“The Methodology of Mathematics”

available as a download from

http://education.lms.ac.uk/the-journal/ ]]>

http://math.huji.ac.il/~ehud/MH/Gauss-HarelCain.pdf

Regarding the first, the author writes:

“This outline of the proof shows that Gauss’s first proof of the FTA

is based on assumptions about the branches of algebraic curves, which might appear plausible to geometric intuition, but are left without any rigorous proof by Gauss. It took until 1920 for Alexander Ostrowski to show that all assumptions made by Gauss can be fully justified.”

Regarding the second, the author writes:

“This proof was purely algebraic and very technical in nature.”

This proof is valid if some extension field of the real numbers is algebraically complete.

Regarding the third, the author writes:

“Gauss’s third proof is easily followed step by step. But how could it be obtained? How was the complicated function y constructed? One can make some reasonable guesses.”

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