Shalma Wegsman is a "writing fellow" at Quanta magazine. I told her some really cool stuff about Noether's theorem, which goes beyond the stuff you always hear. She understood it, was excited about it, and seemed to want to explain it. Alas, her article doesn't mention any of that stuff. At the end it says

“There’s a lot we have left to learn by thinking hard about Noether’s theorem,” the mathematical physicist John Baez said. “It has layers and layers of depth to it.”

But none of these layers of depth are actually discussed. 😿

It turns out she was only allowed 800 words for a short explainer. It's a pity that every pop science explanation of Noether's theorem stops at roughly the same point... just where things are starting to get really cool.

Indeed, there's a lot of cool stuff that science journalists don't discuss. This is why I do my own science popularization. This is why, most times when I read a pop science article, I need to go the paper they're discussing, to get the really juicy stuff.

The *good* news is that Wegsman explains time translation symmetry, and she says Noether's theorem only works for theories described using a Lagrangian.

(I gave her an example of what goes wrong when your theory *isn't* described using a Lagrangian.)

https://www.quantamagazine.org/how-noethers-theorem-revolutionized-physics-20250207/

For my take on Noether's theorem, go here:

https://math.ucr.edu/home/baez/noether/

This is pretty technical, but Wegner helped me figure out a simpler explanation. Maybe I should give a talk about it sometime.