The Infinite! No Other Question

Galileo Was No Idiot. Only An Idiot Could Believe That Science Requires Martyrdom - That May Be Necessary In Religion, But In Time A Scientific Result Will Establish Itself.

Mathematics Knows No Races Or Geographic Boundaries; For Mathematics, The Cultural World Is One Country.

I Do Not Want To Presuppose Anything As Known. I See In My Explanation In Section 1 The Definition Of The Concepts Point, Straight Line And Plane, If One Adds To These All The Axioms Of Groups I-v As Characteristics. If One Is Looking For Other Definitions Of Point, Perhaps By Means Of Paraphrase In Terms Of Extensionless, Etc., Then, Of Course, I Would Most Decidedly Have To Oppose Such An Enterprise. One Is Then Looking For Something That Can Never Be Found, For There Is Nothing There, And Everything Gets Lost, Becomes Confused And Vague, And Degenerates Into A Game Of Hide And Seek.

Geometry, Like Arithmetic, Requires For Its Logical Development Only A Small Number Of Simple, Fundamental Principles. These Fundamental Principles Are Called The Axioms Of Geometry.

However Unapproachable These Problems May Seem To Us And However Helpless We Stand Before Them, We Have, Nevertheless, The Firm Conviction That Their Solution Must Follow By A Finite Number Of Purely Logical Processes.