the giants we stand on

Acknowledgements

Nothing on this site is new mathematics or new science. Every zooid society engages, rediscovers, or is taught by ideas that belong to others. This page credits them — the theorems, results, methods, and thinkers the project builds on. It is the honest companion to the first doctrine: name what you did not make.

Mathematics & the Millennium Problems

Riemann Hypothesis — Bernhard Riemann; equivalent criteria and evidence from Guy Robin, Jeffrey Lagarias, Franz Mertens & August Möbius (the Mertens conjecture disproved by Andrew Odlyzko & Herman te Riele), Nicolaas de Bruijn & Charles Newman (Λ ≥ 0 by Brad Rodgers & Terence Tao); zero statistics from Hugh Montgomery, Andrew Odlyzko, Freeman Dyson, Michael Berry & Jonathan Keating, and the Hilbert–Pólya idea; superabundant numbers from Srinivasa Ramanujan, Leonidas Alaoglu & Paul Erdős. Fermat's Last Theorem — Pierre de Fermat; proved by Andrew Wiles with Richard Taylor (modularity: Taniyama–Shimura–Weil). Four Colour Theorem — Kenneth Appel & Wolfgang Haken. Poincaré Conjecture — Henri Poincaré; proved by Grigori Perelman via the Ricci flow of Richard Hamilton; surfaces via Leonhard Euler. Navier–Stokes — Claude-Louis Navier & George Stokes; Jean Leray; Caffarelli–Kohn–Nirenberg; Beale–Kato–Majda; Ladyzhenskaya–Prodi–Serrin; Escauriaza–Seregin–Šverák; the dyadic/shell models of Katz–Pavlović, Cheskidov, Friedlander; the averaged equation of Terence Tao; the cascade of Lewis Fry Richardson & Andrey Kolmogorov. Arithmetic — Giuseppe Peano; Egyptian/Russian-peasant doubling; John Napier (logarithms); Kurt Gödel (Gödel numbering); the Chinese Remainder Theorem (Sunzi; residue arithmetic of Garner & Svoboda); balanced ternary (the Setun computer).

Physics & field theory

Yang–Mills and the mass gap — Chen-Ning Yang & Robert Mills; lattice gauge theory (Kenneth Wilson); asymptotic freedom (David Gross, Frank Wilczek, David Politzer); constructive QFT (James Glimm & Arthur Jaffe); the axioms of Osterwalder–Schrader and Wightman. The Millennium Prize Problems are stated by the Clay Mathematics Institute.

The great measurements

Eratosthenes, Aristarchus, Ole Rømer, Henry Cavendish & Isaac Newton, Joseph von Fraunhofer, Edwin Hubble, and Johannes Kepler.

Logic, computation & formalization

Resolution proving — John Alan Robinson; the incompleteness theorems and the halting problem — Kurt Gödel & Alan Turing; zeta acceleration via Cohen–Rodriguez Villegas–Zagier; the Lean prover (Leonardo de Moura) and the mathlib community; the blueprint methodology of Patrick Massot; the lineage of machine discovery — AM/EURISKO (Douglas Lenat), the Ramanujan Machine, and FunSearch / AlphaTensor (DeepMind).

Music & sound

Just intonation and additive synthesis; the reverberator of Manfred Schroeder; granular synthesis (Iannis Xenakis, Curtis Roads); the YIN pitch detector (Alain de Cheveigné & Hideki Kawahara); the Krumhansl–Schmuckler key-finding profiles (Carol Krumhansl); the massed-voice choir as a homage to 10cc's "I'm Not in Love"; and the composers the theorem-music borrows — Bach, Mozart, Beethoven, Wagner, Debussy, Bartók, Stravinsky, Schoenberg, Xenakis, Ligeti, Penderecki, Philip Glass.

Living systems & the metaphor

The slime mould (Physarum; the maze experiments of Toshiyuki Nakagaki) and the siphonophore colony; flocking (the Boids of Craig Reynolds); cellular automata (von Neumann, Conway, Wolfram); evolved virtual creatures (Karl Sims).

Mind, society & language

Thorstein Veblen (The Theory of the Leisure Class), William Graham Sumner (Folkways), Robert Park & Ernest Burgess (Introduction to the Science of Sociology), Ron J. Hammond (Sociology of the Family), OpenStax (Introduction to Sociology 3e), Sigmund Freud (The Interpretation of Dreams; A General Introduction to Psychoanalysis), Alfred Binet (The Mind and the Brain), Christopher L. Klein (Essentials of Cognitive Psychology); working-memory limits after George A. Miller.

Tools, standards & texts

The Rust language and its standard library; public-domain texts from Project Gutenberg; open textbooks under Creative Commons from OpenStax and their authors; readability after Rudolf Flesch; accessibility contrast after the W3C's WCAG. The network was designed and written in ongoing dialogue with an AI assistant.

Naming a person, work, or result here credits an influence or an idea this project uses or rediscovered. It does not imply their endorsement, involvement, or affiliation. This project reproduces none of these works — it only stands on them. Corrections are welcome.