provided the field is important within the context of human societal development and in engaging the material I gain a nuanced understanding of the content and a deep appreciation of how the originators created the system.
I’ll suggest investigating the problem of “squaring the circle.” It has it’s roots in the origins of mathematics, passes through geometric proofs (including the notions of formal proofs and proof from elementary axioms), was unsolved for 2000 years in the face of myriad attempts, and was proved impossible to solve using the relatively modern techniques of abstract algebra.
The linked site has references (some already mentioned in this thread) that may be helpful …
R.Courant and H.Robbins, What is Mathematics?, Oxford University Press, 1996
H.Dorrie, 100 Great Problems Of Elementary Mathematics, Dover Publications, NY, 1965.
W.Dunham, Journey through Genius, Penguin Books, 1991
M.Kac and S.M.Ulam, Mathematics and Logic, Dover Publications, NY, 1968.
I’ll suggest investigating the problem of “squaring the circle.” It has it’s roots in the origins of mathematics, passes through geometric proofs (including the notions of formal proofs and proof from elementary axioms), was unsolved for 2000 years in the face of myriad attempts, and was proved impossible to solve using the relatively modern techniques of abstract algebra.
The linked site has references (some already mentioned in this thread) that may be helpful …
including …
which may be of special interest to you.