My colleague and me were confronted with a question concerning the introductory chapter of a text on algebraic geometry. The scenario of a plane curve over a field is considered, for a nonconstant polynomial . It was stated that the function field is obviously of transcendence degree over because is a new relation between and . The prerequisites to this text are basic undergraduate knowledge of algebra and topology. The question was about the obviousness of the above statement. We came up with a proof that only really requires some linear algebra. I found it rather cute. Do you want to see it?
I am writing this blag post from the second annual meeting of the DFG priority programme SPP1489 (algorithmic and experimental methods in algebra, geometry and number theory). Apart from having a lot of fun, I am catching up on the recent developments in open-source computer algebra software. Do you want to know more?