Interesting Math education evolves since 19th century.

“Elementary Math from An Advanced Standpoint” (3 volumes) was proposed by German Göttingen School Felix Klein (19th century) :

1) Math teaching based on Function (graph) which is visible to students. This has influenced Secondary school Math worldwide.

2) Geometry = Group

After WW1, French felt being behind German school, “Bourbaki” Ecole Normale Supérieure students rewrote all Math teaching – aka “Abstract Math” – based on structure “Set” as foundation to build further algebraic structures (group, ring, field, vector space…) and all Math.

After WW2, the American prof MacLane & Eilenburg summarised all these Bourbaki structures into one super-structure: “Category” (范畴) with a “morphism” (aka ‘relation’) between them.

Grothendiek proposed rewriting Bourbaki Abstract Math from ‘Set’ to ‘Category’, but was rejected by the jealous Bourbaki founder Andre Weil.

Category is still a graduate syllabus Math, also called “Abstract Nonsense”! It is very useful in IT Functional Programming for “Artificial Intelligence” – the next revolution in “Our Human Brain” !