Nice article “The Mighty Mathematician You’ve Never Heard Of” in the NYTimes on the occasion of the 130th birthday of Emmy Noether. I remember being stunned when I learned that Noether was a she. There are not that many female mathematicians.

There is an attempt at explaining the Noether’s theorem for a layman:

Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see it’s angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move.

I have to say, I do not find this convincing. I wonder if there is a more intuitive and more direct way to explain this theorem for a layman? That is an interesting thing to ponder about.

P.S. On a more scientific note (and to get back to the research part of this blog :), Noether’s theorem is at the heart of the conservation of momenta on the groups of diffeomorphisms. I am using this conservation (and people have used it many times before, for example, Statistics on diffeomorphisms via tangent space representations) to study statistical variability of the hippocampus dataset. The paper writing is in the progress.