There’s a 'universal' math rule that explains why everything from earthquakes to growing bacteria follows the exact same pattern.
March 26, 2026
Original Paper
Beyond the Central Limit: Universality of the Gamma Distribution from Padé-Enhanced Large Deviations
arXiv · 2603.23567
The Takeaway
Most people are taught that random data eventually forms a "Bell Curve." This paper proves that for anything that cannot be a negative number—like the size of an epidemic or the energy of a forest fire—the Bell Curve is mathematically incorrect, and a different "Gamma" shape is the true universal law.
From the abstract
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical systems described by positive random variable -- from earthquakes to microbial growth to epidemic spreading -- consistently exhibit gamma rather than Gaussian statistics -- what leads to field-specific mechanistic explanations that are non robust to small cha