Get to Know the Math Prof: Christian Houdré

What is your research about?

I am a probabilist, a mathematician studying probability theory - a specialist of the study of chance and randomness. Because we do not really have a definition of randomness, it might appear, at first, contradictory to try to have a mathematical theory dealing with something that is undefined. But everyone has some intuition about randomness.

When flipping a fair coin, the outcome cannot be predicted with certainty, but a couple of assumptions are reasonable. First, one expects to get on each flip either a head or a tail with equal probability. Second, one expects that when flipping this same coin a very large number of times (say 10,000 times) one would approximately get 5,000 heads and 5,000 tails.

 

Both assumptions are reasonable. The first is a case of the use of postulates. The second is based on a theorem now called The Law of Large Numbers. This general theorem was proved only in the 20th century, some 250 years after the proof of its first particular case. Nowadays in popular culture, aspects of something called the "wisdom of crowds" is nothing but a manifestation or application of The Law of Large Numbers.

There is a general level of misconception about probabilists. First and foremost, they are mathematicians whose goal is to prove theorems - and not to compute the odds of winning the lottery. These theorems might not be at all motivated by real-life problems. Probabilists are in that sense closer to "pure" mathematicians than to "applied" ones.

However, because randomness is part of life, some theorems are motivated by real-life applications or by physics, statistics, other sciences, or engineering. Moreover, probability theory is widely applicable: Former students of mine who are not university professors are designing mathematical models for finance in Wall Street, computing the odds and designing casino games, or trading energy options.

I have, myself, some interest in such applications. I have done research in mathematical finance and also proved theorems having potential consequences in bioinformatics. In each case, what was crucial was the unity, the power, and the reach of the mathematics of probability theory.

What advice would you give to a college freshman who wants to be a mathematician?

This is a unique time and opportunity for you, a time of freedom. Explore, learn as much as possible, take risks, follow your intuition, your passion, and do not worry about where it is going to lead you.

If you could not be a mathematician, in what line of work would you be now?

Maybe an oenologist, since I have throughout the years developed a knowledge of various aspects of viniculture.

What unusual skill, talent, or quality do you have that is not obvious to your colleagues?

I have judged high-level coffee/barista national championships.

What is your ideal way of relaxing?

Drinking some good wine with some good friends.

What three destinations are still in your travel to-do list?

I do not have such a list.

If you won $10 Million in a lottery, what would you do with it?

I have never played the lottery.

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  • Christian Houdré