Every Kind Of Science, If It Has

If I Were To Awaken After Having Slept For A Thousand Years, My First Question Would Be: Has The Riemann Hypothesis Been Proven?

In Mathematics ... We Find Two Tendencies Present. On The One Hand, The Tendency Towards Abstraction Seeks To Crystallise The Logical Relations Inherent In The Maze Of Materials ... Being Studied, And To Correlate The Material In A Systematic And Orderly Manner. On The Other Hand, The Tendency Towards Intuitive Understanding Fosters A More Immediate Grasp Of The Objects One Studies, A Live Rapport With Them, So To Speak, Which Stresses The Concrete Meaning Of Their Relations.

Every Mathematical Discipline Goes Through Three Periods Of Development: The Naive, The Formal, And The Critical.

Begin With The Simplest Examples.

[on Cantor's Work:] The Finest Product Of Mathematical Genius And One Of The Supreme Achievements Of Purely Intellectual Human Activity.