Dissertation on Gaussian Error Function

The dissertation on the Gaussian error function represents a pivotal contribution to the field of mathematics, particularly in probability theory and statistics. The work was completed during the author's time at King's College, Cambridge, where he achieved first-class honors in mathematics. The dissertation, titled 'On the Gaussian error function,' was submitted in November 1934, with a formal acceptance occurring shortly thereafter. This research provided a proof of a version of the central limit theorem, which is fundamental in understanding how the sum of a large number of random variables tends to be normally distributed, regardless of the original distribution of the variables. This theorem has profound implications in various fields, including statistics, finance, and natural sciences, as it underpins many statistical methods and inferential techniques used today. The impact of this dissertation extends beyond its immediate mathematical contributions. The central limit theorem is a cornerstone of statistical theory, enabling researchers and practitioners to make inferences about population parameters based on sample statistics. The Gaussian error function itself is crucial in the context of normal distribution, which is widely used in statistical modeling and hypothesis testing. The acceptance of this dissertation marked a significant milestone in the author's academic career, laying the groundwork for future research and developments in mathematical logic and computation. The work has influenced numerous applications, from quality control in manufacturing to risk assessment in finance, demonstrating the enduring relevance of the Gaussian error function in both theoretical and applied mathematics.