What I Learned from Poor Charlie's Almanack (EP.2: Mental Model #1 — Mathematics)
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Charlie doesn't ask us to know everything — just to know what's necessary, deeply enough.
Charlie believed that having around 80-90 mental models would improve how we make decisions in almost every area of life.
Think of them as thinking tools — physics teaches critical mass, psychology teaches confirmation bias, biology teaches evolution, economics teaches incentives and opportunity cost.
But among all of them, only a handful "carry very heavy freight" — meaning they're useful repeatedly across completely different situations. Things like incentives, compounding, and first principles.
Learn those deeply, and you'll be equipped to navigate almost any difficult decision life throws at you.
First Principles — Think from the ground up, not from what you've seen before
Most people think by analogy — they take what they've already seen or heard and use it as a starting point. "Companies like this do it this way, so we probably should too." Or "everyone else is studying this field, so it must be the right path."
But first principles thinking means stepping back and asking —
If I knew nothing at all and had to build the answer from scratch, what would the real answer be?
Elon Musk explained it this way: when he wanted to build rockets, everyone said it was too expensive. Rockets had always been expensive. But he asked from first principles — "what do the raw materials actually cost?" The answer came back at roughly 2% of what rockets were selling for in the market. That was the beginning of SpaceX.
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In everyday life, first principles helps most when we feel stuck in the same old options.
Try asking:
If the constraints I assumed were real didn't actually exist, how would I decide?
Do I actually know this, or do I just believe it because someone told me?
What is the real root of this problem?
Charlie said this is why you have to keep asking "Why, why, why?" — because the first answer you get is usually just the surface, not the foundation.
So how do you actually practice first principles thinking?
Start by observing yourself in everyday life.
1. Notice when you're doing something without knowing why
Why do you take this route to work? Because Google Maps said so? Why do you have a Monday meeting every week? Why does everyone assume a master's degree is necessary? If the answer is "everyone does it this way" or "it's always been like this" — that's a sign you haven't applied first principles at all.
2. Understand something from the ground up before handing it off to someone else
Before investing through a fund or financial advisor, ask yourself — do you actually understand where your money is going? What is it invested in? What are the fees? What happens if the market drops 30%? The goal isn't to manage everything yourself, but once you understand the foundation, you'll know who to trust and how far to trust them.
3. When someone says "it has to be this way," ask "does it really?"
You don't need to argue. Just ask quietly — is there evidence for this? Or has it just been done this way for a long time? Many things people say "have to be" a certain way are really just things that "used to be" that way.
4. Ask "what do I actually need?" before looking for a solution
Most people rush toward answers before they've understood the problem. If you're feeling burned out at work, the instinct is to take a vacation. But asking from first principles might reveal that what you really need is to feel seen and valued — and a week off won't fix that. Find the real cause, and you can address it in a way that actually works.
The hardest part of first principles isn't asking the questions — it's accepting that what you've believed all along might not actually be true.
Mental Model #1 — Mathematics
Beyond compounding, there are two more things worth knowing
The hard part of mathematics isn't the calculation. It's applying the knowledge to real life, every day.
The clearest example is credit card debt — a lot of people see 0.9% monthly interest and think it's not much. But that works out to over 10% per year. Miss one payment and it starts stacking up fast. Most people never stop to do that math. That gap in understanding is exactly what separates people who truly get compounding from those who don't.
Permutations and Combinations — Don't decide before you've seen the whole picture
Think about the last time you were job hunting. Most people's first question is "where should I apply?" — and they start sending resumes immediately.
But if you think like Charlie, there are two questions to ask first.
Layer one: How many options do you actually have? — This is Combinations
Before deciding, you need to see what options you might be overlooking — not just what's right in front of you.
Instead of asking "should I apply to company A or B?", try asking — what else haven't I counted? Freelance? Further study? Moving cities? Using a connection I already have? Once you see the full picture, the decision improves immediately — because you're no longer choosing from a set that was too narrow to begin with.
Layer two: Does the order matter? — This is Permutations
Once you see all the options, the next question is — what should come first?
Build your network first then look for jobs, versus look for jobs first then build your network — same two actions, different order, very different results.
Or with investing — learn first then invest, versus invest first then learn — each gives you a completely different kind of experience.
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Charlie didn't use these concepts to calculate — he used them to stop himself from deciding before he'd seen everything. That's the most important difference.
The Fermat-Pascal System — Think in probabilities, not black and white
Fermat and Pascal were 17th century mathematicians who laid the foundation for modern probability theory. Charlie loved this because it forces you to think in terms of a distribution of outcomes — not certainties.
Instead of asking "will this work?", ask:
What are all the scenarios that could happen? How likely is each one? If you add them all up, what's the expected value?
And this is why Charlie loved saying "invert, always invert" — instead of asking how to succeed, ask first what would make you fail. Then avoid it.
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Let's apply this to a career decision — say you're thinking about leaving your job.
Most people ask "will the new job be better?" But thinking through the Fermat-Pascal lens, the questions become:
What scenarios could actually happen? The new job turns out better than expected / worse than expected / about the same / you leave and struggle to find something new.
How likely is each? No one knows for sure. But if you've done your homework — spoken to people at the company, read reviews, understood the culture — the probability of "worse than expected" shrinks considerably.
If the worst case happens, can you handle it? This is the invert. Instead of dreaming about the best case, ask first: if it doesn't go as hoped, do you have a backup plan? How many months of savings do you have? Will your current skills carry you through?
This kind of thinking doesn't make you afraid of change — it makes you more informed when you decide. And if things don't turn out the way you hoped, at least you know you thought it through.
So how do you give yourself the time to think this way?
Charlie and Buffett both spoke about this the same way — they actively protected their thinking time. Buffett famously said he spends 80% of his day reading and thinking, which sounds impossible for most people. But the point isn't the number of hours. It's
deliberately creating space to think.
Some ways to start:
Don't decide on important things immediately When something big arrives, like a job offer or an investment opportunity, give yourself 24-48 hours before responding. Not because you're unsure, but because mapping out every scenario takes time.
Write it down before you decide When facing an important decision, write out the possible scenarios first. It doesn't have to be perfect. Getting it out of your head and onto paper almost always surfaces angles you wouldn't have seen otherwise.
Find your own quiet time Charlie read. Buffett walked in the mornings. Everyone has a time of day when their thinking is sharpest. Figure out when yours is, and protect it.
Charlie believed this kind of thinking isn't a special talent — it's a habit. But it requires space and time that you have to build for yourself.
Decision Tree — A map for making decisions
A decision tree is Fermat-Pascal in action
— you break every option into branches, and each branch shows probability × outcome. Add them up and you get the expected value of each path.
A simple example:
Accept new job
├── Better than expected (60%) → gain skills and income
└── Worse than expected (40%) → lose time, but gain a lesson
Stay in current job
├── Continue to grow (50%) → stable but slow
└── Stay stuck (50%) → miss other opportunities
Charlie didn't literally draw this every time — but in his head, he was always thinking this way. So was Buffett.
If we don't train ourselves to think like this, and we end up sitting across from someone who does it automatically, we're at a disadvantage without even knowing it.
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The most important thing a decision tree gives you is this — a good decision can still have a bad outcome, and a bad decision can still get lucky. But when you've thought it through carefully, and things don't go as hoped, you're less likely to blame yourself — and more likely to treat it as a lesson.
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The next mental model Charlie covers is accounting — EP.3 coming soon
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