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Every course grows from a book

The Arithmoí series studies existence as a mathematical construct, with mathematics as its language. Buy a book in print or on Kindle, read it online in the library, open to every reader, hear it read aloud, and study it as a course in the school, with quizzes and moving figures.

Arithmoí Book 1

  • Mathematical Foundations and the Singularity

    Mathematical Foundations and the Singularity

    Volume I, Part 1 of A Study of Mathematical Cohesiveness in Physics and Metaphysics

    By Jason Glowney

    • 8 sections
    • 92 parts
    • 207 figures
    • First edition, 2026

    The model the Arithmoí series puts forward is the Arithmocentric model, which places mathematics at the centre: an old idea, the Pythagoreans' « all is number », taken up with the mathematics of the last two hundred years.

    About Book 1: its presentation and its table of contents

Inside Book 1

Eight sections

  • 1 · Matrix Group Theory
  • 2 · Tangent Spaces and Differential Forms
  • 3 · Curvature and Light
  • 4 · Matrix Group Conic Sections
  • 5 · Tangent Space Angles and Path-Connectedness in the Symmetric Cone Group
  • 6 · The Singularity
  • 7 · Prime Numbers and the Geometry of the Minimal Element
  • 8 · The Flowing Point and the Theory of Light

The whole table of contents, with its pages

Its figures, its words

A taste of Book 1

Six of the book's 207 figures, and a few of its sentences.

  • Book 1, Figure 1.7.4
    Figure 1.7.4 · The geometric prime numbers gp₁, gp₂, gp₃, gp₄ = 2, 3, 5, 7, inscribed in the complex unit circle, representing regular polygons.
  • Book 1, Figure 1.8.2
    Figure 1.8.2 · Non-compact Riemann surface plot for the imaginary multi-valued portion of the complex number z.
  • Book 1, Figure 1.8.1
    Figure 1.8.1 · The U(3) sphere wave projection where green waves are waves from the X₁-plane, blue waves are waves from the X₂-plane, and red waves are waves from the X₃-plane.
  • Book 1, Figure 1.4.30
    Figure 1.4.30 · Centered tangent sphere at the origin, with intersecting unit circles on its surface, and the unit hyperbolae intersecting the sphere at e⁰ in the X₁, X₂, X₃- planes.
  • Book 1, Figure 1.7.41
    Figure 1.7.41 · The cyclic group representations of the natural numbers n ∈ t projected onto the unit disc for the reciprocal time function f(t) = 1/t, t ∈ ℝ.
  • Book 1, Figure 1.2.10
    Figure 1.2.10 · The logarithmic spiral z = e^((𝓀+i)θτ)

Arithmoí is a modern-day Pythagorean approach to studying what we can and cannot see around us and within us. We ultimately find that the mind begets body, and the physical universe does not exist without the holographic extension of the singularity.

Arithmoí Book 1, Introduction
123the triangle, with its corners numbereda rotation by 120°a reflection123a reflection
Figure 1.1.3 · The D₃ group permutations

The mind is much more powerful than any giant particle collider that physicists might build because it transcends the physical states of time and space that these empiricist apparatuses are confined to.

Arithmoí Book 1, Introduction
The Lorenz attractor · from the library's Explorations

The ability to learn and gain knowledge is the best gift that has been bestowed upon us. May you see mathematics as the light!

Arithmoí Book 1, Introduction
π2πsin θπ2πsin θ
Part 1.2.2 · A point turning on the unit circle

From Arithmoí Book 1 by Jason Glowney. © 2026 The Arithmoí Foundation. All rights reserved.

The coming courses

Every book becomes a course

Each book the Foundation publishes opens as a course in its turn.

The authors

Who writes the books

  • Jason Glowney, MD, MSc

    Co-founder of the Arithmoí Foundation and author of the Arithmoí series.

    Dr. Glowney is a board-certified Internal Medicine, Emergency Medicine, and Sports Medicine physician from Chicago, Illinois. He is a graduate of the University of Illinois at Chicago College of Medicine and completed a dual residency at the University of Illinois at Chicago in Internal Medicine and Emergency Medicine and a fellowship in Sports Medicine at the University of Colorado. He founded Boulder Biologics, a clinic specializing in orthopedic and medical biologics in Boulder, Colorado.

    Dr. Glowney has a Master of Science degree in applied mathematics from the University of Washington. His primary area of interest and research is mathematics, including the beauty of Lie groups, chaos theory, number theory, differential geometry, geometric algebra, and complex analysis. He is the author of the Arithmoí book series, a study of existence as a mathematical construct.

  • Michaël Perreault, BSc

    Co-founder of the Arithmoí Foundation, contributing editor and didactics director.

    Michaël Perreault has a Bachelor of Science in mathematics from the Université du Québec à Montréal. A musician and mathematician, he is a product manager for an open-source technology company.

    He is the author of the forthcoming The Architecture of Existence, an introduction to the Arithmoí series and a synthesis of ontological mathematics.