IMO questions could not be good Math of deep meaning, given that the contestants have to solve the tricky problems in a short time frame of 2 to 3 hours…IMO Prize is just an indication of Math capability, we can’t equate IMO winners as Mathematicians.
陈省身香港科技大学 演讲经典 (Highly Recommended – spoken in English & Chinese)
他的女婿是香港科大校长。现任校长是 Prof 陈繁星 Tony F. Chan , the ‘Search Algorithm Thesis’ supervising Prof of the 2 Google founders in Stanford University (Applied Math Department)
- SS Chern won the “Wolf Prize” in the same year with the Hungarian “Vagabond” 流浪汉 Mathematician Erdos Paul.
- He was appointed the Scientific Advisor of President Reagan, during which Chern recommended to build the USA Center of Math in Berkeley University. After retirement, Chern built a similar center in China at his alma mater Nankai University 南开大学 where he graduated in 1930.
- SS Chern was an assistant lecturer of Prof Yang WuZhi 杨武之, who liked to invite Chern to his house for dinners, where he saw his 8-year old son Yang ZhenNing 杨振宁 (Nobel Prize Physics 1958).
- SS Chern has guided great PhD students eg. James Simons (Billionaire Financial Investor applying Math Modeling) , Prof ST Yau 丘成桐 (First Chinese to win the Fields Medal).
- Russian Perelman solved The “Poincare Conjecture” usung Ricci Flow.
- Chern won an overseas scholarship from QingHua Preparatory School (now 清华大学) which was built by americans with the money “refunded” from the “Boxer Indemnity” 庚子赔款 over-paid by the previous Manchurian dynasty to the 8 European invaders (USA, UK, France, Germany, Italy, Austria-Hungary, Russia, include Japan).
- He went to Hamburg University in 1934 (Hiltler in power from 1933) for 2 years post-doc, during which he attended a seminar introducing the works of the French greatest Differential Geometry Mathematician Elie Cartan. It impressed Chern but all attendees left the lecture room except him.
- Chern then moved to Paris University to study under the 69-year-old Prof Elie Cartan, who kindly invited Chern to his house for discussions fortnightly during 10 months.
- [Video 57:20 mins] The great contributions of Elie Cartan: Lie Group Symmetry applied in Geometry (after Felix Klein, Sophus Lie “E8” ).
- “Simple Lie Group E8＂ is misleading not so “Simple” – Chern advised those curious minds to look into its potentials.
- Cartan’s 2nd contribution is Exterior Differential 外微分:
数学大师 陈省身访谈 http://www.bilibili.com/video/av18174730
陈省身 微积分22 http://www.bilibili.com/video/av1885439
There are 5 great Geometry Masters in history: 欧高黎嘉陈
Euclid (300 BCE, Greece), Gauss (18CE, Germany), Riemann (19CE, Germany), Cartan (20CE, France), Chern (21CE, China).
Jim Simons (Hedge Fund Billionaire, Chern’s PhD Student) quoted Chern had said to him:
“If you do One Thing that is really good, that’s all you could really expect in a life time.” 一生作好一件事, 此生足矣!
1. Video below @82:00 mins, SS Chern criticised on Hardy’s famous statement: “Great Math is only discovered by young mathematicians before 30.” Chern’s response: “Don’t believe it ! 不要相信它”.
2. Chern’s Conjecture :“21世纪中国将是数学大国。 ” China will be a Math Kingdom in 21st century.
“宇宙世界万象纷呈, 都暗含着一种伟大的秩序, 這种秩序, 可以被数学家发现, 用数学公式表示出来; 而公式的演算, 应该做到由繁就简, 最后的形式最简洁, 才最漂亮。”
CN Yang (杨振宁) Yang-Mills Equation in Quantum Physics and ‘Fibre Bundle’ in Differential Geometry by SS Chern (陈省身) are equivalent, however both men worked independently for 30 years!
Difference Between Good & Bad Mathematicians
S.S. Chern (陈省身): “The former gives many concrete examples, the latter has only abstract theories.”