The Eve Before Calculus : Fermat


The Mathematical Revolution That Was Bred on a Sheep Farm | OpenMind

In 17CE a similar plague like COVID19 forced a young man Newton to be quarantined in a sheep farm for 2 years, he changed the universe with Differential & Integration Calculus, to “move” the planets.

Will COVID19 give birth to another “Newton” in some “kampong” at one corner in USA or China or Europe ?

One of the world’s most influential math texts is getting a beautiful, minimalist edition – The Verge

Little print-edition of Math Classics: Euclidean 《The Elements》(几何原理) – the second printing by volume after 《The Bible》.

The Euclidean Geometry was less emphasised in Secondary school from 1970s in the world (80s in Singapore) to be replaced by Vector Geometry (UK/USA) and Abstract Linear Algebra aka Vector Space / Affine Geometry (in France). It was a pedagogical mistake now these countries recognise – never “Throw the baby (Euclidean Geometry) together with the bath water (Old Maths )”.

IMO Competition usually has 2 out of 6 problems in Euclidean Geometry but no modern math or Calculus, reason being to cater for 100+ countries still with Classical Math. That’s why the Asian countries – South Korea (2017 IMO Champion), China (2nd IMO 2017), Vietnam (3rd IMO 2017) , HK, Taiwan, Thailand, – with old syllabus are top IMO but not the Advanced countries (France, UK, other European, Japan, USA, Singapore…).

Nephew and Maternal Uncle

There is a common proverb in my Chinese dialect Fujian spoken today in China Fujian province, Taiwan, Singapore and Malaysia, which says
“A nephew is like his maternal uncle”  外甥像母舅
In modern Biology we know mother passes some genes to her children. Some disease like colorblind is carried by mother down to her sons, the mother herself is immune but her brothers are colorblind as the nephews.
Interesting behavior, intelligence are also similarly inherited from mother and maternal uncles.

Two greatest mathematicians in the history, Newton and Gauss, were the lucky nephews from their maternal uncles who were highly educated to spot the nephew’s genius, although the boys’ parents were uneducated.

Newton’s father died early, mother Hannah Ayscough had a brother William Ayscough educated in Cambridge. William convinced Hannah to send the talented boy Newton to Cambridge.

Gauss’s father was a bricklayer, mother Dorothy Benz had a younger brother Friedrich Benz, who was an intelligent man, rescued young Gauss from following his father’s footsteps as bricklayer.

I met two talented boys, one won the top International Math Olympiad prize, the other excels in the national PSLE exams, their respective mother and father are not highly educated, but their maternal uncles are top scholars.

However, there are serious consequences of (Parallel or Cross) cousin’s inter-marriage from maternal link. Charles Darwin first discovered this genetic problem because he and his wife were such cousins.

The ancient Chinese liked to marry between cousins from maternal side. We praised the practice as “close relatives getting closer” 亲上加亲. The daughter-in-law would likely get along well with the mother-in-law because of the maternal family blood link. The last Qing dynasty emperors were the products of such marriage custom, and most of them were incompetent emperors who died young.

This widely mal-practice of inter-marriage had probably been the cause of the decline of the brilliant Chinese civilization from 14th century (Ming dynasty). China went to sleep for 500 years till awaken from 1911 – as Napoleon imprisoned by the British in St. Helena Island warned the British not to wake up the ‘sleeping lion’, else China would shake the world (*) (she does today as the World’s 2nd super-power) – by the European colonizers (#) in Opium wars and the Japanese invasion.

This Antropology of Kinship Problem is interestingly a modern math problem in Group Theory, first studied by André Weil for the Australian aborigines.

Notes (*): Napoleon’s famous warning to his British enemy before the Opium Wars which humiliated China:
“Quand la Chine s’eveillera, la terre tremblera.”

(#): England, France, Germany, Russia, Japan, USA, Austria and Italy. Ironically France was led by Napoleon’s nephew Napoleon III.

Eccentric Issac Newton

Newton on how he made his discoveries:
“I keep the subject constantly before me and wait until the first dawnings open little by little into the full light.”

Newton was Lucasian prof of math at Cambridge. It was not obvious to
his students that he would become the greatest scientist in history.

His students wrote:
“… So few went to hear him, and fewer yet understood him, that
oftimes he did in a manner, for want of Hearers, read to ye Walls. ”

“He always kept close to his studies, very rarely went a visiting, &
had as few visitors… I never knew him take any Recreation or
Pastime, either in Riding out to take ye Air, Walking, Bowling, or any
other Exercise whatever, thinking all Hours lost, that was not spent
in his studies… He very rarely went to Dine in ye Hall…& then, if
He has not been minded, would go very carelessly, with shoes down
heels, stockings untied, surplice on, & his head scarcely combed. ”

The genius of Newton was only discovered in 1684, when Dr. Edmund
Halley went to see him : “… Halley asked Newton what he thought the
curve would be subscribed by the planets supposing the force of
attraction towards the Sun to be reciprocal to the square of their
distance from it. Newton replied immediately that it would be an
ellipsis. Halley struck with joy and amazement asked him how he knew
it, why saith he I have calculated it…”

3 years later after the meeting with Halley, Newton published his Principia.

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 !