Fermat

• The Bottom Line: Fermat's Last Theorem is a powerful investing metaphor that warns us: elegant-looking “shortcuts” to wealth are often intellectual traps, while true, lasting value is found through simplicity, rigorous work, and focusing only on what is provably understandable.
• Key Takeaways:
• What it is: A famous mathematical problem (aⁿ + bⁿ = cⁿ) that appeared simple but took over 350 years to prove, illustrating the immense danger of deceptive simplicity.
• Why it matters: It serves as a mental model that teaches investors to be deeply skeptical of “can't-miss” opportunities, complex financial engineering, and speculative narratives. It reinforces a core value investing principle: focus on simple, understandable business fundamentals.
• How to use it: Apply the “Fermat Test” to any investment idea: Can you explain it simply? Is its success based on unproven assumptions? Or is it built on a foundation of verifiable facts and durable advantages?

In the 1630s, a brilliant French lawyer and amateur mathematician named Pierre de Fermat was reading an ancient Greek text on mathematics. In the margin of the book, he scribbled a note that would go on to taunt and torment the world's greatest minds for centuries. You probably remember the Pythagorean Theorem from school: a² + b² = c². It describes the relationship between the sides of a right-angled triangle, and there are countless whole number solutions (like 3² + 4² = 5²). Fermat's note was a riff on this. He wrote that for any whole number 'n' greater than 2, the equation aⁿ + bⁿ = cⁿ has no whole number solutions. In other words, you can't find whole numbers that work for a³ + b³ = c³, or a⁴ + b⁴ = c⁴, and so on, to infinity. Then came the legendary, infuriating kicker. Fermat added: “I have a truly marvelous proof of this proposition which this margin is too narrow to contain.” And with that, he died, leaving behind a mathematical grenade. For the next 357 years, “Fermat's Last Theorem” became the Mount Everest of mathematics. It seemed so simple. Anyone could understand the problem. Yet, generation after generation of brilliant mathematicians tried and failed to find the “marvelous proof.” Countless amateurs submitted flawed proofs, convinced they had cracked the code with a simple, elegant trick. The puzzle was finally solved in 1994 by Professor Andrew Wiles. His proof wasn't a clever one-liner that could fit in a margin. It was 129 pages of dense, modern mathematics, the culmination of seven years of secret, focused work that built upon centuries of collective effort. This story—of a deceptively simple problem, the allure of an easy solution, and the reality of the immense, rigorous work required for a real answer—is one of the most powerful allegories a value investor can learn from.

“There is no reason to get a C on something you can get an A on. It's just as easy! It's just as easy to buy a wonderful business at a fair price as it is to buy a fair business at a wonderful price. In fact, it's easier to do the former.” - Warren Buffett ¹⁾

The world of investing is filled with “Fermat's Last Theorems.” These are the seductive ideas, the complex strategies, and the “new paradigm” stocks that promise a “marvelous proof” of easy riches. They look elegant, sound intelligent at dinner parties, but often have a fatal, hidden flaw. A value investor uses the story of Fermat as a powerful mental filter to separate durable opportunities from these dangerous traps. 1. The Danger of Complexity Disguised as Sophistication: Andrew Wiles's real proof was incredibly complex, but the businesses that make value investors rich are almost always simple. The “Fermat Trap” in investing is the belief that complexity equals sophistication and, therefore, higher returns. Think of the complex derivatives that caused the 2008 financial crisis, or the convoluted business models of companies like Enron. They were explained with jargon and impressive-looking formulas, but they were fundamentally unsound. A value investor knows that if you can't explain an investment on the back of a napkin, you shouldn't own it. This is the heart of the circle_of_competence. 2. The Allure of the “Proof in the Margin”: Every market cycle has its own version of Fermat's “proof in the margin.”

• The Dot-Com Boom: “It's a new economy! Profits don't matter, only eyeballs do.” (A flawed, simple proof that ignored centuries of business reality.)
• The Housing Bubble: “Housing prices have never gone down on a national level.” (A simple observation mistaken for an immutable law of physics.)
• Speculative Fads (Crypto, Meme Stocks): “This time it's different. The community is the value.” (A narrative-driven 'proof' detached from any measure of intrinsic value.)

Value investors learn from Fermat that claims of easy, revolutionary solutions are usually traps. True value is built slowly and demonstrably, not discovered in a flash of speculative genius. 3. Embracing the “Too Hard Pile”: For over 300 years, the smartest thing a mathematician could do with Fermat's Last Theorem was to admit, “I can't solve this,” and work on something else. Charlie Munger, Warren Buffett's partner, famously talks about having a "too hard" pile. A huge part of successful investing isn't about finding the answers to difficult questions; it's about having the discipline to recognize which questions are too hard to answer and avoiding them entirely. Is this biotech company's new drug going to get FDA approval? Too hard. Will this tech startup win the race for AI dominance? Too hard. What will the price of oil be in six months? Too hard. A value investor's focus remains on what is knowable and important, not what is tantalizingly complex.

“Fermat” isn't a formula you can punch into a spreadsheet. It's a mental model, a qualitative test to protect you from your own biases and the market's seductive stories. Here’s how to apply the “Fermat Test” to a potential investment.

1. Step 1: The Simplicity Test.
   • Question: Can I explain why this is a great investment to a reasonably intelligent person, who is not in finance, in three minutes or less, using simple language?
   • Pass: “I'm buying See's Candies. It's a simple business. They make delicious chocolates that people love, especially on holidays. They have a powerful brand, so they can raise prices without losing customers, and they generate a lot of cash.”
   • Fail (Fermat Trap): “I'm investing in this fintech company that uses a proprietary machine-learning algorithm to arbitrage fractional discrepancies in decentralized crypto liquidity pools. Their synergistic paradigm leverages blockchain to disintermediate the legacy banking system…” If you find yourself using jargon and buzzwords, it’s a giant red flag.
2. Step 2: The “Proof in the Margin” Test.
   • Question: Is my investment thesis based on a single, brilliant, and unproven future event, or is it supported by a mountain of past and present evidence?
   • Pass: “This company has increased its earnings and dividends for 30 consecutive years. It has a dominant market share, a fortress balance_sheet, and its products are essential. The future may not be exactly like the past, but there is strong evidence of durability.”
   • Fail (Fermat Trap): “This company is currently losing a billion dollars a year, but if they capture just 5% of the global market for autonomous drone delivery, and if their battery technology improves by 200%, and if regulators approve it, then the stock will be a 100-bagger.” This is relying on a future “marvelous proof” that may never materialize.
3. Step 3: The Durability Test.
   • Question: Does this investment's success depend on a complex system staying exactly as it is, or can it withstand change and chaos?
   • Pass: “People will likely be drinking Coca-Cola and eating McDonald's burgers in 20 years, much as they did 20 years ago. The business is resilient to recessions, technological changes, and political shifts.”
   • Fail (Fermat Trap): A hedge fund strategy that relies on a specific interest rate relationship between three different currencies and low volatility. It works beautifully until it doesn't, and then it blows up spectacularly. True value is anti-fragile; Fermat traps are incredibly fragile.

Let's compare two hypothetical companies through the lens of the Fermat Test.

This doesn't mean no one should ever invest in Quantum Fusion Inc. Venture capitalists might. But for a value investor focused on capital preservation and predictable returns, it's an unforced error.

Applying the Fermat mental model offers powerful benefits, but it's not without its potential blind spots.

• Behavioral Defense: It's one of the best defenses against the psychological trap of envy and FOMO (Fear of Missing Out). When everyone is getting rich on a speculative fad you don't understand, the Fermat Test gives you the intellectual framework to stay disciplined.
• Promotes Intellectual Honesty: It forces you to define the boundary of your circle_of_competence. Admitting “I don't understand this” is a sign of strength, not weakness, in investing.
• Reduces Unforced Errors: The biggest losses in investing often come not from bad luck, but from venturing into complex areas one doesn't understand. The Fermat Test keeps you on the simple, well-lit path.
• Focuses on Business over Story: It forces you to look past a charismatic CEO's exciting narrative (the “proof in the margin”) and focus on the cold, hard facts of the business (the 129 pages of evidence).

• Risk of Stagnation: A dogmatic application could cause an investor to dismiss all innovation. The key is to differentiate between speculative complexity (Quantum Fusion) and learnable complexity (understanding how cloud computing works for a company like Microsoft). Value investors must still do the work to expand their circle of competence over time.
• Can Be an Excuse for Laziness: An investor might place a business in the “too hard pile” simply to avoid the work of analyzing it. The model should be used to avoid unknowable situations, not to shirk the necessary diligence on understandable ones.
• It is Not a Valuation Tool: The Fermat Test helps you screen ideas, but it doesn't tell you what a good business is worth. Once a company passes the test, you must still do the quantitative work of valuation using tools like DCF analysis and demand a margin_of_safety.

• circle_of_competence: The absolute core idea linked to the Fermat model; only invest in what you can truly understand.
• too_hard_pile: The destination for all investment ideas that fail the Fermat Test.
• margin_of_safety: Your protection against being wrong. Even simple ideas can be wrong, so you need a buffer.
• speculation: What you are engaging in when you bet on an unproven “proof in the margin.”
• mr_market: The manic-depressive salesman who constantly tries to sell you Fermat-like traps during bubbles and simple, high-quality businesses during panics.
• inversion: A related mental model. Instead of asking “How can this succeed?”, ask “What are all the ways this 'marvelous proof' could be flawed?”
• mental_models: The broader category of cognitive tools, borrowed from various disciplines, that investors like Charlie Munger use to make better decisions.