Juggling Is Sometimes Called The Art Of

Some People Think That Mathematics Is A Serious Business That Must Always Be Cold And Dry; But We Think Mathematics Is Fun, And We Aren't Ashamed To Admit The Fact. Why Should A Strict Boundary Line Be Drawn Between Work And Play? Concrete Mathematics Is Full Of Appealing Patterns; The Manipulations Are Not Always Easy, But The Answers Can Be Astonishingly Attractive.

The Trouble With Integers Is That We Have Examined Only The Very Small Ones. Maybe All The Exciting Stuff Happens At Really Big Numbers, Ones We Can't Even Begin To Think About In Any Very Definite Way. Our Brains Have Evolved To Get Us Out Of The Rain, Find Where The Berries Are, And Keep Us From Getting Killed. Our Brains Did Not Evolve To Help Us Grasp Really Large Numbers Or To Look At Things In A Hundred Thousand Dimensions.

Juggling Is Sometimes Called The Art Of Controlling Patterns, Controlling Patterns In Time And Space.

Ab=1/4((a+b)^2-(a-b)^2) Is An Amazing Identity, And Unfortunately, I Have To Remind My Current Students How To Prove It.

It Wouild Be Very Discouraging If Somewhere Down The Line You Could Ask A Computer If The Riemann Hypothesis Is Correct And It Said, 'yes, It Is True, But You Won't Be Able To Understand The Proof.' John Horgan.