In the world of Math education there are 3 big schools (门派) — in which the author had the good fortune to study under 3 different Math pedagogies:
“武当派” French (German) , “少林派” Russian (China) , “华山派” UK (USA).
( ) : derivative of its parent school. eg. China derived from Russian school in 1960s by Hua Luogeng.
武当派 : 内功, 以柔尅刚, 四两拨千斤 <=> “Soft” Math, Abstract, Theoretical, Generalized.
少林派: 拳脚硬功夫 <=> “Hard” Math, Algorithmic.
华山派: 剑法轻灵 <=> “Applied” Math, Astute, Computer-aided.
The 3 schools’ pioneering grand masters (掌门人) since 16th century till 21st century, in between the 19th century (during the French Revolution) Modern Math (近代数学) is the critical milestone, the other (现代数学) is WW2 : –
France: Descartes / Fermat / Pascal (17 CE : Analytical Geometry, Number Theory, Probability), Cauchy / Lagrange / Fourier /Galois (19 CE, Modern Math : Analysis, Abstract Algebra), Poincaré (20CE Polymath, Topology), André Weil (WW2, Bourbaki school), Alexander Grothendieck (21 CE, Differential Geometry)…
Note: 1/3 of Fields Medals won by French.
(Germany): Leibniz (18CE, Calculus, Binary Algebra). Felix Klein (20 CE, learnt from French master Camile Jordan) established the Gottingen school (World Center of Math before WW2, destroyed by Hitler). Successors: Gauss ( Polymath), Hilbert , Riemann (Prime Number) , Cantor (Infinity Math), Emile Noether (Axiomatic Algebra, Ring Theory) …
Note: Swiss-German branch – Bernouille father & 3 sons and student Euler (Polymath).
Russia: А. Н. Колмогоров (20 CE, Polymath), Grigori Perelman (21 CE, Topology, who rejected Fields medal).
(China): 华罗庚 (Hua Luogeng, Number Theory), 陈省身 (SS Chern, China/USA, Differential Geometry), 陈景润 (“Chen Theorem”, Number Theory), 丘成桐 (ST Yau, HK/USA, Differential Geometry), 吴文俊 (Wu Wenjun, Machine Proof of Geometry )。
UK: Isaac Newton (18 CE, Calculus), Hardy / Littlewood / Ramanujian (Number Theory), Bertrand Russell (Logic), Andrew Wiles (21 CE, proved 380-year-old Fermat’s Last Theorem).
(USA): 20CE Godël (Austrian / USA), Paul Erdös (Hungary / USA), Eilenberg /MacLane (WW2, Category Theory).
Note: Terence Tao (陶轩哲 Australia / USA, 21 CE, Number Theory)