Not ironic. Instructors allow cheat sheets for this reason as much as for actually looking stuff up.

Instructors were students too. We don't forget.

I got that very early on. The dedication to craft cheating devices (even in primary schools) and cram information as densely as possible meant you had to read it a lot, categorize, prune and simplify it to the point you basically knew it backwards.

It failed in high school when I got a graphing calc capable of storing "large" corpus of text. You didn't have to think a lot (mostly careful typing) and it grew too large to even remember everything you typed in.

Do PhD students have written exams? I thought they did research and wrote papers? How can you write an exam to test a PhD student when they are the ones coming up with the knowledge in the area?

PhD students take classes, and some of them do have written exam (in CS theory more than other parts of CS). In the US, where the PhD is 5 years, you spent a good portion of the first 2 years taking classes.

Before coming up with new knowledge you need to know what's already out there.