1) From 1950 an unknown PhD Math Thesis by French Dr. Bachelier (a PhD student of the 20CE last Polymath Henri Poincaré, who was not impressed with the ‘gambling’ math, gave only an above-average marks to the thesis) – invention of “Options” Trading to eliminate risk in stock fluctuations.

2) The technique is called “Dynamic Hedging”…

3) …by applying the Japanese mathematician “Ito Math”.

In Asian countries, especially Singapore, where there is no proper career guidance from junior colleges / universities, the students and their parents’ herd mentality of following the most trending high-pay career in the past 6 decades, regardless of their personal interest :

Medical doctors (Post WWII, 1950s) – Healthcare of baby boomers

Lawyers (1960s) – Colonial Services

Accountants (1970s) – Trade Business

Engineers (1980s) – Industrialisation

IT (1990s) – Computerisation

BioScience (2000s) – R&D

Applied Math in AI, Big Data
(Now) – 4th Industrial Revolution.

Advice to parents & students : 行行出状元, 男怕当错行

Follow Your Heart！ Every profession is the BEST if you excel in it with a life-long ultmost passion.

When you are stuck with too many choices in life, whether buying houses recommended by agents, finding schools for children, hiring staff among the hundreds of CVs…apply ‘e’ the number from nature (logarithm) to make smart and efficient decision under the constraints of time and resources.

“Theory of Optimal Stopping” = 1/e ~ 37%

where

e = 2.7 1828182845 90 45…

If you do a house search with 20 properties, then by the Theory of Optimal Stopping, pick the first property which is better than the first 7 properties you see (7. 4 = 20 x 37%).

[Note] Ponder over the hidden Philosophy behind – “Brilliant Limit” :

The above survey was 2009 USA Job Market.
By 2018, Number 1 Job is AI / Data Scientist in USA / China / Europe high-tech market, which still needs Mathematics. eg.

The 5-year-old Social Media Startup BUFFER has a transparent salary formula, and all the employees’ payroll are listed online :

It is quite ‘humane’ to consider dependents. I once recruited 2 new fresh graduates – one single, the other a father with a baby. By HR policy, they were both paid at fresh graduate starting salary of $ 2,000 (in 1990). There was no consideration of the extra financial burden the father had to support the baby. With appeal to the CEO for special consideration, he was finally given an extra 10%.

James H. Simons, the Jewish mathematician who made $14 billion using Math modelling for Hedge Fund.

[Watch from 31:00 mins to 35 mins]. He told the Nobel Physicist Frank Yang (杨振宁) that the Math “Gauge Theory on Fiber Bundles(纤维丛)” which Yang was developing already existed 30 yrs ago in “Differential Geometry” by SS Chern (陈省身) from Berkeley.

“James H. Simons: Mathematics, Common Sense and Good Luck”

[Video 54:00 mins]
After being billionaire, at old age Simons went back to Math in 2004 to take refuge of sadness of the loss of a son.
He beat the German mathematicians in Differential Co-homology (Topology).

5 Guiding Principles of Success:
1) Don’t run with the pack – be original
2) Choose wonderful partner(s) in research, business…
3) Guided by Beauty
4) Don’t give up !
5) Have good luck.

Jim Simons | TED Talks
“A Rare Interview with the Mathematician Who Cracked Wall Street”

A person can have ‘Measure’ in Internet’s Big Data sense:
A man’s Self = Measure = ∪ {body, psychic, clothes, house, wife, children, ancestors, friends, reputation, job, car, bank-account, websites visited, online buying pattern, hobbies, interests, lifestyle, …}

You become your algorithmic self: identity and identification shifted to an entirely digital (therefore measurable) plane.

Google, Amazon, etc … collect your quantified “Measure”. Not only they amass large amount of data about you, but also use algorithms to make sense of these data.

Your ‘Measure’ is a big business in the age of Big Data, or ‘DT’ (Data Technology) Age — as coined by Jack Ma of Alibaba.com.

In layman’s terms, “measures” are functions that are intended to represent ideas of length, area, mass, etc. The inputs for the measure functions would be sets, and the output would be a real value, possibly including infinity.

It would be desirable to attach the value 0 to the empty set $latex emptyset$ and measures should be additive over disjoint sets in X.

Definition (from Bartle): A measure is an extended real-valued function $latex mu$ defined on a $latex sigma$-algebra X of subsets of X such that
(i) $latex mu (emptyset)=0$
(ii) $latex mu (E) geq 0$ for all $latex Ein mathbf{X}$
(iii) $latex mu$ is countably additive in the sense that if $latex (E_n)$ is any disjoint sequence ($latex E_n cap E_m =emptyset text{if }nneq m$) of sets in X, then

$latex displaystyle mu(bigcup_{n=1}^infty E_n )=sum_{n=1}^infty mu (E_n)$.

If a measure does not take on $latex +infty$, we say…

Today’s world is Big Data, with explosive unstructured data from Internet, Mobile phones, tablets, soon the IoT (Internet of Things), ie devices such as cars, fridges, ovens, washing machines, iWatches, wearables, Google glasses …equipped with wireless Wi-Fi connectivity to Internet…

Pixar 3D uses all the Math from Primary schools (Arithmetic + – × / ) to Secondary schools (Trigonometry, Analytic geometry) to Undergraduate (Affine Geometry, Linear Algebra, Calculus, Group Symmetry …)

Pixar: The math behind the movies – Tony DeRose:

Math and Movies (Animation at Pixar) – Numberphile: “EigenAnalysis”

Not really true … among the top 17 high-paying jobs (annual earning above US $100,000) in the USA, Mathematician’s job has the lowest stress below 60 (in the scale from 0 no stress to highest stress at 100).

Other high-pay-high-stress professional jobs (Annual Salary above US$100,000) : Orthodontists ($196,270 : 67.0) Computer Hardware Engineer ($106,930 : 67.0) Astronomers ($110,440 : 62.0) Political Scientists ($100,900 : 60.8) Law Teachers ($122,280 : 62.8) Actuaries ($107,740 : 63.8) Physicists ($ 117,040 : 61.3) Optometrists ($111,640 : 70.3) IT Managers ($132,570 : 64.3) Geoscientists ($108,420 : 62.5) Mathematicians ($103,310 : 57.3)

The 3 valuable takeaways (successful and failure experiences) from this 1- hour interview with Steve Ballmer, who co-founded Microsoft with the richest man in the world Bill Gates:

1. Have a great idea before startup.
– The financial, talent, etc, will come later naturally, attracted by the great idea.
Look at the 3-year-old Whatsapp, a great text-video-picture free SMS idea which attracts 400 million users and $19 billion acquisition from Facebook.

2. Great company does one (or two) trick (or forté 看家本领) well.

– Microsoft has 2.5 tricks: PC operating system (Windows); Microprocessors in data center (Windows Servers); the half trick is X-Box game console.

– Apple also has 2 tricks: Mac; Mobile computing in iPhone/iPAD/Appstore

– Facebook (Social Network) and Google (Search Engine) have 1 trick.

– Sony has 2 tricks : Audio & TV, Sony Playstation PS4 Game Console.

– HP has 1 trick: Tester Equipment (now in Agilent).

– IBM has 2 tricks: Enterprise Data Centre Computing; IT Consulting & Solution Services (acquired the trick from Price-Waterhouse).

Many great companies degenerate into smallness or extinction, because they try to diversify into too many non-core activities, wasting financial, human ‘energy’ and precious time resources.

Steve Jobs on his final year gave advice to his competitor Google’s Larry Page: “Focus on one thing and do it well.”

Notes :
1). That explains why Microsoft drains the energy to too many fronts (> 2 tricks). The CEO ‘missed 2 BIG boats’ in Mobile Cloud Computing (Smartphone OS, Tablet) and Search engine (Bing) by playing late catch-up.

2). HP did not treasure the acquired tricks from Compaq iPAQ (the world’s first and top Windows Mobile Smartphone in 2006 before iPhone 3), and Digital Equipment’s (DEC) trick on Vax/VMS Networked Clustering Computing (Bill Gates hired the ex-DEC developers to re-create on Intel servers as the Microsoft Windows Server 200x Operating System for Data Centres).

3) Sony wasted energy in Phone (Sony- Ericsson ) and Notebooks (Viao), ignoring the upcoming threat of TV flat-panel technology from a “小さい” (\chisai) i.e. small, insignificant, or 鼻屎 (\pisai) Korean company Samsung.

3. World Centre of Entrepreneuship:
He said the place must satisfy three criteria –
a. Domestic Market,
b. Top Universities,
c. Global Talents flock there to live and work Steve cited 3 places: USA (e.g. Silicon Valley) : America is the world’s biggest market, Stanford / MIT / Harvard Universities, global talents immigrated there, English Speaking. China : potential (barring political and environmental challenges), Beijing/Tsinghua/Fudan/etc top Universities, 1.3 billion people’s domestic market. UK: Cambridge/Oxford/etc world class top universities, English speaking, European market.

Why not Japan, Singapore, Israel, Australia, France, Germany, India, Canada…? They all fail in 1 or 2 criteria.

Google’s new language Go is invented to replace Java, hence free from Oracle’s threat of Java license in all Android Smartphones.

Go Language is invented by Ken Thompson, the father of Unix and B language, which was transformed into the famous C language by his Bell Lab’s teammate Dennis Ritchie.

Go impresses me of its concurrency best suitable for parallel programming, given today’s most hardware including smartphones are made of multi-core CPU, yet none of today’s languages is designed inherently to take advantage of it, even Java.

If we can say Cobol is for the 1st generation Mainframe computing, C the 2nd generation Unix-based Minicomputer computing, Java the 3rd generation Client-Server computing, then Go will be the 4th generation Mobile-Cloud computing.

Programming language, if you are a mathematician, which one you use to test your math formulas, simulate your conjectures, proving the theorems ?

Ranking high on top is Javascript, most popular among the programmer communities, followed by Java, PHP, Python, Ruby, etc.

From Javascript springs off a family of functional programming language Lisp-like cousins: Clojure and Clojurescript, which are compiled into Javascript to run on the ubiquitous Java Virtual Machine.

In the race the new language Go
developed by Google is a dark horse to watch in the next 24 months.

Lisp is one of the oldest language in the 1960s, created by Mathematicians for mathematics (Mathematica was developed in Lisp by Wolfram) and Artificial Intelligence.

Our brain can store up to 3 terabytes of information, equivalent to 3 sets of this 1-terabyte (TB) hard-disk below.

IBM estimates everyday the world generates 2.5 EXABYTES (EB) of BIG DATA, more than 90% of which was created in the last 2 years via mobile devices (smartphones, tablets).

The next decade will be the “Big Data” Age. Companies and countries which can take advantage of such BIG DATA will rule the market and the world, with accurate forecast of consumer purchasing behavior, investment trends, weather prediction, military espionage, terrorist detection, epidemic prevention, etc.

‘Data-mining’ tools in Analytics applying powerful mathematics will be the tomorrow’s ‘Google Search Engine’.