There Are No Solved Problems; There Are

Consider Now The Milky Way. Here Also We See An Innumerable Dust, Only The Grains Of This Dust Are No Longer Atoms But Stars; These Grains Also Move With Great Velocities, They Act At A Distance One Upon Another, But This Action Is So Slight At Great Distances That Their Trajectories Are Rectilineal; Nevertheless, From Time To Time, Two Of Them May Come Near Enough Together To Be Deviated From Their Course, Like A Comet That Passed Too Close To Jupiter. In A Word, In The Eyes Of A Giant, To Whom Our Suns Were What Our Atoms Are To Us, The Milky Way Would Only Look Like A Bubble Of Gas.

One Would Have To Have Completely Forgotten The History Of Science So As To Not Remember That The Desire To Know Nature Has Had The Most Constant And The Happiest Influence On The Development Of Mathematics.

Need We Add That Mathematicians Themselves Are Not Infallible?

Mathematics Has A Threefold Purpose. It Must Provide An Instrument For The Study Of Nature. But This Is Not All: It Has A Philosophical Purpose, And, I Daresay, An Aesthetic Purpose.

The Task Of The Educator Is To Make The Child's Spirit Pass Again Where Its Forefathers Have Gone, Moving Rapidly Through Certain Stages But Suppressing None Of Them. In This Regard, The History Of Science Must Be Our Guide.