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"Upon looking at these numbers, one has the feeling of being in the presence of one of the
inexplicable secrets of creation."   [D. Zagier]

an older layer of the archive

These pages are older, stranger and more speculative than the number theory and physics archive they sit beneath, and several of them are what caused it to be built. They are preserved here as they were written, rather than rewritten into arguments I would necessarily make in the same form today. The masonry has been stabilised – typography, links, formulae and sources – but the structure is essentially the same.

mysterious occurrences on the interface of physics and number theory How this began: an image that arrived before I had read any of the literature, and the attempt to find out whether it could mean anything. prime evolution notes A notebook begun in 1999 and circulated to mathematicians and physicists, asking whether the primes might be an equilibrium configuration in a larger space of possibilities. Four iterations survive – 1999, 2000, 2004, and a 2026 reconstruction written collaboratively with two AI systems – and the changes of mind between them are part of the record. a Jungian perspective on 'emotional' language in descriptions of number theoretical phenomena Mathematicians describing the primes reach unusually often for ecstatic, religious and mythic language. The observation is documented; the Jungian reading offered here is of its time, and is left as written. prime numbers, the zeta function and li An analogy drawn between the distribution of primes and the Chinese concept of li – organic pattern, poised between regularity and chance. An aesthetic proposal, not a theorem. prime quotes Numerous quotations on the primes, the zeta function and the Riemann hypothesis – the evidence behind the observation the Jungian essay starts from.
Elsewhere: the number theory and physics archive this layer sits beneath, and prime numbers: FAQ and resources for anyone who wants the mathematics first. The Secrets of Creation trilogy by Matthew Watkins (Liberalis, 2015) grew out of this material.