# Franco-Anglo Mathematics Research Cooperation

French people are rational (think before action), English people are imperative (action before think).

17CE French Mathematician & Philosopher René Descarte : “I think therefore I am” 我思故我在 。He invented Analytical Geometry (xyz cartesian geometry).

De Moivre Theorem:
$(cos \: {x} + i.sin \: {x})^{n} = cos \: {nx} + i.sin \: {nx}$

http://www3.imperial.ac.uk/
newsandeventspggrp/imperialcollege/newssummary/news_10-1-2018-16-41-35

# Probability by 2 Great Friends

Today Probability is a “money” Math, used in Actuarial Science, Derivatives (Options) in Black-Scholes Formula.

In the beginning it was “A Priori” Probability by Pascal (1623-1662), then Fermat (1601-1665) invented today’s “A Posteriori” Probability.

“A Priori” assumes every thing is naturally “like that”: eg. Each coin has 1/2 chance for head, 1/2 for tail. Each dice has 1/6 equal chance for each face (1-6).

“A Posteriori” by Fermat, then later the exile Protestant French mathematician De Moivre (who discovered Normal Distribution), is based on observation of “already happened” statistic data.

Cardano (1501-1576) born 150 years earlier than Pascal and Fermat, himself a weird genius in Medicine, Math and an addictive gambler, found the rule of + and x for chances (he did not know the name ‘Probability’ then ):

Addition + Rule: throw a dice, chance to get a “1 and 2” faces:
1/6 +1/6 = 2/6 = 1/3
(Correct: 1 & 2 out of other six faces)

Multiplication x Rule: throw two dices, chance to get a “1 followed by a 2 ” faces : 1/6 x 1/6 = 1/36
(Assume 1st throw does not affect or influence the 2nd throw: independent events)

Pascal never met Fermat personally, only through correspondences (like emails today), but Pascal regarded with respect Fermat as superior in Math than himself.

Fermat and Descartes were not so. Descartes openly criticized Fermat as a second class mathematician. Both independently discovered Analytical Geometry, but Descartes scored the credit in ‘Cartesian’ coordinates.

Fermat never published any books in Math. As a successful judge in Toulous, he spent his free time as an amateur mathematician, especially in Number Theory. He showed his Math discoveries to friends in letters but never provided proofs. Hence the Fermat’s Last Theorem made the world mathematicians after him (Gauss, Euler, Kummer, Sophie Germaine, Andrew Wiles…) busy for 380 years until 1994.

Fermat died 3 years after Pascal. Another Modern Mathematics was being born – Calculus – in UK by Newton and Germany by Leibniz. Probability was put in the back seat over-taken by Calculus.

# De Moivre

De Moivre (1722)

$(Cos A+iSin B)^n = Cos nA + i.Sin \:nA$
– French Protestant, jailed by the Catholic King Louis XIV (14th), exiled to UK.
– Gave Tuition in the Duke home where he met Newton with the newly published book “Principia” and the “New Math” Calculus, he self-paced study to become expert in Calculus.
– He never got a Professor job despite Newton and Leibniz’s help.
– He observed gambling in coffee shops, invented the Game Theory.
– He liked to sleep. One day he declared he would sleep 20 mins more per day. On 73rd day when he accumulated 24 hrs more, he died at 87 yrs old !