“Math is a chess game against the devil”

Charles L. Fefferman was born in Washington D.C in April 18, 1949. Mathematician of the University of Princeton that in 1978 receives the Fields Medal (award given only every four years to mathematicians that are not yet in their 40) for mathematical analysis.

by Daniela Martínez Nava

How was it growing up like a prodigy child?

God let me try to remember… it felt strange until a got to university and then life was good. I got in to university at the age of 14 and at 17 to graduate school, that’s was even better. I remember when I was a little child to the other little children in my class I was some strange ridiculous person interested in all the wrong things but when I went to graduate school all of the sudden if I was different from the other is because I have not red enough philosophy.

It felt wonderful but it was a period when I was old enough to be aware of how different I was from other children but not old enough to study with university people.

But, did you get along with your collage mates?

Yes, yes I did. They were very very nice, they lived different life from mine but it was not an issue for them I think. We talked about various things, it was fun.

When you were a kid, did you dream of doing something else?

When I was a little kid I thought I might be an artist… a painter. I still have a few of my paintings I think my best painting are not bad but I´m very happy that I became a mathematician. For a while a study both math and physics but by the time I was 18 I knew I wanted to be a mathematician.

Just for curiosity, have you ever sold any of your paintings?

I had an interesting offer. My wife had one of my paintings framed and someone from the Princeton University of the art department asks her if we wanted to donate to the museum. So there was no offer of money but … is still hanging on our wall.

How did you felt when you won the fields medal?

Very happy. It wasn´t the best moment in my life I mean I got married, I had children; those were very special moments in my life. But that was definitely a very important moment.

Why did you develop a passionate interest in math?

People are addicted to cross words puzzles or to sudoku and for example I love them too but compare to math they are noting. But is not so different; the thing that makes sudoku so fascinating I think is not so different from what makes math fascinating. For sudoku there are few tricks and you know that they are going to work sooner or later but math is infinitely deep. If you are not hopelessly stock on a problem it means that you are not working on a hard enough problems.

In your opinion, what is the best way to explain math?

Math is like playing chess but you are playing a game against the devil. But you get to take steps back; you get to take back as many moves as you like. So if you play against the devil you get crush and you think about why you lost and you try to change your move and again you are crush; you are simply wrong, whatever reason you thought was the reason for you being crush that’s not the reason at all. But sooner or later maybe you get an idea and then you get a little scare to play and get crush again but you give it a try because the devil will have to make another move, and pretty soon after a few years of playing many games you start to see what is going on and after a while of  fighting you win. But while you play this game God is whispering in your ear “move your peon over there, is all you have to do and then he is in real trouble” But you can´t hear, you are deaf… well not deaf but you have to pay a lot of attention if not you can´t know what God is telling you. But that is the spirit of the thing.

How do you choose your games? I mean, how do you choose your investigations? Just for fun or to solve something?

I make my investigation because the subject fascinates me but in this moment I am working on a specific problem; scientist from the Institute of Mathematics Science in Spain (ICMAT) called me to work on fluids.

What are fluids? What is the project about?

Fluids are water waves, so imagine that you have some water and you have either some air or perhaps vacuum and the water is moving and then, what does the water do? Well to know that you need some equations and these ones are suppose to describe what the water does.  All right, do these equations have a solution? Does the solution continue for all time? Turns out it doesn´t and the reason is very very simple in principal; the water can form a wave and splash and when a splash occurs the equations don’t describe what the water is really doing, the equations don’t solve the problem.

And why is the project useful for society?

Well fluids are very important but nobody understands them. There are equations written down 200 years ago which in principal are supposedly to cover how the fluids behave but people knows almost nothing about how to solve this equations and so they make calculations that they know are wrong but are the best that scientist know  how to do now. Ando those are already very important in whatever we can do on designing airplanes or ships or predicting the weather, is based on that. But fundamentally is not easy to understand fluids. And what we are doing in the ICMAT is part of the big effort of many scientists to try to understand fluids at a fundamental level. If it can be done, and will be in a long time, it will make more accurate and more powerful all the calculating that we do about weather, airplanes, ships, whatever… climate. But we are very far away from that understanding, so this is a step forward but the goal is far away. I think that ultimately there will be significant applications to everyday life but not time soon.

In your opinion, how long will it take to see an application?

If I had to guess I would guess one or two hundred years. But it can happen that some brilliant person is sitting right now… some graduate student is sitting right now in a little room some place with no one else paying attention and has some great idea that no one thought of before and perhaps that’s the day of the great discovery and you publish an article quoting me “I would say one or two hundred years” said Charles Fefferman in 2012. That could happen. Would be great.

What would it be a particular problem that researches should work on right now?

It would be ridiculous for me to say what mathematicians should work on. There is a tremendous variety of fascinating problems in math so maybe a very long time ago one person could understand all of math but right now there are few scientist that understand 5% nobody understand 20% of mathematics. Peoples have strong taste I mean math is a science but it ´s also an art. So researchers have strong feeling of what is important for them which will be a disagreement with other researchers. Things that appear to be important aren´t; things that appear to be substantially were not. But it takes a really long time to know and in the mid time we´re only guided by likes and dislikes.

Keeping in mind what you just said, which project would you consider that in the beginning was not that important and it turned out to be valuable?

Of all the thing that I´ve done there is one thing that is close to be useful, they´re called wavelet. I won’t tell you what they are because is really complicated but I´ll tell you what they are use for. I believe they are use in cell phones; well actually they are use in the voice. For example this machine which is recording our conversation in principal has to absorb a tremendous amount of information most of which is it not interested of us. You really don’t care exactly how loud my voice is at this moment if it were 110 of a percent louder or less loud you would not care, but the machine is storing all that information. There are ways to take the information, lets say the human voice in a movie and to compress it so that a computer that could only store one movie now can store a thousand movies because it doesn´t all the information it only keeps the information that matters. That is what wavelets are used for.

I am not the inventor of wavelets but a lot of the work that I did in the 1970´s was relevant to the development of wavelets but if someone had ask me if it was useful I would have say “there is no way that this could be useful” So one doesn’t know what developments will be useful but the ones that are turned out to be tremendously useful.

Can you mention a different project of significant use for society that you work on?

Think about the sound of a violin. The violin has a string, has a fundamental note and a first over tone and a second over tone and if you just have the fundamental note it´s r a very boring sound but as you add more over tones the you increased the richness of the sound and you increased the detail. This is in some way opposite of what happens in some odd photograph, when you take away some over tones you get a better image.

Which has been the very best research you’ve done?

I couldn’t tell I just couldn’t tell you. Is like asking me to choose between one of my children. I can tell you that maths are really fun.

Been a mathematician has been everything that you expected?

I´ve done very well, I’ve prove theories, I received the Medal Fields which I did not expect at all… I think I have been more successful that I expected.

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