Mathematics aimed at systems that actually exist.
13 topics · 15 curated works
No prior grounding assumed.
Game Theory: An Open Access Textbook with 165 Solved Exercises
Giacomo Bonanno · 2015
Builds non-cooperative game theory from extensive and normal form up through Nash equilibrium and backward induction, arguing the formal apparatus is…
+2 more at this level
Assumes you know the vocabulary.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Eugene Wigner · 1960
Argues that mathematics developed for its own internal reasons repeatedly turns out to describe physical law with a precision no theory of knowledge…
+4 more at this level
Primary sources and full treatments.
Dynamical Systems
George D. Birkhoff · 1927
Treats a system's long-run behaviour geometrically, as the structure of trajectories in phase space, laying out the recurrence and stability concepts…
+6 more at this level
12 of 15 works
Giacomo Bonanno
Builds non-cooperative game theory from extensive and normal form up through Nash equilibrium and backward induction, arguing the formal apparatus is teachable from high-school algebra alone if the exercises carry the weight.
link checked 17 Sept 2026Matt Parker (The Royal Institution)
Uses collapsed bridges and aviation errors to argue that mathematical mistakes recur in a small number of predictable forms, most of them unit and rounding failures rather than deep errors.
link checked 17 Sept 2026Derek Muller (Veritasium)
Traces chaos theory back to Lorenz's accidental discovery that tiny rounding differences explode into wildly different weather forecasts, arguing determinism and long-range predictability are not the same thing.
link checked 17 Sept 2026Eugene Wigner
Argues that mathematics developed for its own internal reasons repeatedly turns out to describe physical law with a precision no theory of knowledge explains, and that this fit is a mystery rather than something to take for granted.
14 pageslink failing as of 17 Sept 2026Stephen Boyd & Lieven Vandenberghe
Argues that convexity, not linearity, is the real dividing line for which optimisation problems can be solved reliably, and gives the recipe for recognising a convex problem in disguise.
716 pageslink checked 17 Sept 2026Dimitris Bertsimas (MIT OpenCourseWare)
Develops linear and integer optimisation from the geometry of the feasible polytope, arguing that duality and sensitivity analysis, not just the simplex algorithm, are what make an optimisation model usable in practice.
link checked 17 Sept 2026Computerphile
Explains that floating point trades exact representation for range, so the familiar arithmetic surprises are a consequence of the format rather than bugs in the machine.
link checked 17 Sept 2026David Krakauer (Santa Fe Institute)
Distinguishes complexity from mere complication by locating it in systems that compute and adapt, and argues the useful measure is how much history a system's structure encodes.
link checked 17 Sept 2026George D. Birkhoff
Treats a system's long-run behaviour geometrically, as the structure of trajectories in phase space, laying out the recurrence and stability concepts the whole later field is organised around.
link failing as of 17 Sept 2026R.A. Fisher
Derives a reaction-diffusion equation for a favoured gene spreading through a population in space, showing it advances as a wave travelling at a constant speed set by the gene's selective advantage and the population's dispersal rate.
15 pageslink checked 17 Sept 2026Richard W. Hamming
Shows that adding redundant bits according to a fixed algebraic rule lets a receiver not just detect but locate and correct a transmission error, founding coding theory on the idea of distance between codewords.
link checked 17 Sept 2026Edward N. Lorenz
Shows that a simple deterministic system of three ordinary differential equations produces trajectories that never repeat and diverge without bound from arbitrarily close starting points, undermining the assumption that determinism implies long-range predictability.
12 pageslink failing as of 17 Sept 2026