# The Map of Mathematics

Show to your schooling children why they need to study Maths – the Queen of all Sciences – which pushes the frontier of human evolution in last 3,000 years. Maths is always invented few centuries or decades before it becomes useful. For examples:  Complex numbers invented accidentally by the 16th century Italian Mathematicians for solving polynomial equation of 3rd degree, became useful in Physics Electrical and Magnetic Fields (19 CE) ; Invention of Analytic Geometry (17 CE) allowed Newton to trace the earth-sun orbit; Calculus propelled Physics and Physical Chemistry; Leibniz’s Binary Math (18 CE) discovery applied in Computing (20 CE)…

Latest Examples

1. Topology was invented in 1900 by French PolyMath Henri Poincaré, today applied in Big Data, AI…

2. His PhD student invented “Derivatives” Partial Differentiation, today applied in Commodity Trading, Stock Trading, Financial Derivatives… with Black-Sholes formula. 1998 USA Sub-Prime Crisis due to the misuse and lack of understanding of its limitation (“fat tail” ).

3. Mathematician SS Chern 陈省身and Nobel Physicist Yang Zhen-Ning 杨振宁were working independently in the USA for 40 years, Chern on Differential Geometry, Yang on Yang-Mill Equation (one the 7 unsolved Math Problems in 21st century). Through a common friend the hedge fund billionaire James Simons – Chern’s former PhD Math student and university colleague of Yang – they realised that the Math “Fiber Bundles” (纤维丛) invented by Chern 30 years earlier could apply in Yang’s Physics (Gauge Theory).

# Trump’s Speaking Math Formula

The lower in the score the better : Trump (4.1) beats Hillary (7.7) who beats Sanders (10.1)

Trump defied most expectation from the world to win the 2017 President of the USA. His victory over the much highly educated Ivy-league Yale lawyer-trained Hilary Clinton who speaks sophisticated English is “SIMPLE English“: seldom more than 2-syllable words.

1-syllable words mostly: eg.dead, die, point, harm,…

2-syllable words to emphasize: eg. pro-blem, ser-vice, bed-lam (疯人院), root cause, …

3-syllable words to repeat (seldom): eg. tre-men-dous

His speech is of Grade-4 level, reaching out to most lower-class blue-collar workers who can resonate with him. That is a powerful political skill of reaching to the mass. Hilary Clinton’s strength of posh English is her ‘fatal’ weakness vis-a-vis connecting to the mass.

In election time, it is common to see candidates who win the heart of voters by using the local dialects of the mass, never mind they are discouraged in schools or TV: Hokkien, Teochew, etc.

# Singapore Math (PSLE)

This is the typical Singapore PSLE Math for 12-year-old school students sitting for Primary School Leaving Exams (PSLE).

The Primary 6 kids have not learnt Algebra, which will be taught only 1 year later in Secondary schools.

Singapore is proud of her unique “Singapore Math“, characterised by Polya-style Problem-Solving Process , aided with visual Modelling and Guesstimation techniques.

It is Singapore’s secret of being the World’s 2nd position in PISA Test (Math), after China (Shanghai) which beats us with Algebra teaching at this age.

See if you can solve this problem without Algebra.

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# 数学名词妙翻译

Homology: 同调 (江泽涵 教授)
Homotopy : 同伦 (江泽涵 教授)
Manifold : 流形 (源于文天祥的《正气歌》: 天地有正气，杂然赋流形)
Geometry: 几何 (明朝 徐启光 / Italy Jesuit 利马窦 )
Topology: 拓朴 (杜甫诗)

# Truth = Knowledge + Understanding + Believe

K = Knowledge (comes from Proving)
U = Understanding
B = Believe

U is the mediator between K & B

Truth = KUB
Eg. Mathematics:
1 + 1 = 2

KB = Know & believe but do not understand.
Eg. Diseases like cancer, Chinese Accupuncture, …

B: Believe but do not understand or know.
Eg. Axioms, Religion

K : Know but do not understand or believe.
Eg.

KU : Know, Understand but do not believe.
Eg.

U: Understand but do not know or believe.
Eg. ?

UB: Understand, believe but do not know.
Eg. [Impossible]

# 3rd Isomorphism Theorem

This 3rd Isomorphism Theorem can be intuitively understood as:

G partitioned by a bigger normal subgroup H
is isomorphic to:
{G partitioned by a smaller normal subgroup K (which is a subgroup of H)}
partitioned by
{H partitioned by a smaller normal subgroup K}

or, by ‘abuse of arithmetic’: divide G & H by a common factor K.

$(G / H ) = (G / K ) / (H / K )$

Analogy:
\$100 / \$50 = 2 (two \$50 notes makes \$100)
is same (isomorphic) as
\$100 / \$10 = 10, (ten \$10 notes makes \$100)
\$50/\$10 = 5, (five \$10 notes makes \$50)
then 10/5 = 2 (ten notes split into five is two )