This paper is a good example of why mathematicians often ignore philosophy of maths.
"When a community of mathematicians is small then our modern standards of truth aren't necessary"
Proof is needed to provide confidence in the intuition. Lots of historical examples of mathematical intuition unsupported by rigorous proof going astray.
Also, on p11 it is not enough just to complete the square and derive the formulae for quadratic roots, the substitution on p12 is also necessary. Otherwise, one has just shown the possible form roots can take if they exist, but not that they exist.
i.e. showing A=>B is true, does not show that B is true.
"When a community of mathematicians is small then our modern standards of truth aren't necessary"
Proof is needed to provide confidence in the intuition. Lots of historical examples of mathematical intuition unsupported by rigorous proof going astray.
Also, on p11 it is not enough just to complete the square and derive the formulae for quadratic roots, the substitution on p12 is also necessary. Otherwise, one has just shown the possible form roots can take if they exist, but not that they exist.
i.e. showing A=>B is true, does not show that B is true.