Hello?… The first thing I remember feeling moments later was panic.
Five years before that day, I was a graduating senior at MIT pursuing a Bachelor of Science in Mathematics with Computer Science (18C for all the fellow nerds out there). I had been close to some of the most brilliant people I have ever met, like my undergraduate adviser Michael Sipser and my undergraduate research mentor in bioinformatics, Bonnie Berger. I had applied to several graduate schools to study mathematics, but had been summarily rejected by most of them. It was a humbling experience, which ultimately led me to the day I got the call. I remember clearly what day it was: February 6th, 2008. I was eating breakfast with two friends at a local diner in Davis, CA. Yes, the one place which had enthusiastically accepted me to their Ph.D. program was the Mathematics Department at UC Davis. In fact, being an international student from Greece, and given the tight State budget of California at the time (all the time), it was a miracle that UC Davis said yes. True, I had a good GPA and lots of research experience at MIT, but I did not have any direction. I did not apply to work with any particular Professor, I just applied by school name and reputation. And if it weren’t for Prof. Berger’s suggestion to apply to UC Davis, I would have applied to the top 5 graduate schools in Applied Mathematics and would be trading stocks in New York right now. I was naive.
So here I am five years later, eating my sunny-side-up eggs when Matt Hastings calls:
–Hi Spiros, this is Matt.
–Is this a good time to talk?
At this point I was thinking that it took Matt only a day to decide that I was not going to be his first postdoc. Hence the panic.
–Yes, good to hear from you. What’s up?
–When are you getting your Ph.D.? Can you start some time this summer at Los Alamos?
I would like to put the next few moments in perspective… Matt had been looking for his first postdoc for some time. Many must have applied given that he had already published some of the most spectacular results of the past decade in the field of Quantum Many-Body Physics, like the Area Law for One Dimensional Quantum Systems and the Lieb-Schultz-Mattis in Higher Dimensions, among several other strong results. And Los Alamos National Labs (LANL) paid postdocs really well (and still does). So, what was it about me that changed his mind? It was probably desperation, but I would like to think that it was partially respect for the great work that my Ph.D. adviser, Bruno Nachtergaele, had done on research related to Matt’s interests. In fact, when asking Bruno if I should apply to be Matt’s postdoc, he simply said: “He is an intellectual tornado. But if you survive, you will become very strong.”
The truth is that during my visit to LANL the days before the call, I had impressed Matt with my tea-serving technique, while we were discussing the true scaling of the area-law bound with respect to the inverse gap of a Hamiltonian. He was asking me if I thought it should be linear, instead of the exponential bound he had derived, and I was thinking that the sushi was not very fresh. Finally, I said linear and he seemed pleased. It was a good day and he had been a gracious host, but I did not expect to get an offer the next day, or ever…
First day at Los Alamos
One of the most exciting problems at the intersection of mathematics and physics is the explanation of macroscopic properties of materials (known as topological quantum order) that arise from genuine quantum behavior. This stuff is important because of its connection to scalable quantum computation and the behavior of exotic phases of matter. To me it is important because my first day in Los Alamos, Matt asked me the following question: “Spiros, do you want to work on something easy, or on something interesting?” I swear I said to him “Something easy”, but he still told me to work on Problem #2 on Michael Aizenman’s list of important Open Problems in Mathematical Physics (go ahead, look here for the problem titled Quantum Hall Conductance).
I remember clearly that when I heard his response, the look on my face was not one of disbelief that he expected me to solve something akin to a Millennium problem in Mathematical Physics. The look on my face was that of a normal person who didn’t know what the words they were hearing meant (my Ph.D. was in Math, not Physics!) Still, he left me with a book and a “You can do this” kind-of-look. It took me 3 months until I knew what the words meant (and the book was not all that helpful). It took me another 3 to write down the question I was supposed to answer (and here the book was helpful). Then I started reading all the relevant research on the subject that I could understand. Matt was very busy with travel at the time, but whenever he was back at the Lab, he would ask about my progress. He would also make suggestions from time to time, but every time it felt like he was speaking an alien language and I did not want to admit to him that I did not understand. It was, again, a very humbling experience. But then… success. I know I am skipping a lot of details in that last part, but you can find them all here: Quantization of Hall Conductance For Interacting Electrons Without Averaging Assumptions. In order to solve this non-trivial problem (if scientists ever use “non-trivial” next to something they have done, they really mean “groundbreaking, Nobel-Prize worthy”), we had to combine some of the best existing ideas with several new techniques that allowed us to turn the analysis of a purely quantum phenomenon, into one with a fighting chance of being solved by classical minds.
A brief historical detour
Back in 1879, a young scientist named Edwin Hall was working on his doctoral thesis at Johns Hopkins University, on a question first posed by James Clerk Maxwell. Maxwell, who was at Harvard at the time, had (literally) written the textbook on electromagnetism, presenting the world with an astonishing set of equations (now known simply as Maxwell’s Equations), which put electricity and magnetism on equal footing. But, in his textbook, Maxwell had written that the force exerted by a magnetic field on a conducting material with electric current passing through it was due to the influence of the magnetic field on the conductor itself and not on the current of electrons zooming through. Hall thought otherwise and proceeded to test his hypothesis that the electrons in the current were the ones that felt the magnetic field pulling on them. And he was right. The electric current was being diverted in a perpendicular direction to its initial path and Hall had measured that effect 18 years before electrons were discovered! It must have been awe-inspiring (and petrifying) to prove someone of Maxwell’s stature wrong, and so Hall was offered a Professorship at Harvard, where Maxwell could keep an eye on him.
A century later, Klaus von Klitzing, then a young professor at the Technical University of Munich, was re-enacting Hall’s famous experiment, but at much lower temperatures and much stronger magnetic fields. What he saw, he didn’t even appreciate immediately. As the strength of the magnetic field perpendicular to the conductor was increased, the intensity of the electric current that was diverted due to the Hall effect did not increase in proportion. It jumped! Whenever the magnetic field attained a certain value, the conductance of the Hall current jumped to a new level and stayed there until the next magical value of the magnetic field was reached. And these values came in nearly perfect integer multiples of $latex e^2/h$, where $latex e$ is the electron’s charge and $latex h$ is the Planck constant. When the world of science realized what this result meant, they awarded von Klitzing with the Nobel Prize in Physics. The world had discovered something amazing: Order at the level of the macroscopic universe, orchestrated by the concerted dance of a trillion trillion (yep, not a typo) interacting electrons. And I was tasked with figuring out how…
The paper is now in review for over two years at one of the most prestigious journals in the field. It is living in some sort of limbo, where it will be published as soon as we find the time to sit down and update the result to the strongest one we have obtained within these last two years (Matt, I am working on it, I promise). It will also make the proof shorter and more elegant. And I think it would be neat to have a fiery Solved! icon next to the problem in the list mentioned above. My parents would be proud, though they wouldn’t know why, really.
Now, this accomplishment would not have been possible without the work that many physicists (including my mentors) have done in their spectacular careers. I am pretty certain that Matt could have solved the problem himself in a few months and taken all the credit for himself. Still, I remember how often I asked for help and how, almost every time, I heard: “Spiros, this is your project. You can do this.” He believed in me and he wanted to see me succeed. I also remember the autumn afternoon at UC Santa Barbara, when he came back to my office and said: “You did it. I cannot find any mistakes. There are a few places which call for better notation, but that’s it.”
I had worked on this project non-stop for fourteen months! I went to sleep thinking about it and woke up depressed that I was nowhere close. Actually, I couldn’t sleep normally. My mind only switched off after days of no sleep. I think I solved the problem because I didn’t want to die. First, I wanted to make progress in order to look smart. Here was a problem that had several Nobel prizes to its name already and was ranked next to the only problem solved so far on Aizenman’s list, which yielded a Fields Medal. I “solved” the problem several times, which lead to the second stage of survival and the hardest to endure. Emotional exhaustion – the lows that come from realizing that your proof is bogus are far more extreme than the adrenaline highs of thinking you have solved an impossible problem. I wanted to make small, infinitesimally small progress that was real! I was ready to sell my own mother to see an inch of progress (she doesn’t read English very well, so please don’t tell her; I love her very much.) The last stage was physical exhaustion. I don’t remember much about this stage, beyond a feeling of calm and humility; that you are fighting against a vastly superior opponent and all you can gain is wisdom from the pain you have endured in helpless desperation. The support of my mentor (and co-author) at this stage was crucial. It was three simple words: “You are close.”
I trusted those words with my life, but I was close to giving up. I remember calling my mom back in Greece on a Wednesday and saying matter-of-factly: “I am so tired. I think it is fair if I sleep now. Mom, I don’t know if I want to wake up…” My mom simply replied: “Θα σε σκοτώσω αν κάνεις καμμία βλακεία!” (I will kill you if you do anything stupid!) It helped. Absurdity was more translucent to me than any logic at that point. And my mentor was right. I was close. Pretty freaking close actually. The last piece did not appear in a moment of genius. It appeared in two more months of sleepless nights, inch by stupid inch. Which is when I learned something important about myself: I was not a quitter. And even if I were a quitter, the people who believed in me wouldn’t let me quit. Which kinda sucks when you are seriously sleep-deprived and all you can think of is that you have been swept up by an intellectual tornado…
Matt, congratulations on your recent recognition as a Simons Investigator. And thanks for taking a chance with me.