Well done, you've said "compiler research". You've just spent 10 seconds explaining 'what is mathematics' instead of what project he's actually working on. Plus your explanation would leave someone with very little idea about computers even more confused: is he going through some novel and translating it into another language like french? You made him sound like a translator.

The CEO you've now explained what he does now has a good idea - translating between human languages usually loses some of the intricacies of the statement and makes it seem unnatural. It's better to just get someone to write directly in french rather than translating it from english, right? So the CEO will fire the compiler researcher and hire someone to code in ASM. Good job.

I'm being silly here, but the point still stands: explaining something complex is fraught with dangers when there is no mutual understanding of the subject matter. You might think you've explained something, and the listener might thing he has understood, but in reality you have now simply created completely invalid assumptions in a person's mind. The greatest example of this I've seen is regarding quantum mechanics and observation collapsing the wave. There is a whole quasi-spiritual movement that now believes that the world is shaped by conscious observation - talk about missing the point!

Well, there's a minimal set of things you must mention to fully explain something. The only way to explain his PhD fully would be to read his PhD dissertation, as that's what the definition of a dissertation is.

Summarizing is about maximizing the amount of information conveyed per word. Saying "you have failed to explain what he does in two sentences" is a bit silly, since, if one could fully explain his PhD in two sentences, it wouldn't be a PhD.

That applies to any contribution to compiler research, and is hardly a good answer to "what is your PhD about?", namely if asked in an academic setting.

What I meant was that explaining my work to a layman would necessarily start with "I work on compilers", and then I'd have to explain what a compiler is before going into the specifics of my own contributions.