Projective Geometry Has Opened Up For Us

The Developing Science Departs At The Same Time More And More From Its Original Scope And Purpose And Threatens To Sacrifice Its Earlier Unity And Split Into Diverse Branches.

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

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

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.

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