"...to understand what he did / had done."

Question

The context is that a mathematician solves a great problem and publishes his proof.

He was known as a great mathematician and everyone wanted to understand what he had done.

Everything is clear here. He did something before people wanted to understand it. But can we make the sentence a bit simpler?

...and everyone wanted to understand what he did.

Does it mean the same thing, or it is ambiguous now? I see it ambiguous in the sense that suppose he published his proof, and nobody knew what he was doing after that. Maybe he worked as a teacher, maybe he did some other research. So everybody wanted to understand what he did (at the moment).

Answer 1

I don't think we can use past simple here. It's not (in my opinion) a question of ambiguity. The reason is this: we're referring to a very specific "had done", which is "what he had done to solve this great problem". Therefore, "understand what he had done" allows the reader to immediately understand we are talking about the solution he devised, rather than achievements over the course of his lifetime (which is what the use of past simple implies).

As a standalone segment, your supposition (in the last part of your question) regarding:

Everyone wanted to understand what he did.

Is correct. I take this to mean "what he did (for a living)", which is obviously not what we want to echo in this case.

As a general observation about past perfect; this is the "strictest/most self-explanatory" tense in the English language in my opinion. I say this because it almost always goes hand in hand with a past simple giving reference to the order the two events occurred (the two events being the past simple one and the past perfect one), without having to use other elements of speech to qualify the order (though allowing for qualifying words to be used).

Here's an example of what I mean:

I finally got to wear the t-shirt I had made (some days before/earlier/etc).

The use of past perfect explicitly references the prior action without requiring further explanation.

I really feel this is the case with your example and so I conclude that "making it simpler" is counter-intuitive. It is already the plainest it could possibly be.

Answer 2

Both forms are correct, the difference between "had done" and "did" is that the Past Perfect conveys the idea of an action which lasted for a period of time and was still existing at the time in the past we are referring to. While the Past Tense refers to an action in the past already finished at that time.

Answer 3

Before answering this, I would like to clarify this. I think you missed it a bit.

He was known as a great mathematician and everyone wanted to understand what he had done.

I don't think it means-He did something before people wanted to understand it. If this was the case, it would have been...

He was known as a great mathematician; he simplified (formula?) that everyone wanted to understand. There was something already known to everybody but it was not understandable (for instance, everybody knows that human heart pumps but then it was not understandable how does it do that?).

Even simplified... compare this -

You did something and I wanted to understand what you did -you did it first and then I wondered how did you do it or what is it?
You did something that I wanted to understand -I already wanted to understand something, you just simplified and made me understood.

Back to your original sentence -

He was known as a great mathematician and everyone wanted to understand what he had done. - this means everyone wanted to understand what all he did. In other words, he invented/revealed something and that people always wanted to understand/learn.

...and everyone wanted to understand what he did.

It'd mean the same but then a subtle difference (you already nailed it!) he did is recent and he had done is a bit more in past.

Given the context, everybody would understand that everybody wanted to understand what he did/had done in his research.