The World’s Best Mathematician 

Terence Tao 陶哲轩 : 

  • Research style: both Collaborative à la  “PolyMath” Project & “Lone Wolf” à la Andrew Wiles (“The Fermat’s Last Theorem”), G. Perelman (“The Poincaré Conjecture”) or Zhang Yitang 张益唐 (“70-million Gap in Twin Primes”)
  • Not attempting the Riemann Hypothese: tools not there yet.
  • His Weakness in Math: Algebraic Topology (拓扑代数) [*]

[*] Algebraic Topology: apply algebra (linear) in Topology: eg. Homology (同调), Co-homology (上同调), Homotopy (同伦) or Homological algebra, etc. A powerful applied mathematics used in Big Data Analytics.

3 Phases of Math Training:

  1. Pre-rigourous: intuition à la Ramanujian 
  2. Rigorous: formal proof
  3. Post-rigourous: 1 + 2 (intuitive bold “cheating” guess, followed by rigorous proof)

The genius who rejected Fields Medal & Clay Prize: Grigori Perelman 

Russian Jewish mathematician Grigori Perelman proved the Poincaré Conjecture in 7 years of solitude research in his Russian apartment  – same 7 years of solitude for Andrew Wiles (The Fermat’s Last Theorem) in the Cambridge attic house and Zhang Yitang  张益唐 (7-Million-Gap Twin Primes) in the “Subway” sandwich kitchen.

7 is the Perfect Number. 1 week has 7 days,  according to the “Book of Genesis”, God created the universe in 6 days and rested “Sabbath” on the beautiful 7th day.

People involved in his journey: 

  • His mother who supported his early education in Math, all the way to his international fame and adulthood — Erdös Paul also had a mother supporting her single son in the entire Mathematical life.
  • Prof Hamilton who “unintentionally” gave him the inspiration of the “Ricci-flow” tool – the first key to the door of The Poincaré Conjecture.
  • His closed Chinese friend the MIT Math Prof  田刚 (Tian Gang) – a PhD student of Prof S.T. Yau.
  • Fields Medal which he rejected — reason being he felt Prof Hamilton deserved a share of the credit.
  • Clay Prize which he rejected the U$ 1 million — for the same reason as the Fields Medal.
  • Prof  S.T. Yau (邱成桐) ‘s lawsuit against “The New Yorker” jounalists on “The Poincaré Conjecture” article regarding the purported claims by his 2 Chinese mathematician students.