Three Interviews

My interview in the Israeli Academy interview series

Interviewer: Alex Lubotzky

At the beginning of the interview, I mentioned two lessons from my father. One was the formula for ((a+b)^2), which he showed me at a young age; the other was that everything becomes interesting if you devote yourself to it. (These two lessons were included in a short “promo” for the interview prepared by the Academy.)

We spoke about my mathematical activities in high school, where Alex and I first met, and about my years as a research student of Micha A. Perles, alongside a remarkable group of fellow students. We also talked about my wife Mazi, the best choice of my life, and about our children, Neta, Hagai, and Lior, as well as life in Jerusalem and Boston in the 1980s. Mazi and I first met in 1979 on a student trip to Sinai, just a week before it was returned to Egypt.

Most of the interview was devoted to mathematics: convex sets and polytopes, Helly-type theorems, high-dimensional trees, the Borsuk conjecture, linear programming, influences, the KKL theorem, noise, and quantum computing. I even brought along some polytopes and solids of constant width for demonstration.

Alex recalled that after my 2018 ICM plenary lecture he jokingly told me that my lecture had caused stock markets around the world to fall. I responded that Google’s flawed 2019 “quantum supremacy” announcement arguably caused investors in Bitcoin to lose ten billion dollars or so. We also briefly discussed the free-will problem in the context of the inherent noise sensitivity of physical systems.

At the end, we reminisced about two trips we took together: one in the 1970s to the Jordan River, and another in 2004, with our wives Yardena and Mazi, to the Amazon River and Rio.

Top two pictures, taken from the video. Right: my parents with my sister and me, around 1958. Left: Micha Perles carefully checking the proof of my main thesis result and writing out every step. At the end he triumphantly added “QED!!!” and “תושלב״ע”.

Bottom two pictures, taken during the interview. Right: with Alex Lubotzky and Yael Ben Haim. Left: with a few of my favorite polytopes.

My interview in ECAA.

Interviewer: Toufik Mansour

Toufic Mansour founded the journal Enumerative Combinatorics and applications, and has conducted an impressive series of interviews with combinatorialists (and mathematicians with interests in combinatorics). Here is Toufik’s 2022 interview with me.

Some of Toufik’s questions are common to all his interviews, while others were specific to my research. If I ever decide to write a scientific autobiography, this interview could serve as a starting point.

Toufik asked about my formative years, and I told him about a book I received from my mother.

Mansour: We would like to ask you about your formative years. What were your early experiences with mathematics? Did these come under the influence of your family or other people?

Kalai: “… My mother gave me her high-school calculus book (she did not like mathematics very much, but realized that I did), and I remember trying to read it. I could understand various things (like functions), but I got stuck on the expression . I knew that x was a variable representing numbers, but I did not understand how numbers could be added to triangles.”

Toufik also asked about problems I have worked on for many years, and I mentioned three of my own: the cascade conjecture from 1974, the influence-entropy conjecture, and the following problem from the 1980s: find a (weighted) enumeration of Laman graphs with labeled vertices that gives .

Toufik asked me if there are there are topics in mathematics that are more important than others. I answered that I suppose there are such topics but then concluded with the statement  “I am not sure if importance is that important.” Looking back, sometimes this remark strikes me as clever, and at other times as rather silly.

My interview in the “Superposition Guy”

Interviewer: Yuval Boger

Yuval Boger interviewed me on his podcast.  Transcript; Spotify.

Yuval Boger asked excellent questions about my position on quantum computing, and I was quite pleased with the substance of my answers. As for my delivery and English, at times I was reminded of what one of my MIT students in Calculus 18.011 wrote about me in 1983: “The TA mumbles, fumbles, and bumbles.” (In that course, taught by the legendary Frank Morgan, Noga Alon, Paul Seymour, and I were among the TAs.)

Toward the end, Yuval asked what I hoped the quantum computing community would take from my work, regardless of who ultimately turns out to be right.

In my response, I mainly elaborated on what might be learned from my work if I am right and, as I expect, scalable quantum computing, and even significant early milestones toward it, cannot be achieved. Such a possibility could have implications beyond quantum computing itself and may shed light on several questions in physics. I mentioned, for example, the scope of the time-energy uncertainty principle and the question of whether the new phases of matter required for topological quantum computing (“Majorana zero modes”) can actually exist.

At the same time, I said that if I am correct about quantum computers, then a great deal of the effort invested in this area will ultimately reach a dead end. In this context, I expressed my enthusiasm for the many smaller problems that arise within this grand endeavor, and my broader view that what we do has value, scientifically, intellectually, and personally, even if things do not go our way or according to our hopes.

This applies to many efforts toward quantum computing, which would become considerably less important if my theory is correct. It also applies more broadly to the work of mathematicians and scientists in a future where AI may be able to replace some of us.