Hadamard estimated that :
About 90% of mathematicians think visually, 10% think formally.
Usually, they think in steps:
- Get the right idea, often think vaguely about structural issues, leading to some kind of strategic vision;
- Tactics to implement it;
- Rewrite everything in formal terms to present a clean, logical story. (Gauss’s removal of ‘scaffolding’ – middle working steps)
Source: [NLB #510.922]
The 7 Fields Medalists are:
2014 – Maryam Mirzakhani (1977-2017) – 1st lady Fields medalist
2010 – Cédric Villani (1973- )
2006 – Grigori Perelman (1966- ) – 1st declined the award
1998 – Andrew Wiles (1953- ) [silver plaque] – Fermat’s Last Theorem
1990 – Edward Witten (1951- ) – Physicist won Fields medal
1982 – Alain Connes (1947- ) – Quantum Theory
1966 – Alexander Grothendieck (1928-2014) – Hermit mathematician
Key Words: 250 years anniversary
- Yesterdays: Fourier discovered Heat is a wave , Fourier Series, Fourier Transformation, Signal processing…
- Today: IT imaging JPEG compression, Wavelets, 3G/4G Telecommunications, Gravitational waves …
- Friends / bosses: Napoleon, Monge… Egypt Expedition with Napoleon Army.
- Taught at the newly established Military Engineering University “Ecole Polytechnique”.
- Scientific Research: Short period but intense.
- Before Fourier died (he wrapped himself with thick blanket in hot summer), he was reviewing another young Math genius Evariste Galois’s paper on “Group Theory”.
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.