WILLIAM SHAKESPEARE Shakespeare invites Newton to watch his new play in Globe Theatre. They meet backstage. "How goes it, Will?" asks Newton. "I am doing well, thank you, but you don’t look good. Have you been writing another one of your silly theorems?" says Will.

"Writing a theorem is more difficult than writing a play," says Newton. "Mathematics bores me. In mathematics, 63 is just 63, but in poetry, I can make it equal to 64," Will replies. "It happens in mathematics, too, dear Will. Allow me to demonstrate this. Give me your undivided attention," says Newton and picks up a piece of paper. On it, he draws the two figures that have been reproduced here.

He cuts the rectangle marked in red into two pieces (upper and lower) along a staircase line marked in bold black. This 7x9 rectangle overlaps an 8x8 square marked in black. "Drag the upper piece that I have cut one square up and to the right, Will. Try to fit the upper portion into its new position," says Newton. Will does what Newton says and is surprised to find that a 7x9 rectangle fits exactly into an 8x8 square.

Will says, "I think it proves that..." "That 63 (7x9) is equal to 64 (8x8)," says Newton, "however, you believe that I have cheated you somewhere, isn’t that so?" "Right, Sir Issac, but where have you cheated me?" says Will. Newton says, "Mathematics in general and geometry in particular are deductive sciences, Will. Only rigorous thinking produces the proof."

"Correct me if I am wrong, but I believe that 7x9=(n-1)x(n+1) where n=8 (from the 8x8 square in the background). If this is true, then, (n-1)x(n+1)=n2-1. The area of the red rectangle is (n-1)x(n+1) for a given value of n. The area of the final square is n2. The upper row of the square is the one that does not fit into the rectangle. Also, the leftmost column of the rectangle is the one that does not fit into the square. The row contains n small squares, whereas, the column contains only n-1 small squares. It proves that the area of the square exceeds that of the rectangle by one small square."

"Mathematics is highly graphical and draws heavily on human imagination and one’s ability to visualise. N1=(n-1)x(n+1) is the area of the original rectangle and N2=nxn is the area of the square. Try to split the rectangle into the first column and the remaining rectangle. Also, split the square into the upper row and the remaining rectangle (the distributive law). So, N1=(n-1)+(n-1)n and N2=n+n(n-1). So, N2-N1=[n+n(n-1)]-[(n-1)+(n-1)n]=1. The rest is illusion."

Will says, "A rather mad proof Sir Issac. The way you proved for a moment that 63 was equal to 64 was splendid. There is a madness in your method." "Playwrights don’t go mad, Will, mathematicians do. It is in finding logic and not imagination and romance that the difficulties lie. Enough of it! Now, tell me about your play, what’s the story?" Will says, "Well, there are these two lovers..."

— Aditya Rishi