Friendship in probability

When I was twenty years old, I read a book called "Introduction to Stochastic Processes". Although the book involves "advanced" mathematics, it has an elegant and a well-structured style. There is also a short fable at the end of each chapter to relate the content with wisdom. That’s unusual for a math book. Also, one chapter is entitled "Potential". The concept of potential is quite well known in physics, but appearing in a mathematics book is novel, and caught me by surprise and fascinated me. After graduating from college, despite doing many other things, that book lingered in my mind. So a few years later, I managed to became the author’s student and started working on probability. Then while I was studying probability I came to know it can be applied to finance, so I found a job on Wall Street and have since done that for more than twenty years. I can really say every day my work has something to do with that book. So I think this book changed my life.

One day, while I was working for Morgan Stanley in London, our chief risk officer Keishi Hotsuki went to London on a business trip and invited us to a dinner. In the dinner, he said, instead of me boasting for the whole evening, each of you say something that happened around your 20, and that changed your life. So people started talking. One said when he was 18 years old, he worked at McDonald's and suffered so much that he decided to go to college and change fate, it has been a smooth sailing ever since. Another said that her parents divorced when she was seventeen, so she worked hard to get into college, and it's been a smooth sailing ever since.

Then it’s my turn. I told him about the stochastic process book. Keishi liked it as he mentioned it later on a few occasions, and a few people even asked me about this book.

The book is by Erhan Cinlar, a professor at Princeton. He was the founding chairman of department of operations research and financial engineering, though he is not so interested in finance.

Still, I mentioned the story, including my original one and the following CRO episode when I visited Erhan one day, he was quite happy.

That happened at the Small World coffee shop on Witherspool Street in Princeton, when I just moved back to US from England. Erhan was older and had more gray hair. I brought him two nicely packaged boxes of English tea, thinking he might like it, being from a Turkish aristocrat family. And he traded this with a book, “Uncertainty: Einstein, Heisenberg, Bohr, and the Obsession of the Spirit of Science” by David Lindley.

Erhan explained, I walked from the department, and passed the U bookstore on the way. Every time I walk there, I always find it irresistible to look through used book stand, and then buy a book to read here while drinking coffee.

I said I also have that habit, there are many small book stalls in London, I always find it irresistible to see what books I like, sometimes people put out some old books on the roadside, I also could not help stop to see if there are any treasures.

I am not sure if I was the first Chinese student of Erhan, but he certainly has an unusual friendship with an outstanding Chinese probabilist K. L. Chung.

On June 2, 2009, Erhan had a Chinese female student come to do a summer project with him. Erhan asked her if she had heard of Kai Lai Chung, and the student said no. Erhan froze for a moment and said, "Strange, he told me that he is quite famous in China."

Erhan asked her again later that day, "You never heard of Kai Lai Chung?" She shook her head again. Erhan said, "Oh, Chung passed away yesterday. I have known him for more than forty years." Erhan did not appear particularly sad, but was silent for a few seconds, and then began to assign her tasks related to the research.

That morning, Chung's son told Erhan that Kai Lai had passed away. As I later know, Erhan and the world's top probability theory master, Kai Lai Chung, have cooperated for forty years.

Kai Lai is super smart but as smart people usually are, he doesn’t always behave in an usual way.

After Kailai went to study in the United States, he studied under John Tukey and Harald Cramér. We will talk about Cramer later. But it is said that Tukey once used a red pen to mark out the grammatical errors in Kailai's thesis one by one. Kailai went to the library to find all the works of John Tukey, and marked all the grammatical errors in them with a red pen.

Kailai Chung and Erhan co-founded a series of workshops on difficult problems in probability theory at different universities, and edited many academic papers in their journals. I know a story that worths a laugh. A workshop was held on a Tuesday afternoon at Stanford University, where Chung is a professor. Erhan told Kailai, "Stanford has a statistics workshop on Tuesday afternoon, and many statisticians definitely want to come to both conferences. You might as well change the time." Kailai clapped his hands and said with a smile, "I did it on purpose. Schedule it exactly at this time! So all the statisticians can't come to our workshop. I hate statisticians."

As to Erhan, his probability theory course is one of the most difficult courses, but he is the most popular professor because he is humorous and well prepared. He always wears neatly and writes on the blackboard with beautiful calligraphy. At the beginning, students who were used to writing on the Powerpoint blackboard complained that they could not understand cursive characters. Soon, everyone was moved by the humor of this short Turkish old man.

When I was at Princeton, our department was called the Department of Operational Research and Civil Engineering, because operations research is too small to be a department of its own, and several professors' research are related to transportation and logistics.

Then financial engineering became quite needed on Wall Street and there are sponsors who are willing to contribute. Erhan was the chairman and helped build the Department of Operations Research and Financial Engineering. They moved into a separate new building.

Erhan and I walked out of the coffee shop and took two photos in front of the entrance, one with our coffee shop in the background, and one with “the best French restaurant in Princeton" Lahiere's".

Why so? It has something to do with Kai Lai.

In 1945, Kai Lai received the Boxer Indemnity Scholarship to study in the United States at Princeton University for a doctorate. On his first day there, he thought, "Today is my first day in a American Campus, and I must have a big meal at the best restaurant in town!" Thus he dragged his luggage from the train station all the way to “The best French restaurant” in Princeton, Lahiere's. He has so many bags, and is dusty and unkempt, so it took some time to be allowed into the restaurant. The idea at the restaurant is a God sent. He recognized one of the diners as Harald Cramér. Cramér was the number one person in the world in the field of probability and statistics at the time. He was a visiting scholar from Stockholm University, and had only been in Princeton for a few days. Kailai ran to Cramér, introduced himself, and had a meal together. After the meal, Cramér became Kailai's doctoral supervisor. Cramér only stayed at Princeton for two years. After that, Kailai received his Ph.D., and Cramér returned to Stockholm University.

Erhan and I walked back to the department. “The most beautiful building” is a modern building. One side of the indoor patio wall is a three-story decoration with oriental patterns, probably Erhan's favorite. Many students working there are Chinese. I said to Erhan, Chinese still work hard. Erhan said they had nothing to do anyway. We laughed together.

Erhan came to the United States in 1959 and went to the University of Michigan. He obtained a bachelor's degree in 1963, a master's degree in 1964, and a doctorate in 1965. One degree a year, who can do it today?

While we talked, I said I wanted to write a popular book on probability theory, so he took out a few and gave me some suggestions. Also he gave me a copy of his new book "Real and Convex Analysis" with hand writing: Dear Dawei, for your enjoyment!

I was about to leave, Erhan asked if I need something more, I said I've got a few books and that's enough. Erhan said, I'll give you another one, and as he said, he took out a small diamond-like stuff from the drawer: here you are, a twenty-sided dice, you can do simulation with it manually!