The Most Complex Object In Mathematics, The

I Spent My Time Very Nicely In Many Ways, But Not Fully Satisfactory. Then I Became Professor In France, But Realized That I Was Not - For The Job That I Should Spend My Life In.

A Cloud Is Made Of Billows Upon Billows Upon Billows That Look Like Clouds. As You Come Closer To A Cloud You Don't Get Something Smooth, But Irregularities At A Smaller Scale.

If You Look At A Shape Like A Straight Line, What's Remarkable Is That If You Look At A Straight Line From Close By, From Far Away, It Is The Same; It Is A Straight Line.

If You Look At Coastlines, If You Look At That Them From Far Away, From An Airplane, Well, You Don't See Details, You See A Certain Complication. When You Come Closer, The Complication Becomes More Local, But Again Continues. And Come Closer And Closer And Closer, The Coastline Becomes Longer And Longer And Longer Because It Has More Detail Entering In.

Some Mathematicians Didn't Even Perceive Of The Possibility Of A Picture Being Helpful. To The Contrary, I Went Into An Orgy Of Looking At Pictures By The Hundreds; The Machines Became A Little Bit Better.