Wikipedia Theory of equations. I've always wanted to master
theory of equations, since the early 1990s. Didn't really got
anywhere, except knowing it is just today's abstract algebra.
Since 2000s, i understand, more specifically, it's about Galois
theory. But today, Wikipedia gives a more complete picture. A
related aspiration was to understand a proof of Fundamental
theorem of algebra. As it was popularly known, Gauss is first to
prove it. But actually, according to Wikipedia, not so, and gave
quite some detail. Also of interest is this Wikipedia quote: In
spite of its name, there is no known purely algebraic proof of
the theorem, and many mathematicians believe that such a proof
does not exist. Besides, it is not fundamental for modern
algebra; its name was given at a time in which algebra was
basically about solving polynomial equations with real or
complex coefficients. Wikipedia is incredibly fantastic today.
Now, the question is, what are some candidates that'd be
considered as most important in algebra