This question was submitted by West Germany to the IMO Committee, the examiners could not solve it in 6 hours.
In the IMO (1988) only 11 contestants solved it, one of them proved it elegantly. Terence Tao (13, Australia) only got 1 mark out of 7 in this question.
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:
- Pre-rigourous: intuition à la Ramanujian
- Rigorous: formal proof
- Post-rigourous: 1 + 2 (intuitive bold “cheating” guess, followed by rigorous proof)
Scala is a non-pure FP (Functional Programming) language with the Object-oriented feature, unlike the pure FP such as Haskell or Clojure (Lisp). It is popular in Android platform as an alternative to Java.
Part 1: Compare 3 paradigms:
- Object- Oriented
- Functional Programming
Introduction to Haskell
Part 2: Example – The 8 Queens Problem
Note: A simpler Haskell coding here.