This week we want to introduce one of the biggest personalities in the world of mathematics. Who is** Charles Fefferman**? Thanks to the **ICMAT**´s communication team, we will be able to know more about the youngest full professor ever appointed in the United States and winner of the Fields Medal.

**Charles Fefferman **(1949, EE. UU) started to read Physics books on his own when he was 9, because he wanted **to know how rockets work**. His impressive career in Mathematics began when he realized that he needed this science for a deep understanding of many problems that fascinated him. **He graduated with the highest distinction at the University of Maryland at the age of 17 and was awarded his PhD in Princeton three years later.** He lectured at Princeton for one year, and in 1970 he moved to the **University**** of Chicago** where after a year he was promoted to full professor, which earned him the distinction of becoming **the youngest full professor ever appointed in the United States.** In 1973 Fefferman returned to Princeton and he has stayed there ever since.

He graduated with the highest distinction at the University of Maryland at the age of 17 and was awarded his PhD in Princeton three years later.

He won **the Fields Medal** in 1978 for his work on **convergence and divergence on trigonometric series.** However, when asked about his favourite contribution to research, he wouldn´t say it was this one, but his most recent ones.

**Question: **When and how did you become interested in mathematics?

**Answer:** When I was a little boy I was interested in children’s science: how rockets work and things like that, but I wasn’t satisfied with simple explanations, so I checked a Physics textbook out of the public library and I couldn’t understand anything. I was nine years old, and my father told me: “Of course you can’t understand this book, there’s Math in it!” So I asked him if I could study Math. I was in the fourth grade, and he bought me a 4^{th} grade math textbook. That was the beginning.

**Q: **How did you realize that you had a special talent for mathematics?

**A:** Very soon after that, because I read the 4^{th} grade math textbook in a day or two. My father didn’t believe me, so he asked me a few questions and realized that I understood. Then he bought me a 5^{th} grade textbook, and I read it in a day or two, and so on until I studied calculus and that took longer than a day or two. But **I was just a little boy studying calculus so it was obvious that I had talent.**

**Q:** You wrote your first scientific article when you were 15; could you tell us about that?** **

**A:** At that time I had a wonderful professor of mathematical logic: Carol Carp, who was interested in **what you might you say if you could speak in infinitely long sentences.** There was a question about how many different things could be distinguished depending on what kind of infinity was in the infinitely long sentence. I was supposed to present a very complicated solution in class and I couldn’t understand the very complicated proof, so** I thought about my own proof and it turned out that it could be generalized.** My professor was very supportive and said: “Why don’t you work this out and go further?”, and then: ‘Why don’t you write it down?’ After that he said: ‘Let’s send it to a journal and see what happens’, and it was accepted.

** Q: **At this point you where already at the

**University of Maryland.**What was that like?

**A:** When I was I boy I lived near the University and **when I’d learnt so much Math that the public schools couldn’t offer me anything else**, the professors at the University of Maryland, a big state university, took an interest in me. **Part of my education was leaving the school system and going to the University of Maryland as boy of fourteen.**

** Q:** Did you take regular lessons there?

**A: **I took a lot of Math and Physics courses, **maybe not enough Philosophy and Literature** **courses**. But in addition to that I worked on projects outside of class. The professors suggested problems to me, and if I had any concerns they were always there for me. **It felt to me like an army of private tutors**; they where wonderful and they had a big impact on me.

**Q: **A few years later you became

**the youngest full professor ever appointed in the United States.**What was that experience like for you?

**A:** It felt great. The process of getting tenure is usually very arduous but for me it happened instantly. I got my PhD in **Princeton**, then I was very young faculty member at Princeton for a year, and after that an Assistant Professor in Chicago for one year. I**n the spring of my first year at the University of Chicago they offered me tenure.** At first it felt strange to be around all the other professors because of the age difference, but they were very nice and it became natural.

**Q: **When you were at Princeton, you were awarded

**the Fields Medal**in 1978; what can you tell us about that? What did it mean to you?

**A:** At the time it simply made me happy: **it was the highest recognition that I could get**. Afterwards, when as it often happens I was completely stuck on one problem for a very long time and was getting nowhere, developing no theorems, I could easily get depressed, but then I would think to myself: “Well, after all I won the Fields Medal”.

**Q: **How do you arrive at the questions you work on?

**A:** **I don’t choose to work on a particular problem; the problem chooses me.** I hear about it, I can’t stop thinking about it, sometimes I solve it, sometimes I don’t, and it could go on for a long time. Sometimes it emerges when speaking with other mathematicians, or just following my own thought processes, sometimes reading…

“I don’t choose to work on a particular problem; the problem chooses me”.

**Q:** And after the problem chooses you, how do you arrive at the answer? How do you usually work?

**A:** ** I try to find a simplified version of the problem**: simple examples in which the main issue is possible and it’s present but everything else has gone. **The hope is to find a lead to follow**, **and you understand one step at a time**. In the beginning it’s not obvious how to find such a lead, and **so usually I’m completely stuck for a very long time.** But then eventually I get an idea and the idea turns out to be wrong, then there’s more delay, but then I get another idea which also turns out to be wrong. However, pretty soon there are enough ideas to balance each other out and combine, and if there is some grain of truth there, then eventually I’m able to solve some easy version of the problem, and that’s the first step of the lead. **Then I can try to generalise the problem**, although sometimes lose the lead, because I didn’t realise that there was something wrong,** so it’s not all progress.**

**Q: **What’s the longest period you’ve invested in thinking about the same problem?

**A:** 15 years.

** Q: **What was that about?

** A: **It was a problem in Quantum Mechanics,** I was wondering why atoms form.** You can read in a quantum mechanics textbook that if you take one nucleus (let’s say, a proton) and one electron it makes a hydrogen atom, but if you have 10^26 protons and 10^26 electrons and you put them in a box, nobody can tell you why they form 10^26 atoms. I thought about that and was able to prove that from the basic mathematical formulation in quantum mechanics, if a certain constant is less than 1, then it is true that, given the right conditions, atoms form. Now this constant can be measured in the laboratory and I tried to prove that it is less than 1.

**Q:** Did you finally solve that problem?

**A:** No. It took a very long time, I didn’t prove it and it’s still not known. I was able to prove that some related constants have some properties, but not the original question.

This text is an extract of the original interview with Charles Fefferman by Ágata Timón, of ICMAT (Institute for Mathematical Sciences). You can read the complete interview in ICMAT’s **Newsletter.**

**Instituto de Ciencias Matemáticas (ICMAT)**

Mathematical research center set up by the Consejo Superior de Investigaciones Científicas (CSIC –

Higher Council for Scientific Research) and three universities in Madrid:

Autónoma University (UAM), Carlos III University (UC3M) and Complutense University (UCM).

## Comments on this publication