Among Mathematicians In General, Three Main Categories

Mathematics In General Is Fundamentally The Science Of Self-evident Things.

Thus, In A Sense, Mathematics Has Been Most Advanced By Those Who Distinguished Themselves By Intuition Rather Than By Rigorous Proofs.

Everyone Knows What A Curve Is, Until He Has Studied Enough Mathematics To Become Confused Through The Countless Number Of Possible Exceptions.

It Is Well Known That The Central Problem Of The Whole Of Modern Mathematics Is The Study Of Transcendental Functions Defined By Differential Equations.

The Presentation Of Mathematics In Schools Should Be Psychological And Not Systematic. The Teacher, So To Speak, Should Be A Diplomat. He Must Take Account Of The Psychic Processes In The Boy In Order To Grip His Interest, And He Will Succeed Only If He Presents Things In A Form Intuitively Comprehensible. A More Abstract Presentation Is Only Possible In The Upper Classes.