Jordan Ellenberg's How Not to Be Wrong opened doors. These essays walk through them — exploring probability, game theory, statistical traps, chaos, networks, and the cognitive biases that make us human. Every essay includes working simulations, calculators, and games.
Part I: The Bets You Make
Mathematics of risk, ruin, and the irrational mind.
The Kelly Criterion
Why knowing how much to bet matters more than knowing what to bet on. The formula that keeps you from going broke even when you're right.
Ergodicity
The difference between the average and the actual. Why GDP per capita lies about your life, and what Ole Peters proved to the economists.
Gambler's Ruin
The mathematical certainty that the house wins. Not luck — the asymmetry of absorbing barriers.
Prospect Theory
Why cab drivers quit early on good days and work late on bad ones. Kahneman and Tversky's demolition of homo economicus.
Part II: When to Decide
The mathematics of optimal stopping, belief updating, and impossible voting systems.
Bayes' Theorem
The theorem that reads your mind and catches your cancer. Why a 99% accurate test doesn't mean 99% probability.
Optimal Stopping
When to stop looking and start choosing. The 37% rule for hiring, dating, and apartment hunting.
Arrow's Impossibility Theorem
Democracy is mathematically doomed — but vote anyway. Why no voting system satisfies three reasonable conditions.
Part III: Hidden Structure
Patterns that emerge from numbers, from Benford's Law to the birthday problem.
Benford's Law
The law that catches liars. How the first digit of a number reveals fraud, from Enron to election audits.
Power Laws
When the average doesn't exist. Why one earthquake can release more energy than all others combined.
The Birthday Problem
The coincidence that isn't. Why 23 people have a 50% chance of a shared birthday — and why this breaks encryption.
Regression to the Mean
The most important statistical concept you've never heard of. Why the Sports Illustrated cover jinx isn't a jinx.
Part IV: The Data Lies
When aggregation reverses trends, selection creates phantom correlations, and the dead don't talk.
Simpson's Paradox
When the data tells two opposite stories. Berkeley's 1973 admissions scandal and when to aggregate vs. disaggregate.
Survivorship Bias
The dead don't talk. Abraham Wald's armor problem, mutual fund illusions, and why you don't hear about failed dropouts.
Berkson's Paradox
The phantom correlation. Why attractive people seem to have terrible personalities and restaurants are food OR ambiance.
The Inspection Paradox
Why the bus is always late, your friends have more friends than you, and class sizes are larger than advertised.
Part V: Systems That Eat Themselves
When measures become targets, and the old outlast the new.
Part VI: The Shape of Chance
Probability and randomness — the patterns hiding inside coin flips, doors, and infinite games.
The Monty Hall Problem
Why switching doors doubles your odds, and why your brain refuses to believe it. The gameshow puzzle that fooled a thousand PhDs.
The Gambler's Fallacy
The roulette wheel has no memory, but you do. Why "due" isn't a thing and streaks mean less than you think.
The St. Petersburg Paradox
A game worth infinite money that no one would pay $25 to play. The 300-year-old puzzle that birthed expected utility theory.
Streaks & the Hot Hand
When is a pattern real and when is it just noise? The hot hand debate that reversed itself after 30 years.
Martingale Theory
The mathematically perfect betting system that guarantees ruin. Why doubling down always sounds good and always ends badly.
The Law of Large Numbers
Why casinos always win and insurance companies rarely lose. The theorem that turns randomness into certainty — eventually.
Part VII: The Geometry of Choice
Game theory and decision theory — when rational agents collide, cooperate, and confound each other.
The Prisoner's Dilemma
Why rational self-interest makes everyone worse off. The Cold War game that explains climate change, doping, and price wars.
Nash Equilibrium
The beautiful mind's ugliest insight. When nobody can do better by changing strategy — even if everyone's miserable.
Tragedy of the Commons
When everyone's rational decision destroys the shared resource. Hardin's pasture, overfished oceans, and carbon emissions.
Mechanism Design
How to build games people can't cheat at. The reverse game theory behind auctions, kidney exchanges, and school choice.
Newcomb's Problem
The philosophy puzzle that splits rational people in half. One box or two? Your answer reveals your decision theory.
Braess's Paradox
When adding a road makes everyone's commute longer. The counterintuitive math of selfish routing and network design.
Part VIII: Numbers That Lie
Statistical traps and fallacies — six ways data misleads even the careful.
Base Rate Neglect
Why rare diseases produce mostly false positives. The probability error that trips up doctors, judges, and jurors.
The Ecological Fallacy
When what's true of groups is false of individuals. How aggregate data creates correlations that don't exist at the individual level.
The Texas Sharpshooter Fallacy
Painting the bullseye after you shoot. P-hacking, the Bible Code, and why testing enough hypotheses guarantees a "discovery."
The McNamara Fallacy
When you measure what's easy instead of what matters. Body counts in Vietnam and engagement metrics in Silicon Valley.
The Will Rogers Phenomenon
How moving patients between groups "cures" cancer — without helping anyone. Stage migration and the statistical illusion of progress.
Stein's Paradox
Why a baseball player's batting average predicts Tokyo's rainfall. The most counterintuitive result in statistics.
Part IX: Growth, Decay & Time
Dynamics and long-run behavior — compound growth, S-curves, chaos, and tail risk.
Compound Interest
Einstein's (alleged) eighth wonder and its dark twin: compound debt. The Rule of 72, Benjamin Franklin's experiment, and the birth of e.
Logistic Growth
Why everything that grows exponentially eventually stops. The S-curve from lily pads to COVID to startup valuations.
Chaos Theory
The butterfly, the weather, and the limits of prediction. How Edward Lorenz discovered that determinism doesn't mean predictability.
Heavy Tails & Black Swans
Why Gaussian thinking fails in Extremistan. Taleb's turkey, 25-sigma events, and the distributions that don't have averages.
Benford's Law II: The Forensic Frontier
How digit patterns catch tax cheats and election fraud. Second-digit analysis, MAD tests, and the limits of forensic mathematics.
The Ergodic Hypothesis in Economics
Why GDP growth doesn't mean you're getting richer. Ole Peters's argument that economics has been making an ergodicity error for 300 years.
Part X: Networks & Complexity
Systems thinking — small worlds, scale-free networks, segregation, and the limits of parallelism.
Six Degrees of Separation
Small world networks and why Kevin Bacon connects to everyone. Milgram's letters, weak ties, and Watts-Strogatz rewiring.
Metcalfe's Law
Why networks are worth the square of their users — and why that's dangerously wrong. N², N·log(N), and the tipping point.
Preferential Attachment
How the rich get richer in networks, science, and language. The Matthew Effect, Barabási-Albert, and why hubs dominate.
Voting Paradoxes Beyond Arrow
Gerrymandering, strategic voting, and the deeper math of manipulation. The sequel to Arrow's Impossibility Theorem.
Schelling Segregation
How mild preferences create extreme outcomes. The cellular automaton that explains residential segregation without assuming bigotry.
Amdahl's Law
Why throwing more people at a project makes it slower. Serial bottlenecks, Brooks's Law, and the limits of parallelism.
Part XI: The Human Equation
Behavioral mathematics — how our brains systematically betray us, and what the numbers say about it.
The Dunning-Kruger Effect
The mathematics of not knowing what you don't know. McArthur Wheeler's lemon juice, the viral myth, and the statistical artifact underneath.
Anchoring & Adjustment
Why the first number you see hijacks your brain. Rigged wheels, salary negotiations, and the dice rolls that change prison sentences.
The Paradox of Choice
When more options make you worse off. Iyengar's jam study, maximizers vs. satisficers, and the math of decision paralysis.
These 50 essays extend Jordan Ellenberg's How Not to Be Wrong: The Power of Mathematical Thinking (2014). Each covers a concept Ellenberg might have written — with original research, working simulations, and hand-crafted illustrations. Built with math, not magic.