“Algebraic Topology” can detect the Multi-dimensional neural network in our brain – by studying the Homology (同调) and co-Homology (上同调) with the help of Linear Algebra (multi-dim Matrix) & Computers.

Homology = compute the number of “holes” in multi-dim space.

Neurons formed in the brain can be modeled in Math (Topology) by Simplex 单纯 (plural : Simplices), billions of them interconnected into a complex – “Simplicial Complex” (单纯复体)。

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 22ndCentury:

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):