Pure Mathematicians versus Applied Mathematicians

“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

Ref: https://www.quantamagazine.org/20151203-big-datas-mathematical-mysteries/

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A Day in the Mathematician’s Life 

“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.

​https://anthonybonato.com/2016/09/20/a-day-in-the-life-of-a-mathematician/?from=timeline&isappinstalled=0

Ultimate Mathematician

引用巴拿赫Banach的名言,体现举一反三的境界:

A mathematician is a person who can find analogies between theorems;

A better mathematician is one who can see analogies between proofs

and

The best mathematician can notice analogies between theories.

One can imagine that the ultimate mathematician is one who can see analogies between analogies.

Algorithm with Life, Love, Happiness

Applications of Algorithm:

1) Economic : “Stable Marriage” Algorithm (2012 Nobel Economic)
◇ Boston Medical Students Matching Hospitals
◇ Schools & Students’ Choice
◇ Racial Segregation Housing Policy

2) Evolution: Genetics “Mixability” thru the algorithm “Sex” (mix of genes past down from father and mother to their children).

“God did not create species. He designed the Algorithm for creating them.”

3) Multiplicative Weights Update Algorithm: choose the best expert (C1, C2, …Cj…)

Cj = Cj (1 + 0.00001*$)
Weight = 0.000001
$ = profit or loss made by the Financial expert

Auspicious Year 2016

2016很神奇

2016=168+168+168+168+168+168+168+168+168+168+168+168

总共12个168,祝大家2016年每个月都一路发!

2016=666+666+666+6+6+6
祝大家2016年顺心隨意、顺风顺水、六六大顺!

2016=888+888+88+88+8+8+8+8+8+8+8+8,
祝大家2016年事业兴旺发达!发发发!

2016 = 999+999+9+9
祝大家在2016年幸福的日子长长久久!
恭祝2016年新年快乐,身体健康,阖家欢乐,实现梦想

Arrow’s Theorem

The Axioms for a fair voting system (eg. Political Election) :

1. Non-dictatorship:
◇ Outcome decided not by one ‘dictator’, but more than one person.

2. Unanimity
◇ If everyone votes that A is better than B, then A will be ranked higher than B in the final result.

3. Independence of irrelevant alternatives
◇ The ranking of A relative to B should not be affected by someone changing their mind about C.

Arrow’s Theorem says that if there are more than 2 people (parties) to vote for, then there is no fair voting system.

Note:
Most democratic voting systems violate the 3rd axiom (independence of irrelevant alternatives).