Here are my two cents. Read the proof it will help you understand and build intuition because it is constructive. It explicitly shows you what the conserved quantity is, given the group of symmetries. If it is too hard to follow and you can't see the forest because of the trees, try a few examples it should help. Also here is a link that may help a bit.

http://math.ucr.edu/home/baez/noether.html

Can Noether's theorem be understood intuitively?
I bought a no-name but decent multimeter, and it came with a thermocouple. Let's say I broke it in some way. Can I just replace it with any other thermocouple, or is each thermocouple calibrated for one specific model of a multimeter?

I have been looking at thermocouples, eg on eBay, e.g. this one. They write some specs but they don't write which multimeter it fits with?

So does any thermocouple fit with any multimeter (or digital thermometer)?
