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)

$latex (Cos A+iSin B)^n = Cos nA + i.Sin \:nA$
- 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 !

Quotations

1. Issac Newton: Hypotheses non fingo (I frame no hypotheses)

2. Gauss: Pauca sed matura (Few but ripe)

3. Descartes: Bene vixit qui bene latuit (he has lived well who has hidden well.)

Newtonian Calculus not rigorous !

Why Newton’s Calculus Not Rigorous?

$latex f(x ) = \frac {x(x^2+ 5)} { x}$ ...[1]

cancel x (≠0)from upper and below => $latex f(x )=x^2 +5 $

$latex \mathop {\lim }\limits_{x \to 0} f(x) =x^2 +5= L=5 $ ...[2]

In [1]: we assume x ≠ 0, so cancel upper & lower x
But In [2]: assume x=0 to get L=5
[1] (x ≠ 0) contradicts with [2] (x = 0)

This is the weakness of Newtonian Calculus, made rigorous later by Cauchy's ε-δ 'Analysis'.