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Key Discoveries and Contributions:
1. De Moivre’s Theorem:
* A fundamental formula linking complex numbers and trigonometry.

* This theorem is crucial in complex analysis, and its proof relies on mathematical induction and trigonometric identities.
2. Probability Theory:
* De Moivre’s most important contribution is his work on probability, published in “The Doctrine of Chances” (1718).
* He advanced methods for calculating probabilities of complex events, such as gambling outcomes.
* Introduced concepts that later led to the normal distribution (the bell curve). He showed how the binomial distribution approximates the normal distribution as the number of trials increases — an early form of the central limit theorem.
3. Mortality Tables:
* De Moivre created one of the earliest mortality tables, used for calculating annuities and insurance risks.
* His work helped develop actuarial science, laying the groundwork for modern life insurance calculations.
4. Stirling’s Approximation:
* Though often credited to James Stirling, De Moivre also independently contributed to what is now known as Stirling’s approximation — an approximation for factorials used in probability calculations.

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