The Long Math is an independent website providing tools and explanations that make the long-term arithmetic of personal financial decisions visible.
No opinions. No hidden assumptions. Just arithmetic.
See how fees affect $500,000 invested for 30 years at 7%
A small annual percentage becomes a very large number when compounded over decades.
Illustrative annual compounding over 30 years. Slider adjusts the fee in the model only.
Interactive models that show how fees, taxes, inflation, and time interact over decades.
Clear explanations of the concepts behind investing and long-term financial arithmetic.
Essays on careers, training pipelines, long-horizon trade-offs, and the financial arithmetic behind building a professional life.
The early essays focus on medicine — the author's professional world — but the section will expand into other career structures, training pipelines, and major life decisions where long-horizon arithmetic shapes the outcome.
Read Essays →Examples of questions this site addresses using explicit assumptions and inspectable arithmetic:
Financial conclusions are often presented without the math behind them. The Long Math focuses on the arithmetic itself.
Every model on this site shows:
Nothing is hidden.
Models that make long-term financial trade-offs visible.
See how advisory fees compound into large long-term costs over time.
See how inflation changes the purchasing power of money across time.
Compare the long-term arithmetic of accelerated mortgage repayment versus investing.
If you are new to investing, begin with these ideas:
Future tools will explore long-term financial arithmetic in areas such as:
The goal remains the same: make the arithmetic visible.
Explore the arithmetic behind financial decisions.