Geometry Is The Art Of Correct Reasoning

A Small Error In The Former Will Produce An Enormous Error In The Latter.

The Mathematical Facts Worthy Of Being Studied Are Those Which, By Their Analogy With Other Facts, Are Capable Of Leading Us To The Knowledge Of A Physical Law. They Reveal The Kinship Between Other Facts, Long Known, But Wrongly Believed To Be Strangers To One Another.

The Advance Of Science Is Not Comparable To The Changes Of A City, Where Old Edifices Are Pitilessly Torn Down To Give Place To New, But To The Continuous Evolution Of Zoologic Types Which Develop Ceaselessly And End By Becoming Unrecognisable To The Common Sight, But Where An Expert Eye Finds Always Traces Of The Prior Work Of The Centuries Past. One Must Not Think Then That The Old-fashioned Theories Have Been Sterile And Vain.

In One Word, To Draw The Rule From Experience, One Must Generalize; This Is A Necessity That Imposes Itself On The Most Circumspect Observer.

Talk With M. Hermite. He Never Evokes A Concrete Image, Yet You Soon Perceive That The More Abstract Entities Are To Him Like Living Creatures.