As more of a layperson, I have mixed feelings. As science journalism goes, it's excellent, but reading this sort of frontier news feels like a waste of time to me now. I only really found out that progress is being made in fields I don't understand. I bothered to check this article out because multiple people posted that it's very good, but the time I spent reading it would've been better put into getting a little bit more real understanding of old related discoveries like the unsolvability of the quintic, which is within reach at my level.

As someone who is maybe somewhere in the middle (I have a Masters in Maths, but haven't used it in earnest since graduating ~10 years ago) - I found this spot-on. Engaging enough to pull me in, technical enough to give some idea of what exactly is going on, but not too far in either direction.

Depends on what you mean by counter productive. You wouldn't cite Quanta Magazine if you were writing the next journal article on this topic intended for peer review. Instead, you would go to the original paper "Geometrization of the local Langlands correspondence" and pull that apart to look for ways you can improve upon what has already been done.

But mathematics is a big area (there is a reason why it's a plural: it's better to think of it as more of a family of topics than a single science.) And if you're a mathematician from an unrelated branch of mathematics, an article like this is written in a way where you can understand most of the underlying concepts reasonably intuitively.

There is nothing that can help laypeople if the goal is to understand the math. I mean the official harthstone text is hundreds of pages of hard grad math.this was the 70s .a lot has transpired.

I need more pictures. I'm obvious a layperson.