Artin Reciprocity

I will tell you a story about the Reciprocity Law. After my thesis, I had the idea to define $latex {L}&fg=000000$-series for non-abelian extensions. But for them to agree with the $latex {L}&fg=000000$-series for abelian extensions, a certain isomorphism had to be true. I could show it implied all the standard reciprocity laws. So I… Continue reading Artin Reciprocity

Why do roots come in conjugate pairs?

This is an expanded version of an answer I gave to a question that came up while I was assisting the 2014-2015 WOOT class. It struck me as an unusually good way to motivate higher math using stuff that people notice in high school but for some reason decide to not think about. In high… Continue reading Why do roots come in conjugate pairs?