Articles from the Institute Letter

Additional articles from new and past issues of the Institute Letter will continue to be posted over time and as they become available.

By Andris Ambainis

The study of quantum information could lead to a better understanding of the principles common to all quantum systems.

When I was in middle school, I read a popular book about programming in BASIC (which was the most popular programming language for beginners at that time). But it was 1986, and we did not have computers at home or school yet. So, I could only write computer programs on paper, without being able to try them on an actual computer. Surprisingly, I am now doing something similar—I am studying how to solve problems on a quantum computer. We do not yet have a fully functional quantum computer. But I am trying to figure out what quantum computers will be able to do when we build them.

The story of quantum computers begins in 1981 with Richard Feynman, probably the most famous physicist of his time. At a conference on physics and computation at the Massachusetts Institute of Tech­nology, Feynman asked the question: “Can we simulate physics on a computer?”

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New physics suggests a profound conceptual revolution that will change our view of the world.

The following excerpts are drawn from Professor Nathan Seiberg’s public lecture “What’s Next?” available at https://video.ias.edu/seiberg-2013/. 

I do not know what the future will bring. I guess nobody knows; and we do not know what will be discovered, either experimentally or theoretically, and that’s actually one of the reasons we perform experiments. If we knew for sure what the outcomes of the experiment would be, there would be no reason to perform the experiment. This is also the reason scientific research is exciting. It’s exciting because we’re constantly surprised either because an experiment has an unexpected outcome or theoretically someone comes up with a new insight. . . .

We are in an unusual and unprecedented situation in physics. We have two Standard Models. The Standard Model of particle physics describes the shortest distances and the Standard Model of cosmology describes the longest distances in the universe. These models work extremely well over the range of distances for which they were designed to work. However, there are excellent arguments that this story is not complete, and there must be new physics beyond these models. . . .

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By Milton Cameron

Albert Einstein in living room, Fallingwater, 1939
Albert Einstein in living room, Fallingwater, 1939

Einstein's reputation gained him a following among architects who were out to transform American architecture and design.

When Albert Einstein first met Frank Lloyd Wright, he mistook the architect for a musician. Leaping from his chair, Einstein announced that he was returning home to fetch his violin and would be back shortly to perform a duet. Only upon his return did he learn that Wright was not a pianist. It was early 1931, and the two men were guests of Alice Millard, a rare book and antique dealer. The setting, ironically, was the dining room of La Miniatura, the house that Wright had designed for Millard at 645 Prospect Crescent, Pasadena. But if the architect was taken aback by Einstein’s gaffe, he did not show it. Wright had just met the most famous person in the world, and was determined to exploit the opportunity for all it was worth.

Wright liked to groom important public figures to complement his social circle and support his campaigns. The latest of these, which would obsess him for the remainder of his life, was to replace congested, disease-ridden cities and their skyscrapers with a dispersed, horizontal form of development that would spread across the countryside and capitalize upon the increasing availability of automobiles. Wright knew he would need all the help he could get to achieve such a radical transformation of the fabric of American society. Einstein’s name and reputation was just what he required.

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By Edward Frenkel

How a conference at IAS began a new theory bridging the Langlands program in mathematics to quantum physics

The Institute for Advanced Study has played an important role in my academic life. I have fond memories of my first visit in 1992, when, a starstruck kid, I was invited by Gerd Faltings and Pierre Deligne to talk about my Ph.D. thesis, which I had just completed. In 1997, I spent a whole semester at the IAS during a special year on quantum field theory for mathematicians. I returned to the IAS on multiple occasions in 2007 to collaborate with Edward Witten, and then in 2008–09 to work with Robert Langlands and Ngô Bao Châu.

Perhaps one of the most memorable visits was the one that happened exactly ten years ago, in March of 2004. It is described below in the (slightly abridged) excerpt from my book Love and Math. A few months earlier,  Kari Vilonen, Mark Goresky, Dennis Gaitsgory, and I were chosen to receive a multimillion dollar grant from the Defense Advanced Research Projects Agency (DARPA) to work on a project aimed at establishing links between the Langlands program and dualities in quantum field theory. We felt like we were in uncharted territory: no mathematicians we knew had ever received grants of this magnitude before. Normally, mathematicians receive relatively small individual grants from the National Science Foundation. Here we were given a lot of resources to coordinate the work of dozens of mathematicians with the goal of making a concerted effort in a vast area of research. This sounded a bit scary, but the idea of surpassing the traditional, conservative scheme of funding mathematical research with a large injection of funds into a promising area was really exciting, so we could not say no. We turned to the Institute for Advanced Study as the place to foster innovation. As they say, the rest is history.

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By Ralph Kaufmann

To be fully grasped, mathematical ideas have to be rediscovered or reimagined, much like in the translation of poetry.

Mathematical language is becoming more and more pervasive. This phenomenon ranges from the mundane (imprints on T-shirts or mugs) to the more scientific (its use in reporting or in disciplines outside of mathematics) and even includes art in its span. This begs the question, why and how does it work? Or more poignantly: What is the form and function of mathematical language inside and outside its community of speakers?

In the field of mathematics itself, the situation is not as homogenous as one might think. How much truth is contained in a proof by pictures is quite different in algebra versus geometry, and, historically, there is great variation in what is considered a proof—mainly how stylized the language should be. Being too relaxed can lead to foundational crises and questions like those Helmut Hofer is working out in symplectic geometry. An extreme position, which I call Frege’s dream, is also alive today with Vladimir Voevodsky and his colleagues through their endeavors to formalize language as much as possible to maximize verifiability. Some might argue that Bourbaki represented a golden age for striking a balance between the formal, the communal, and the communicable. 

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