1. The Foundation of Science has changed since Newtonian Era, except Biology / Medicine and Psychology which don’t keep up:
Math => Fractal Math
Newton Physics (Matter)=> Quantum Physics (Energy)
(Organic) Chemistry => Electro-Chemistry
Energy = Field = 气 Chi / Qi
3. Environment -> Mind -> Perception -> Genetic Control
4. Consciousness (5%), Subconscious-ness (95%)
- Driving car: inexperienced driver (consciousness), experienced driver (subconscious).
- Dating (conscious behavior)
Note: The successful Deeplearning AI is using the concept of Perception called “Perceptrons” by analysing the Environmental (BIG DATA) pattern with the help of Mathematics (Calculus : Gradient Descent, Statistics : Bayesian Probability, Algebraic Topology, etc).
这位中国留英数学专业的小伙子有很好的口才: 数学之美, 他的数学遗憾。
华威大学（The University of Warwick)，famous for mathematics in UK.
Einstein用 Riemann Geometry 数学救了Newton 物理。
3位大师救近代中国数学: 华罗庚, 陈省身, 苏步青
数学光明的未来: AI, Big Data, Cloud Computing
时代的”指数” exponential快脚步, 不要追风, 要一以贯之 : Prof. Andrew Wiles proved 350-year-old “Fermat’s Last Theorem” (FLT).
[纠正]: Andrew Wiles 超过40岁, 没赶上Fields Medal, 只得个”奖励”。他看到椭圆(Ellipse)气球, 得到突破 FLT “工具”的灵感 – “Elliptic Curve” 。
数学是什么: 爱情, 艺术, 音乐, 科技
“A pure mathematician, when stuck on the problem under study, often decides to narrow the problem further and so avoid the obstruction. An applied mathematician interprets being stuck as an indication that it is time to learn more mathematics and find better tools”
— Distinguished differential geometer Eugenio Calabi
拓扑: 两绳困绑, 只要一人翻手就能解脱。
“Mathematician is a person who turns coffee into Theorems” – Erdös Paul , the Hungarian Mathematician who had no home, no wife, travelled around the world to visit his math collaborators proving 1000+ theorems. 数学界的”丐帮洪七公”! 他是华罗庚的好友, 和 陈省身 同年得 数学Wolf Prize.
A mathematician is a person who can find analogies between theorems;
A better mathematician is one who can see analogies between proofs
The best mathematician can notice analogies between theories.
One can imagine that the ultimate mathematician is one who can see analogies between analogies.