"[...]the blog will have to explain what a field is, what a cubic field is, and what a discriminant (of a field) is, in every post."
At most once. Links are what the internet is for:)
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Moving the explanations out of the blog posts into a separate page or pages makes the problem harder, not easier, because it keeps you from omitting parts of the background that aren't necessary to understand the relevance of some particular result.
If you want links, here they are:
http://en.wikipedia.org/wiki/Field_(mathematics)#Definition_...
http://en.wikipedia.org/wiki/Cubic_field
http://en.wikipedia.org/wiki/Discriminant_of_an_algebraic_nu...
The thing is, those articles probably aren't brief enough for many people to stay interested, and they probably also don't go deep enough to make any particular one of impendia's results comprehensible. (And I'm also not sure if they're readable to people with only an engineering background in math.)
(In case you think I'm being snooty about engineers, I dropped out of college and have never published a theorem; instead, I have made my living writing software.)
Many people wouldn't stay interested; I'd say the vast majority wouldn't. But, after explaining those things to the extent that you thought was worthwhile, you ended up with 100 long term readers out of the x billion on the internet, I'd count that as a huge win, myself.