# What is math?

What is Math ? Interesting article below:

https://infinityplusonemath.wordpress.com/2017/06/17/what-is-math/

• Mathematics = “that which is learned“ –(Pythagoras)

Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)…

What is Axiom, Lemma, Proposition ? Why rigorous Calculus was needed hundred years after Newton & Leibniz had invented it – “Epsilon-Delta” Analysis.

Difference between Riemann Integral & Lebesgue Integral ?

# Singapore Math for  Primary School Kids

Singapore scores the 2016 PISA Test World’s First in Math.

Below is the “Singapore Math” shown by a USA School adopting the pedagogy.

I had the opportunity to meet the inventor of the “Singapore Math” Prof Lee PengYee (李秉彝) in a Math seminar at NUS few years ago, who took the inspiration of the 1960s ~ 1970s Chinese School (P.S.L.E.  / Secondary 1) Math 算术 (literary means “Counting Technique” sans Algebra), combined with the Polya 4-Step Problem Solving Methodology [Video by Polya], with a visual tool called “The Model Diagram”.

Note: This pedagogy is based on Concrete Visualisation, while good for majority of young students (7 to 13 years old) to learn computation and problem solving, it doesn’t train the opposite skill from young in “abstractness” (eg. Basic Set Theory) which is the foundation required in university Advanced Math, where the French, Russian and USA university students excel more than the Asian cohorts.

The Ideal Math Education for the next 22nd Century

1) Singapore Math (Computation for Primary schools ) +
2) English Math (Applied Math for High Schools) +
3) French Math (Abstract Math for Universities)

Current Math education is biased towards any one &/or two (out of the three):

# 中国初中生集体挑战美国高考数学SAT题

[Hint]:

$(a + x)^{\frac {1}{3}} + (a - x)^{\frac {1}{3}} = 2(a)^{\frac {1}{3}} + 2(x)^{\frac {1}{3}}$

# The Legend of Question Six (IMO 1988)

This question was submitted  by West Germany to the IMO Committee, the examiners could not solve it in 6 hours.

In the IMO (1988) only 11 contestants solved it,  one of them proved it elegantly. Terence Tao (13, Australia) only got 1 mark out of 7 in this question.

Solution