Meaning of 'high-level overview' in a Maths talk?

An illustrative example:
Let's say you have been working for a very long time on a great paper in which you finally manage to construct a widget which has some amazing properties, which have important consequences for some other area of math.

Now, most of the paper consists of the construction which is extremely deep and technical (this is, after all, why nobody else had been able to construct this widget before you).

To give a high level overview of your work, you need to talk mainly about what the widget does, rather than how it is constructed. Talk about these properties and the amazing consequences to other areas in generic terms that can be understood by everyone.

Maybe towards the end, you can talk a bit about the construction. But you should still keep it high-level, meaning that you can talk for example about the main ingredients ("we use a construction analogous to the one for constructing wadgets, but whack it with a hammer in certain places to make it fit our needs"). But leave out any actual technical details.


It may help to consider an analogy: flying over the topic at high altitude (=level), the details can't be seen, but the shape of the whole landscape can be appreciated.

This is "high-level" in the same sense as a high-level programming language, i.e. highly abstracted from the fiddly details.


This means that you don’t derive each equation shown in the paper but focus on the, perhaps generic, results and conclusions.