en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem
1 correction found
hence the name the "fundamental theorem of algebra".
This sentence conflates two different ideas. The historical search for radical formulas for higher-degree equations is not the “fundamental theorem of algebra”; that theorem is the statement that every complex polynomial has a complex root.
Full reasoning
Authoritative mathematical references define the fundamental theorem of algebra as the theorem that any polynomial with complex coefficients has a root in the complex numbers. They do not use that name for the historical problem of finding radical formulas for quintics and higher-degree equations.
The historical survey in the Encyclopedia of Mathematics separates these topics explicitly:
- it says the early problem was to derive formulas expressing roots in terms of coefficients by radicals;
- and then says that, in connection with that, the problem of proving the existence of a complex root became important.
So the sentence in the post mislabels the radical-formula problem as the “fundamental theorem of algebra,” when that name belongs to a different theorem entirely.
2 sources
- Algebra, fundamental theorem of - Encyclopedia of Mathematics
The theorem that states that any polynomial with complex coefficients has a root in the field of complex numbers.
- Algebra(2) - Encyclopedia of Mathematics
The purpose was to derive formulas expressing the roots of the equation in terms of its coefficients... During the following three centuries fruitless efforts were made to find similar formulas for solving equations of higher degrees; in this connection, the problem of finding at least a "formula-free" proof of the existence of a complex root... became of major interest.