He never published a single book. He wasn't a professor. He didn't even have a degree in math. Pierre de Fermat was, by all accounts, a busy government lawyer in 17th-century Toulouse who happened to spend his evenings ruining the lives of future mathematicians.
It's kinda wild when you think about it. Most people know him for a single "Last Theorem" that took over 300 years to solve, but the real story of Pierre de Fermat is much weirder. He was the king of the "marginalia"—scribbling world-changing ideas in the borders of books and then basically ghosting the scientific community. He didn't want the fame. He wanted the puzzle.
The Mystery of Pierre de Fermat and the Empty Margin
Fermat was born in Beaumont-de-Lomagne, France, around 1601 (historians still bicker over the exact date). He lived a double life. By day, he was a magistrate, a "Counselor at the Parliament of Toulouse." It was a high-stakes job involving local law and order. But by night? He was the most prolific amateur mathematician in history.
He didn't write for journals. Instead, he sent letters. He’d write to guys like Marin Mersenne or Blaise Pascal, drop a massive mathematical truth bomb, and then refuse to show his work. It was the 17th-century equivalent of "trust me, bro."
The most famous instance of this happened in the margins of his copy of Arithmetica by Diophantus. Around 1637, he looked at the Pythagorean theorem—$a^2 + b^2 = c^2$—and wondered what happened if the power was higher than two. He wrote down that $n$ cannot be greater than 2 for $x^n + y^n = z^n$ to have whole number solutions. Then, he wrote the sentence that launched a thousand breakdowns: "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."
He died in 1665 without ever sharing that proof.
For 358 years, the greatest minds in the world, from Leonhard Euler to Sophie Germain, tried to find that "marvelous proof." It wasn't until 1994 that Sir Andrew Wiles finally cracked it using 20th-century modular forms and elliptic curves—math that Fermat couldn't possibly have known. This leads to a spicy debate among math nerds: Did Fermat actually have a proof, or was he just trolling? Most modern experts, like Simon Singh, author of Fermat's Enigma, suspect Fermat was either mistaken about having a proof or was playing a very long game.
He Basically Invented Calculus (And Nobody Gave Him Credit)
Everyone talks about Isaac Newton and Gottfried Wilhelm Leibniz when it comes to calculus. They get the statues. They get the textbooks. But Pierre de Fermat was doing the heavy lifting decades before they even started.
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Fermat developed a method for finding the maxima and minima of curves. It's called "adequality." Basically, he was looking at the slopes of lines and finding the peaks and valleys of functions before the term "derivative" even existed.
Newton actually admitted in a letter that his own work on calculus was based on "Fermat's way of drawing tangents." That’s a huge admission. If Fermat hadn't been so secretive—or if he had bothered to actually publish his methods—we might be calling it "Fermatian Math" instead of Calculus.
He was also a pioneer in optics. If you've ever wondered why light bends when it hits water, you’re looking at Fermat’s Principle of Least Time. He hypothesized that light always takes the path that requires the least amount of time, not necessarily the shortest distance. This was revolutionary because it suggested a sort of "efficiency" in nature that hadn't been quantified before.
Gambling, Probability, and a Mid-Life Crisis
In 1654, a professional gambler named the Chevalier de Méré asked Blaise Pascal a question about how to divide the stakes in an unfinished game of dice. Pascal, feeling the pressure, reached out to Fermat.
What followed was a series of letters that effectively birthed the modern theory of probability.
Before these two started nerding out over dice, people thought luck was just... luck. Or God. Or fate. Fermat and Pascal realized you could use math to predict the future—or at least the likelihood of it. They mapped out the "Problem of Points," figuring out how to fairly split a pot of money if a game is interrupted.
This wasn't just about gambling. It changed everything.
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- Insurance? Probability.
- Risk management? Probability.
- The stock market? Probability.
- Your weather app? Fermat and Pascal’s letters.
Honestly, it’s hilarious that a lawyer and a religious philosopher created the foundation for the entire modern financial industry while trying to help a guy win at dice.
The Man Behind the Math
Fermat wasn't a social butterfly. Because he held a high-ranking legal position, he was actually discouraged from socializing too much. The idea was to prevent bribery or corruption. If he didn't have friends, he couldn't be influenced.
This isolation probably fueled his obsession with math. It was his escape. He was known to be a bit prickly in his correspondence, often challenging other mathematicians to solve problems he had already cracked. René Descartes, the "I think, therefore I am" guy, absolutely hated Fermat. He called him a "braggart" and tried to discredit his work on tangents.
Fermat didn't care. He just kept scribbling.
He survived the plague in 1653. In fact, his death was actually reported prematurely during the outbreak. He lived for another twelve years, eventually dying in Castres. His son, Samuel, was the one who finally published his father’s notes, including that infamous margin scribble. Without Samuel, Pierre de Fermat might have been a complete footnote in history.
Why Fermat Still Matters in 2026
You might think 17th-century number theory is irrelevant to your life. You'd be wrong.
Fermat’s Little Theorem (not the "Last" one, but a different one) is the backbone of modern cryptography. Every time you buy something on Amazon or send an encrypted WhatsApp message, you are using math that Fermat messed around with in his study.
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The theorem states that if $p$ is a prime number, then for any integer $a$, the number $a^p - a$ is an integer multiple of $p$.
$$a^p \equiv a \pmod{p}$$
This property is what allows RSA encryption to work. We use massive prime numbers to lock our data, relying on the fact that Fermat’s patterns hold true. If Fermat hadn't been obsessed with the "purity" of numbers, our digital world would be significantly less secure.
How to Think Like Fermat
Fermat wasn't a genius because he knew more than everyone else. He was a genius because he looked for patterns where others saw chaos. He was an amateur who outperformed the pros because he wasn't afraid to play.
If you want to apply "Fermatian" logic to your own life or work, here are a few things to consider:
- Solve for the sake of solving. Fermat didn't care about the "use case." He cared about the truth. Sometimes the most "useless" hobby becomes your greatest legacy.
- The Power of Marginalia. Don't just consume information. Interact with it. Scribble in your books. Challenge the assumptions of the authors you read.
- Prime focus. He obsessed over the fundamentals—prime numbers. In any field, the most complex problems are usually solved by understanding the simplest building blocks more deeply than anyone else.
- Embrace the "unsolved." He left a problem that lasted three centuries. It's okay to leave things unfinished if the pursuit itself pushes the world forward.
Fermat’s life reminds us that you don't need a fancy title or a laboratory to change the world. You just need a pen, a margin, and a really good question.
Next Steps for Deepening Your Knowledge:
- Read "Fermat's Enigma" by Simon Singh. It is widely considered the definitive narrative on the hunt for the Last Theorem's proof.
- Explore Number Theory Basics. Look into the difference between Fermat's Little Theorem and Fermat's Last Theorem to see how they impact modern coding.
- Investigate the Pascal-Fermat Correspondence. Read the actual translated letters from 1654 to see how the logic of probability was built from scratch.
- Study "Adequality." If you're into math, look at Fermat's pre-calculus methods to see a different way of conceptualizing slopes and curves.