If Leonard Baum supplied a piece of mathematics, James Ax supplied something just as important: the first real attempt to turn Jim Simons' hunch about markets into an actual trading operation. Ax was a number theorist — serious, decorated, the kind of mathematician who'd made his name proving deep results long before he ever looked at a price chart. In the early 1980s, he and Simons formed a partnership that would eventually become Renaissance Technologies. But the company didn't start there. It started as Axcom Trading Advisors, a smaller, rougher, far less certain venture — and its early years looked nothing like the legend that came later. A Partnership Before There Was Proof When Simons and Ax began working together, there was no Medallion Fund, no track record, no thirty-year story to point to. There was a theory: that markets contained statistical structure a rigorous enough model could find, and that this structure could be traded systematically instead of on ...
Before there was a Medallion Fund, before Renaissance Technologies existed as a name, there was a piece of mathematics almost nobody outside a narrow academic circle had heard of, and a mathematician who had never set out to solve a market problem. The mathematician's name was Leonard Baum. Leonard Baum spent his career on a problem that sounds abstract to the point of uselessness: how do you infer the hidden state of a system when all you can see is a noisy, partial signal generated by it? Working through the 1960s alongside colleagues like Lloyd Welch, Baum helped develop what's now called the Hidden Markov Model — a mathematical framework for figuring out what's probably happening beneath the surface of data, using only the messy, incomplete observations that surface produces. It was built for speech recognition and codebreaking, not stock charts. And that's precisely why it mattered so much when Jim Simons brought Baum into the fold. The Insight Nobody in F...