Blog
Occasional Random thoughts from us.
The Mathematics of Discounts, Markups, and Sales Tax
20% off plus an extra 10% off is not 30% off. Here is the math of stacked discounts, markup vs. margin, and why the order of tax and discount doesn't matter.
The Math Behind Retirement: 4% Rules, Compounding, and Sequence of Returns
Two retirees can earn the exact same returns and end up with wildly different outcomes. The order of those returns matters, and the math explains why.
The Mathematics of Inflation: Why Prices Compound
Inflation is compound interest running in reverse on your cash. At a "modest" 3%, prices double in about 23 years. Here is the math.
How Credit Card Interest Really Works — The Mathematics Behind Your Balance
A 22.99% APR is not really 22.99%. Here is how daily compounding, average daily balances and minimum payments turn a $5,000 balance into a 19-year commitment.
The Math Behind a Mortgage: From Interest Rates to Amortization
Your mortgage payment never changes, but what it buys changes every month. Here is the formula behind it and why the first decade mostly pays the bank.
Why Does the Rule of 72 Work?
Divide 72 by an interest rate and you get the years to double your money. The real magic number is 69.3, so why 72? Logarithms, a handy set of divisors and a 1494 textbook explain it.
From Earth to Exoplanets: The Math Behind Discovering New Worlds
The search for exoplanets—planets orbiting stars other than our Sun—is one of the most exciting frontiers in modern astronomy. Mathematical techniques…
The Mathematics of Compound Interest: Why Time Is More Powerful Than Money
Most people obsess over finding the best interest rate. The math says they're optimizing the wrong variable — time does far more work than rate ever will.
The Prisoner's Dilemma and the Mathematics of Cooperation
Two rational players who each make the smartest choice end up worse off than if they had trusted each other. Here is the game theory, and the four-line strategy that won a famous tournament.
What Does a Probability Actually Mean?
"70% chance of rain" means different things to different people, and mathematicians have argued about the meaning of probability for centuries. Here are the main interpretations and why they matter for forecasts and AI.
The Birthday Paradox: Why 23 People Are Enough
In a group of just 23 people, there's a better-than-even chance two share a birthday. Here is the calculation, why intuition fails, and how the same math threatens computer security.
The Monty Hall Problem Explained
Switching doors wins two-thirds of the time. When Marilyn vos Savant said so in 1990, thousands of readers, including PhDs, wrote in to say she was wrong. Here is why she was right.