One equation spawned four multi-trillion dollar industries and fundamentally changed how humans think about risk. That's the kind of claim that makes you stop and pay attention — and Derek Muller delivers on that promise in "The Trillion Dollar Equation," a piece that traces how a single mathematical breakthrough transformed finance from a guessing game into a quantifiable science.
The Physics of Finance
The narrative begins with Jim Simons, a mathematics professor who founded the Medallion investment fund in 1988. Muller writes, "every year for the next 30 years The Medallion fund delivered higher returns than the market average and not just by a little bit it returned 66% per year — at that rate of growth $100 invested in 1988 would be worth $8.4 billion today." This isn't a typo. Simons didn't become wealthy through some secret trading system — he built his fortune on applying mathematical rigor to financial markets when the rest of Wall Street was still guessing.
The contrast with Isaac Newton is deliberate and devastating. Muller recounts how "Newton invested in stocks" and put money into the South Sea Company, which was shipping enslaved Africans across the Atlantic. When asked why he didn't see the crash coming, Newton responded: "I can calculate the motions of the heavenly bodies but not the madness of people." This is the central puzzle the piece poses — what did Simons know that Newton didn't?
The answer lies in Louis Bachelier, a physicist who found his way to the Paris Stock Exchange in the 1890s and saw "hundreds of traders screaming prices, making hand signals and doing deals." What captured his interest were contracts known as options — financial instruments that had been around for hundreds of years without any reliable pricing mechanism. The earliest known options were purchased around 600 BC by the Greek philosopher Thales of Miletus, who paid olive press owners a small fee to secure the right to rent their machines at a specified price during harvest.
The Discovery
Bachelier realized that stock prices follow what he called "a random walk" — essentially a coin flip determining whether prices move up or down. Muller explains: "the best you can do is assume that at any point in time the stock price is just as likely to go up as down and therefore over the long term stock prices follow a random walk." This insight was the key to pricing options fairly, and Bachelier had rediscovered it independently of Einstein's work on Brownian motion.
The piece walks through how options work — call options give you the right but not the obligation to buy something at a later date for a set price, while put options protect against downward movements. The "three advantages" Muller outlines show why derivatives became so powerful: limiting downside risk, providing leverage, and serving as hedges.
Bachelier's insight was that "the fair price is what makes the expected return for buyers and sellers equal — both parties should stand to gain or lose the same amount." This mathematical framework would eventually become the Black-Scholes equation, discovered independently by Fischer Black and Myron Scholes in the 1970s.
The Missing Piece
But here's where Muller tells a compelling story about neglect: "when Bachelier finished his thesis he had beaten Einstein to inventing the random walk and solved a problem that had eluded options traders for hundreds of years but no one noticed — the physicists were uninterested and traders weren't ready." The equation existed without anyone understanding how to make money from it. The piece notes this as the key gap — mathematics alone doesn't create financial markets; you also need infrastructure, regulation, and capital to actually trade on these insights.
I can calculate the motions of the heavenly bodies but not the madness of people.
Bottom Line
The strongest argument in this piece is that finance is a physics problem — and understanding risk requires the same rigor as understanding heat diffusion or Brownian motion. The vulnerability is that the trillion-dollar claim oversimplifies history: the equation alone didn't create modern derivatives markets; regulation, computing power, and global capital flows did the heavy lifting. Still, Muller makes an irrefutable case that mathematics transformed how we think about risk — and that transformation has shaped every major financial institution on the planet.