees; understanding how a btree works can inform how you structure and query data, resulting in substantially better software. They're also a generalization of the binary search pattern, which every programmer should be able to describe and utilize.