Mathematics Knows No Races Or

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

Who Of Us Would Not Be Glad To Lift The Veil Behind Which The Future Lies Hidden; To Cast A Glance At The Next Advances Of Our Science And At The Secrets Of Its Development During Future Centuries? What Particular Goals Will There Be Toward Which The Leading Mathematical Spirits Of Coming Generations Will Strive? What New Methods And New Facts In The Wide And Rich Field Of Mathematical Thought Will The New Centuries Disclose?

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.

Keep Computations To The Lowest Level Of The Multiplication Table.

As Long As A Branch Of Science Offers An Abundance Of Problems, So Long It Is Alive; A Lack Of Problems Foreshadows Extinction Or The Cessation Of Independent Development.