Infinite Cake

The Big Internet Math-Off, Round 1 – James Tanton v Nira Chamberlain | The Aperiodical

http://aperiodical.com/2018/07/the-big-internet-math-off-round-1-james-tanton-v-nira-chamberlain/

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Celebrates Mathematician Gottfried Wilhelm Leibniz’s 372nd Birthday

https://www.forbes.com/sites/kionasmith/2018/06/30/sundays-google-doodle-celebrates-mathematician-gottfried-wilhelm-leibniz/

My favorite mathematician is German Leibniz, who co-invented Calculus with Newton.

Today we thank Leibniz for his elegant Calculus symbols:

\boxed {\frac{dy}{dx}}

\boxed{\int_{0}^{\infty}x^{n}e^{-x}dx}

Leibniz also invented 01 binary algebra, which he later found it was already in the 3,000-year-old Chinese “Yin-Yang” (阴阳 八卦), so impressed that he recommended to the most powerful western (French) king Louis XIV (14th) to use Chinese as the Universal Language of the world.

The rich Newton sued Leibniz for plagiarism of Calculus, until Leibniz died poor in bankruptcy, buried in a common unknown grave.

The war between Newton & Leibniz extended & lasted 100 years between UK Math Community and Continental Europe Math Community. As a result UK lost its math leadership after Newton, France (Lagrange, Fourier, Cauchy, Galois… ) followed by Germany (Felix Klein, Gauss, Hilbert, Riemann …) took over as the world center of math. After WW2 many German mathematicians (mostly Jewish eg. Noether, Gödel, Artin, …) fled to the USA which is now the Kingdom of Advanced Math.

困扰了人类358年 费马大定理 Fermat’s Last Theorem

Keywords:

  1. Fermat’s Last Theorem (FLT): \boxed {x^{n} +y^{n} = z^{n} \; \; \forall n >2 }
  2. Pierre de Fermat (France 1637 AD): FLT Conjecture or Prank ?
  3. Euler (n= 3)
  4. Taniyama(谷山)-Shimura(志村)-(André) Weil Conjecture (now Theorem)
    Modular Form = Elliptic Curve
  5. Galois Group Symmetry
  6. Andrew Wiles (UK Cambridge 1994):
    (Modular Form = Elliptic Curve) <=> FLT (q.e.d.)

Notes:

1. Do not confuse Prof Andrew Wiles (proved FLT) with (French/American) Prof André Weil (Founder of Bourbaki School of Modern Math in POST-WW2 universities worldwide).

2. When Shimura heard that FLT was proved finally by Andrew Wiles using his Conjecture (Theorem), he was very calm, said, “I told you so”.

3. There is another “Fermat’s Little Theorem” used in computer cryptography.

4. The journey of proving FLT in 358 years by all great mathematicians worldwide had created many new math tools and Number theories (eg. “Ideals” in Ring Theory, etc).

World Cup Math Analysis : Korea vs Germany (2:0)

World Cup 2018

Surprising Result:

World No.1 (Germany) Lost to World No.59 (Korea) – why ?

Reason: Math !

For weak Korea to win, the best strategy is to keep the goal number as low as possible with strongest defence.

Conclusion: Highest chance for Korea to beat Germany is either 1 or 2 goals !

Germany lost by not launching a strong attack to score as many goals as possible.

Note : 2017 International Math Olympiad (IMO) World Champion Team was Korea.

The actual Game proved the Korean “Math” strategy was right: (2:0)

The Software War : Object-Oriented Programming (OOP) vs Functional Programming (FP)

The “war” of OOP vs FP is akin to Applied Math vs Pure Math.

The formers (OOP & Applied Math) are not “rigourous” but practical, compared to the laters (FP & Pure Math) which are elegant but too abstract for popular usage.

OOP: SmallTalk and its followers – C++, C#, Objective-C, Java…

FP: LISP and its followers – Haskell, Clojure, …

The “hybrid” (OOP&FP): Scala, Kotlin (Google: Java ‘cousin’), Swift (Apple: Objective -C ‘cousin’), F# (MicroSoft)

The “cons” of OOP, which are bad for concurrency / parallel computing in multi-cored CPU:

  1. State changed
  2. Side-effect
  3. Mutability of data
  4. Polymorphism

https://blog.cleancoder.com/uncle-bob/2014/11/24/FPvsOO.html