I Spent Half My Life, Roughly Speaking,

One Couldn't Even Measure Roughness. So, By Luck, And By Reward For Persistence, I Did Found The Theory Of Roughness, Which Certainly I Didn't Expect And Expecting To Found One Would Have Been Pure Madness.

The Extraordinary Fact Is That The First Idea I Had Which Motivated Me, That Worked, Is Conjecture, A Mathematical Idea Which May Or May Not Be True. And That Idea Is Still Unproven. It Is The Foundation, What Started Me And What Everybody Failed To **** Prove Has So Far Defeated The Greatest Efforts By Experts To Be Proven.

Many Painters Had A Clear Idea Of What Fractals Are. Take A French Classic Painter Named Poussin. Now, He Painted Beautiful Landscapes, Completely Artificial Ones, Imaginary Landscapes. And How Did He Choose Them? Well, He Had The Balance Of Trees, Of Lawns, Of Houses In The Distance. He Had A Balance Of Small Objects, Big Objects, Big Trees In Front And His Balance Of Objects At Every Scale Is What Gives To Poussin A Special Feeling.

If One Takes The Kinds Of Risks Which I Took, Which Are Colossal, But Taking Risks, I Was Rewarded By Being Able To Contribute In A Very Substantial Fashion To A Variety Of Fields. I Was Able To Reawaken And Solve Some Very Old Problems.

The Theory Of Chaos And Theory Of Fractals Are Separate, But Have Very Strong Intersections. That Is One Part Of Chaos Theory Is Geometrically Expressed By Fractal Shapes.