Mathematics In General Is Fundamentally The Science

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

Among Mathematicians In General, Three Main Categories May Be Distinguished; And Perhaps The Names Logicians, Formalists, And Intuitionists May Serve To Characterize Them.

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.

Regarding The Fundamental Investigations Of Mathematics, There Is No Final Ending ... No First Beginning.

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