OVO

Wikipedia: “Stanislaw Marcin Ulam (April 13, 1909 – May 13, 1984) was a Polish mathematician who participated in the Manhattan Project and proposed the Teller-Ulam design of thermonuclear weapons. He also invented nuclear pulse propulsion and developed a number of mathematical tools in number theory, set theory, ergodic theory, and algebraic topology.”

For our purposes, we will concentrate on a single day of Ulam’s life in 1963. To distract himself from a tedious meeting, Ulam began writing numbers on a piece of paper. He started with 1, then wrote 2 to the right of 1, then 3 above 2, then 4 to the left of 3 and above 1, then 5 to the left of one, then 6 below 5 and to the left of 1, and so on in a counter-clockwise spiral. He then idly circled the prime numbers. Ulam knew that primes are natural numbers which have exactly two distinct natural number divisors (1 and itself), and that an equation that explains the distribution of primes has evaded mathematicians for thousands of years. To his surprise, Ulam saw that the circled prime numbers formed diagonal lines. Where no pattern had been seen before, Ulam saw a pattern. This pattern of primes became known as The Ulam Spiral, or the Ulam Rose.

17 16 15 14 13
18 05 04 03 12
19 06 01 02 11
20 07 08 09 10
21 22 23 24 25

Ulam Spirals appear with as few as three coils of the Spiral and the apparent pattern holds even when the Spiral has hundreds of coils. But there is no ‘proof’ for Ulam Spirals. They may or may not be scientific. This story brings two thoughts to mind. The first thought is that it was an act of idleness, not labor, that brought this curiosity forth. I place this discovery in the realm of dreams and not wakefulness. The second thought is a renewed sense of wonder for a topic that is presented as the very model of what is without wonder: mathematics. Mathematics is far, far from resolved. The distribution of prime numbers is one example of a discovery yet to be made in mathematics. The Four-Color Theorem is another.

I will likely never be as skilled as mathematics as Ulam was. I’m too old. But I can avoid work as he did, and I have open challenges before me. Chasing these mathematical non-physical mysteries seems so much more appealing than chasing any phantom of superstition. Atheists are said to be without wonder, and mathematicians doubly so. There’s a lovely spiral in front of me now that says otherwise.