Mathematics & Probability

A mathematical framework for updating beliefs based on new evidence, proportional to how surprising that evidence is.

Rare, unpredictable events with extreme impact that are retrospectively rationalized — the events that shape history are the ones nobody saw coming.

Small consistent gains accumulate exponentially over time — the most powerful force in investing, learning, and building.

The critical distinction between two variables that move together and one actually causing the other — confusing the two is among the most common reasoning errors.

The distinction between ensemble averages and time averages — what works across many individuals simultaneously may not work for one individual across time.

Growth that accelerates proportionally to its current size, producing deceptively slow initial progress followed by explosive acceleration.

An estimation technique that breaks seemingly impossible questions into tractable sub-problems, producing order-of-magnitude answers from minimal data.

The distinction between the best possible outcome and merely the best nearby outcome — getting trapped at a local maximum prevents reaching the global one.

The practice of thinking backwards — instead of asking how to achieve X, ask what would guarantee failure and avoid that.

A formula for optimal bet sizing that maximizes long-term geometric growth rate of wealth while avoiding ruin.

Systems where outputs are not proportional to inputs — small changes can produce massive effects and vice versa.

A statistical pattern where a small number of items account for a disproportionate share of outcomes — the vital few versus the trivial many.

Replacing binary yes/no judgments with probability estimates to make better decisions under uncertainty.

The mathematical framework for quantifying uncertainty, enabling rational decision-making when outcomes are not certain.

Extreme outcomes tend to be followed by more moderate ones — exceptional performance contains a luck component that does not persist.

The ability to distinguish meaningful information from irrelevant data — the foundation of good judgment in information-rich environments.