Amazing Abraham de Moivre!

Abraham de Moivre. A French Mathematician whom is best known for his work on complex numbers (As seen in FP2 of the A Level Syllabus) and areas of trigonometry. Also, de Moivre is known for his work on probability theory and on the normal distribution (As seen in Statistics 1 of the A Level Syllabus).

He was born in France in 1667 and was pushed by his father to succeed in education as it is known that he was a person who highly believed in the value of education. Abraham went to the Christian Brothers’ Catholic school in Champagne, France which was very unusual given the religious conflict which was apparent in France at the time. He eventually went to the Protestant Academy of Sedan where he studied Greek.

De Moivre enrolled into Saumur to study logic which eventually he leads onto reading Mathematics on his own before he moved to Paris to study Physics where he had his first formal form of education for Mathematics.

Abraham then went through persecution in France and within two years he had moved to England where he became a private tutor of Mathematics and in meeting the Earl of Devonshire he saw Newton’s new book, Principia Mathematica where he vowed to be able to understand it. It is known that he carried scraps of the book around to read in his very limited time as he taught his students.

Arguably his most influential work was that of his formula:

formula 1

From which as you learn in the FP2 A Level Syllabus that this hold for all of the integer values (∀ n ∈ Z).

And then you can derive the more well-known form of this formula:

formula 2

Where this also holds for all of the integer values (∀ n ∈ ℤ). In 1749 though Euler proved this for all values of n which are real numbers (∀ n ∈ ℝ).

This is used in the expressed forms of complex numbers where z=x+iy both where x, y ∈ R. So we can express complex number z as z = r(Cos(ϑ)+iSin(ϑ)), where r = |z| (Modulus of Z) and ϑ is the principal argument. Building on the work of Euler we can express complex numbers in the exponential form where z = rℯ where again ϑ is the principal argument and r = |z| (Modulus of Z).

So to conclude, Abraham de Moivre was an influential Mathematician in the work of complex numbers and within probability theory even though he didn’t begin formally learning maths until in his teens. He came under stress from the French Persecution by King Louis XIV and moved to England where he then became good friends with Newton also.  De Moivre is most certainly one of Mathematics greatest minds.


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