And now, a message from the odd positive integers, my grandson Keegan, and myself.


Part I: I decided simply to graph the values of the (Adjusted) Ceiling Square and its remainder for all of the odd positive non-prime integers I’ve put in my 3D graph so far (1 through 441). The result jumped out at me with its near-symmetry of dots, which appear in the graph below. But as you can see, I saw more, as did my grandson Keegan.

Part II: I immediately saw a space the shape of a heart in what appeared to be an arrangement of dots that look to me like a flower. I went ahead and imported a heart and scaled it to fit in the space, and then I colored the area around it, plus the stem and leaves, green. Keegan then observed that “flowers are a sign of peace, and hearts are a sign of love, so this is Peace and Love.”

What a beautiful message for mathematics to send to me!

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