Earlier today, I was rummaging through old notes I had organized nearly seven years ago. You see, over the years, I’ve collected countless notes. And, as I go through my old notes, I realize I’ve dedicated so much time to building and creating products for others that I’ve often overlooked working on my own growth by sharing these notes publicly. Now, as I continue to build in public and write to you here in 2025, I want to share some of those notes more often.

The following particular notes explore ancient concepts in risk management. If you’re a trader or investor, I think you’ll find them fascinating.

1. Leibniz and Bernoulli: The Power of Patterns and Exceptions

Back in 1700, the polymath Leibniz once remarked that nature operates in patterns—“but only for the most part.” Meaning, there are clear and distinct patterns in nature all around us, often even following mathematical principles. However, not always! In trading, it’s tempting to rely on historical trends and established models, but the most critical risks often arise when the pattern fails. Traders can learn from this ancient insight: understanding the usual helps, but always be ready for the unusual. The unpredictable moments often determine the greatest losses or gains, so keep a portion of your strategy flexible and responsive to what lies outside the norm.

2. The Roman Republic’s Prudent Reserves

In the early Roman Republic, leaders were known for keeping emergency grain supplies stored for times of famine or war. This smart tactic was key to Rome’s early success and often goes overlooked despite its immense importance. They couldn’t predict exactly when disaster would strike, but they understood that preparing for the worst was critical to survival. Modern traders can draw a lesson from this ancient practice: even if you don’t know when a market downturn will occur, having a “reserve” in the form of manageable position sizes, a well-thought-out cash buffer, or hedging strategies can prevent one bad trade from becoming a catastrophic loss.

3. Diophantus and Iterative Solutions: Embrace Adjustment

Diophantus, a pioneer of algebra, solved complex problems by finding approximate solutions and refining them over time. In a way, he was the original tinker of mathematics. Try, fail, tinker, try again, and so forth. Sometimes he would succeed, only to revisit the problem to tinker again. Modern software developers would be fascinated by his approach as, in a way, he was working on new versions over time. In trading, this teaches the importance of adapting and iterating no differently than a software developers rather than insisting on one perfect plan that can be copy and pasted endlessly. Your initial position size, stop-loss level, or hedging strategy might not be ideal, but by monitoring the results and making small adjustments, you can continuously improve your approach. Just as ancient mathematicians didn’t settle for a single answer but refined their methods, traders should treat their strategies as works in progress—always evolving to better handle risk.

All in all, for those of us interested in markets, some of the most fascinating stories come from ancient history. More on these concepts coming in the future.