Mathematics In General Is Fundamentally The Science

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

The Teacher Manages To Get Along Still With The Cumbersome Algebraic Analysis, In Spite Of Its Difficulties And Imperfections, And Avoids The Smooth Infinitesimal Calculus, Although The Eighteenth Century Shyness Toward It Had Long Lost All Point.

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

The Greatest Mathematicians, As Archimedes, Newton, And Gauss, Always United Theory And Applications In Equal Measure.

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.