The Initial Conditions.
“We choose the path of maximum density: deep dives into seminal works and original manuscripts themselves.”
This is not a reading list. This is a path. Each book builds on the previous. Each concept prepares for the next.
We begin with nothing. No points, no numbers, no space; and we forge the entire edifice through logical grammar, ontological commitment, and epistemological rigor. Arithmetic emerges as a consequence of stable identity and discrete separability.
Readings:
A Logical Introduction to Proof — David A. Schmidt
Sets for Mathematics — F. William Lawvere & Robert Rosebrugh (structural/category-theoretic sets)
Zeno’s paradoxes are resolved not by motion, but by the static adversarial game of epsilon-delta limits and the topological notions of connectedness and compactness. Differentiation becomes linear approximation (Fréchet), complex holomorphy enforces infinite rigidity (Liouville), and uncertainty itself is revealed as continuous integration via measure theory, martingales, and Brownian motion (Lévy characterization).
Readings:
Understanding Analysis — Stephen Abbott
Complex Analysis — Lars Ahlfors
Measure, Lebegue Integrals, and Hilbert Spaces — Kolmogorov & Fomin
Probability with Martingales — David Williams
From invariance we derive vector spaces, operators, tensors, Lie groups, and categories as the universal language of structure-preserving maps.
Readings:
Linear Algebra — Georgi Shilov
Lie Groups, Lie Algebras, and Representations — Brian C. Hall
Algebra — Serge Lang
Geometry is born locally flat (manifolds), measured by holes (cohomology, simplicial complexes), and finally transcended in algebraic geometry (schemes, sheaves) and representation theory (Virasoro, Monstrous Moonshine).
Readings:
Topology and Groupoids — Ronald Brown
Lectures on Differential Geometry — Shlomo Sternberg
Linear Algebra & Geometry — Alexei I. Kostrikin & Yu. I. Manin
Riemann Surfaces — Simon Donaldson
Differential Forms in Algebraic Topology — Raoul Bott & Loring W. Tu
Algebraic Geometry — Robin Hartshorne
A Concise Course in Algebraic Topology — J. Peter May
Vertex Operator Algebras and the Monster — Igor Frenkel, James Lepowsky, Arne Meurman
Physics is rebuilt without Newtonian crutches: symplectomorphisms replace conservation, connections replace forces, particles are irreps of Poincaré, and quantum field theory is tamed by renormalization and topological indices.
Readings:
Mathematical Methods of Classical Mechanics — Vladimir I. Arnold
Foundations of Differential Geometry (Vol. I & II) — Katsumi Nomizu & Shoshichi Kobayashi
Geometry of Yang-Mills Fields — Michael Atiyah
Renormalization and Effective Field Theory — Kevin Costello
Geometric Quantization — N. M. J. Woodhouse
Note: Specific discussion on these texts occurs in the corresponding channels in the Discord.