If one were to pinpoint a singular turning point in the understanding of risk, it would likely be the development of probability theory in the 17th century through the correspondence between Blaise Pascal and Pierre de Fermat.
Before the formal development of probability theory, the concept of risk was largely approached through intuition, superstition, or experience. There wasn't a systematic or mathematical way to quantify uncertainty.
Precursor to Modern Risk Analysis: The groundwork laid by Pascal and Fermat allowed for the systematic study of random events. This transformed games of chance into mathematical problems, introducing concepts like expected value.
Application Across Fields: This mathematical foundation eventually permeated various fields like economics, insurance (actuarial science), and later, finance. Being able to mathematically model uncertainty made it possible to predict, manage, and insure against risks in unprecedented ways.
Influence on Decision Making: As the understanding of probability grew, it began to influence decision-making processes, emphasizing rational choices based on potential outcomes and their likelihoods. This would later give rise to utility theory and the understanding of human behavior concerning risk.
The Pascal-Fermat development of probability theory represents a paradigm shift in the understanding of risk. By introducing a structured, mathematical approach to uncertainty, it set the stage for sophisticated risk assessment and management techniques that have since become foundational in multiple disciplines.