"Arithmetic has a very great and elevating effect ..." – Plato
"I'm interested in arithmetic, in the end." – Peter Scholze, Fields Medal Winner, 2018
"Arithmetic can be a gateway drug for mathematics." – Paul Lockhart, Arithmetic, 2017
"Might poets and visual artists consider searching in the real world outside the range of ordinary dreams for unexplored dimensions, depth, and meaning?" – Edward O. Wilson, The Meaning of Human Existence
Gary Croft is a research arithmetician and pattern divinator well-schooled in "lower" mathematics. For more than three decades, Croft has pursued the secret of prime numbers as a visual artist and composer seeking the beauty one would expect of a sequence deemed for two millennia to be fundamental, powerful and mysterious.
Ignorance being the mother of necessity, his method–if you can call it that–has been to 'go native' and engage directly with numbers in a hermeneutic circle (or should we say spiral?). As he puts it, "Self-taught? No. Number-taught would be more accurate. Almost everything I know about numbers I learned from numbers."
These numeracy 'lessons' involved thousands of experimental trials, errors and the occasional 'Eureka!' What makes this math unique is that it was produced employing only the four fundamental operations of arithmetic: addition, subtraction, multiplication and division. Restricting the experimental and analytical tools to simple arithmetic helped ensure the relative simplicity and universal intelligibility of the results, i.e. you don't have to possess higher math skills to grock any content on this site.
Regardless, like a chess player never losing sight of the object of the game, i.e., to checkmate the opponent's king, virtually all of Croft's experiments were designed to shed light on the distribution of prime numbers.
Croft first made his Prime Spiral Sieve 'public' in July, 1993, when he presented it to City University math instructor Mark Wahl while attending his class "Mathematics: Its Meaning, Mystery and Methods" (July/August, 1993). Mr. Wahl, who authored A Mathematical Mystery Tour: Higher-Thinking Math Tasks was intrigued enough by Croft's 8-dimensional / modulo 30 spiral sieve that accounted for all prime numbers greater than 5 that he made copies for his records. More than a quarter century later, it turns out that the algorithm transcends its exceptional efficiency (in fact, the fastest of its kind), by serving as a deeply illuminating gateway to a beautiful and mysterious universe of number patterns and geometric symmetries that provide deep insight into the distribution of prime numbers, et alia.
Croft's Career Highlights::
– Sr. Director, Global Procurement & Business Operations, Microsoft Corporation (retired from Microsoft in 2005 after 10 years there)
– Director, Purchasing and Accounts Payable, University of Washington
Croft currently resides on beautiful Whidbey Island, appropriately in the little unincorporated town of Freeland (originally established as a commune), where he lives on a hill looking down on his soul place, Holmes Harbor.
Return to Home Page: primesdemystified.com
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For samples of the art of Gary Croft (aka Hemi Boso), click here: hemiboso.com.
For a short story published by Gary Croft on Aphelion, the Webzine of Science Fiction and Fantasy, click here: Stencil.
For periodic updates on new material added to this site, Croft publishes notices on LinkedIn.