Noga Alon is a Professor of Mathematics at Princeton University and a Baumritter Professor Emeritus of Mathematics and Computer Science at Tel Aviv University, Israel. He has also held visiting positions at several other notable institutions such as MIT and Microsoft Research. He is known for making significant advancements in the fields of combinatorics and theoretical computer science. Alon was elected as a fellow of the American Mathematical Society in 2015. In addition to publishing over 500 research papers, he has received numerous awards, including the Israeli Emet Prize for Art, Science, and Culture.
1. What events in your life have contributed to where you are today with your career? How would you describe your interaction with math during high school?
I grew in Haifa, Israel. Already at a young age, I was interested in Mathematical puzzles, read a book or two about the history of mathematics and participated in some mathematics competitions in Israel (at that time Israel did not take part in the International Math Olympiads). I had a superb teacher in the last two years in high school, and in the last year, I also met Paul Erdos, a legendary Hungarian mathematician who used to travel around the world, delivering lectures in mathematics, focusing mainly on open problems in Combinatorics and Number Theory. One fact I found fascinating about Mathematics is its objectivity. A specific story I recall is that when I was roughly 12 years old, my parents had friends visiting during the Eurovision song contest. They amused themselves by trying to guess the final results of the contest determined by the votes of the participating countries before watching these votes. There were 17 competing countries, but to simplify the story and explain it better by examples let us pretend there have been only 4, denoted by A, B, C, D. Each of the guests in my parents house wrote down his guess for the final results: a ranking of all countries. Thus, for example, guessing C, A, B, D means that the guess is that country C will be ranked first, country A second, country B third.
This objective nature of the subject is a property that I found particularly appealing already then. I am not claiming that this was the exact moment I decided to be a mathematician, but I do view this story as one that may have had an impact on this decision.
2. Please describe your specific field of study and what it is that sparked your interest.
I work in Combinatorics, which is the mathematics of finite objects, on its applications in Theoretical Computer Science, Information Theory, Number Theory and Geometry, and on the interactions between these areas. The problems in the area are often very simple to state and understand, and yet their solutions often require not only a significant amount of ingenuity but also applications of sophisticated, deep tools.
3. In your list of papers, you have collaborated with many mathematicians across multiple institutions. How do these groups form and what are particular moments from these collaborations that you cherish?
In the old days, such collaborations often started in personal meetings during workshops, conferences, or research visits, but more recently joint research sometimes start by email communication. You read on the Internet a paper, have an idea on a problem mentioned there, and write to the author(s). If indeed this is a new idea that they find helpful, they may respond, possibly suggesting some related ideas they already had and starting a collaboration. While in most cases such an electronic discussion does not lead to a collaboration, it sometimes does. Besides that, there are joint research grants that fund mutual visits. A face to face collaboration that may start in such a visit, or in meetings in conferences or workshops, is still the most effective way to collaborate. I have several examples wherein joint discussions with a colleague we found a crucial novel idea. The fact that each person has a different point of view and expertise is often helpful and productive. One example I recall and cherish is a joint work with a colleague from MIT, who was visiting me when we had a joint grant, and during a discussion, we found a key idea for settling an old well-known problem in Combinatorial Geometry. Naturally, it then took quite some time and effort to complete the details, but the crucial idea emerged during that initial discussion.
4. What is it like to attend a mathematics conference?
When you are still very young, during the first few conferences you attend, it is fascinating to see and hear the researchers you have only known by name and speak with them, especially if they happen to attend a lecture you give and have some comments about it. Later, it is nice to keep meeting in conferences people you already know and discuss problems of mutual interest. It is also interesting to listen to lectures, and worthwhile to try to follow as much as you can. Finally, it is great to meet new young talented researchers at the beginning of their career.
5. What advice would you offer to youth today looking into pursuing mathematics?
It is crucial to have a passion for the subject and see the beauty of the questions studied. It is also important to realize that essentially all areas in modern mathematics apply a significant amount of sophisticated techniques, and there is a substantial amount of background that has to be studied. One has to find the right balance between the study of new topics and the time spent on attempts to tackle problems and develop methods.