In 1809 Gauss published Theoria motus corporum coelestium, which contained his method for determining planetary orbits from noisy observations. Central to this work was the principle that the best estimate of a quantity is the one that maximises the probability of the observed data — the foundation of maximum likelihood estimation. Gauss showed that when errors follow a normal distribution, this reduces to the method of least squares.
While de Moivre first derived the bell curve, Gauss gave it its modern form and its deepest justification. He proved that the normal distribution is the unique distribution that makes the arithmetic mean the optimal estimator. This result — the Gauss-Markov theorem in its simplest form — is why the normal distribution appears everywhere: it is the natural consequence of averaging many small, independent errors.
Gauss introduced the concept of probable error — the predecessor of the confidence interval. He showed how to quantify not just an estimate but the precision of that estimate. This framework for reasoning about uncertainty in measurements translates directly to quantitative finance: every signal has an estimate and an error bar, and rational allocation requires knowing both.
Every signal our scoring engine produces has both a value and an uncertainty estimate. Gauss's error theory is the framework that lets us distinguish genuine signals from noise, and allocate capital proportional to our confidence.