Friday, December 21, 2007

Abraham de Moivre

Abraham de Moivre was born on May 26, 1667 in Champagne, France. His parents were protestants. When in 1685, Louis XIV overturned the Edict of Nantes which protected the rights of protestants. In this same year, de Moivre was arrested and put in prison for being a protestant. By 1688, he left France for protestant England.

When he was younger, de Moivre had studied classic mathematical works. He had read Christian Huygens text on probability. In the College de Harcourt had taken classes on physics and had studied under the French mathematician Jacques Ozanam. In London, de Moivre became a math tutor.

As a math tutor, de Moivre would teach at the homes of his students or at the London coffee houses. It was at this time that de Moivre learned about Newton's recent book Principia. De Moivre acquired a copy and managed to master it. He did so by removing the pages so he could carry parts of it with him and read it as he had free time.

De Moivre's reputation rose and he soon began meeting the famous mathematicians of England. He became friends with Edmund Halley and Sir Isaac Newton. He presented a paper to the Royal Society in 1695 and became a fellow of the Royal Society in 1697.

In 1710, he served on the committee that investigated the claims of Newton and Leibniz to be the inventors of calculus. Not surprisingly, this English committee ruled in favor of Newton.

De Moivre made many advances in the mathematics of his day. He made important progress in analytic geometry and probability theory. He wrote a textbook on probability in 1718. He did important work on mortality statistics and the study of annuities. Stirling's formula (which should perhaps be properly named De Moivre's formula) first appears in a work by De Moivre in 1733. The famous De Moivre formula never appears directly in any of his work but it is clearly spelled out in a paper in 1722.

Despite his impressive work, de Moivre was unable to find a permanent post and continued to earn his income as a math tutor. As such, he never rose to the same level of wealth as his mathematical peers. While England gave him free reign to be a protestant, it still discriminated against him for being French. De Moivre stayed poor throughout his life and never married.

Legend has it that de Moivre was able to correctly predict the date of his death. Supposedly, he noticed that he was sleeping 15 minutes longer each night. Based on his current duration of sleep, he predicted that he would sleep for 24 hours starting on November 27, 1754.


Roger Cotes' Formulas

Roger Cotes thoroughly investigated the factorization of x4 + a4. In doing so, he found the following formulas which he presented without proof:

Formula 1:

Formula 2:

Formula 3:

Formula 4:

These formulas demonstrated that Leibniz's supposition about x4 + a4 was incorrect.

The proof for these formulas would later be provided by Abraham de Moivre as he investigated the properties of the roots of unity.