Crossing fields Math + Physics : Yang-Mills Equation

Yang-Mills Equation : 杨振宁

Prof Alice Chang Sun-Yung: Abel Prize Selection Committee


数论的世界 Number Theory

【数学之美 | 数论的世界】
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Four Categories of Mathematicians

Four Categories of Mathematicians:
1. Math PhD, Applied Math Engineers : eg. Huawei 700 mathematicians,Larry Page (Google)

2. Math Profs : eg. 5G Polar Code Turkish prof

3. Masters : ,陈景润 ,张益唐,Perelman, Fields Medalists, 丘成桐,Terence Tao, Grothendieck, Andrew Wiles (Fermat Last Theorem), Andre Weil, Ramanujian, …

4. Grand Masters : Gauss, Hardy, Paul Erdos, Noether, Hilbert, Riemann, Newton, Leibniz, Descartes, Fermat, Pascal, Poincare, Cauchy, Abel, Galois,… 华罗庚,陈省身.. 杨振宁, Betrand Russell

Note: Most of the Grand Masters are polymath crossing multi-disciplines from math to physics to art / philosophy, or invented a whole new branch of Maths (eg. Calculus, Topology, Abstract Algebra, Group,…)

A Programmer’s Regret: Neglecting Math at University – Adenoid Adventures

Advanced Programming needs Advanced Math: eg.

Video Game Animation: Verlet Integration

AI: Stats, Probability, Calculus, Linear Algebra

Search Engine : PageRank: Linear Algebra

Abstraction in Program “Polymorphism” : Monoid, Category, Functor, Monad

Program “Proof” : Propositions as Types, HoTT

Abstraction: Monoid, Category


谁说数学家不时尚 ? Cédric Villani


Key Points:

  • Classe Preparatoire (预科班) – most rigorous and toughest math training (2 years) after high school.
  • Grande Ecole (大学校)
  • “Bourbaki school” – secretive Math club still exists today.
  • French Thinking
  • Ecole Normale Superieure where he spent 8 years (Graduate, PhD, Teaching assistant)
  • His PhD Advisor Pierre Louis Leon (Fields Medalist)
  • American universities use “Engineering Way” to train mathematicians, French is different.
  • IMO Math vs French Abstract Math
  • Paris is still a World Math Center