Question:
There is a Fundamental Theorem of Arithmetic,
Fundamental Theorem of Algebra, Fundamental Theorem of Calculus,
and several other "Fundamental Theorems," but why is there no
Fundamental Theorem of Geometry?

Replies:
Some theorem designated "The Fundamental Theorem of ....." is a
bit arbitrary since any of the mathematical disciplines you refer
to rests upon a number of definitions, theorems, etc. I suppose for
example that the "Fundamental Theorem of Euclidean Geometry" is the
parallel line theorem, since that distinguishes plane geometry from
convex and concave geometries. And what distinguishes complex
variable analysis from the analysis of ordered pairs of real
numbers (x,y) is the rule(s) of multiplication. I think the bottom
line is there is nothing "fundamental" about the "fundamental"
theorems. It just means that those theorems are significant
departures from some contrasting prior discipline.

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