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.

Of Historical Note

The following excerpt is from the article “Can We Survive Technology?” by John von Neumann, published by Fortune magazine in 1955. Von Neumann was among the Institute’s first Professors and its youngest. Having pioneered the modern computer, game theory, nuclear deterrence, and more, von Neumann illuminated the fields of pure and applied mathematics, computer science, physics, and economics. He remained a Professor at IAS until his death in 1957.

"All experience shows that even smaller technological changes than those now in the cards profoundly transform political and social relationships. Experience also shows that these transformations are not a priori predictable and that most contemporary 'first guesses' concerning them are wrong. For all these reasons, one should take neither present difficulties nor presently proposed reforms too seriously.

"The one solid fact is that the difficulties are due to an evolution that, while useful and constructive, is also dangerous. Can we produce the required adjustments with the necessary speed? The most hopeful answer is that the human species has been subjected to similar tests before and seems to have a congenital ability to come through, after varying amounts of trouble. To ask in advance for a complete recipe would be unreasonable. We can specify only the human qualities required: patience, flexibility, intelligence."

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by Monica H. Green

Monica Green (left) joins a conversation hosted by Alan Alda (right) on engaging a general audience through the craft of storytelling. (Photo: Amy Ramsey)
Monica Green (left) joins a conversation hosted by Alan Alda (right) on engaging a general audience through the craft of storytelling. (Photo: Amy Ramsey)

A Year (Well, Nine Months) in the Life of an IAS Member

The Institute is a remarkably modest place. Like all Members of the School of Historical Studies, I was provided a lovely apartment, a simple office (with computer), access to both the Institute’s libraries and those of Princeton University, lunch in the dining hall, tea in the afternoon. So how does new knowledge come out of such a simple mix? Juxtaposition! So much of the wealth of insight I’ve had this year (and there’s been a lot of it) has come from the chance conversations, the oblique reference in a lecture, the reference exchanged in the hallway.

The world of scholarship is a very different place than when I was a Member here for the first time in 1990–92. There was an Internet then, I suppose, but I was not yet a user. I was not yet using email, there was no Google, no online digital reproductions of unique medieval manuscripts that I could call up for viewing within seconds, rather than having to travel thousands of miles to get to distant libraries during their rare opening hours or buying expensive films that had to be strung up on a microfilm viewer (ugh!) for long, eyeball-shrinking, mind-numbing sessions. So much of the world of knowledge is now at my fingertips; I can go for hours without ever leaving my desk. So what is the value of the IAS in such a hyper-connected world? Even more than twenty years ago, I found that the richness of this place lies in the human interactions, the analogueness (if you will) of life at this community in the woods.

Much of my work this year has been in collaboration with scholars elsewhere, building on projects already many years in the making. But my work and theirs has been infinitely enriched by the daily stimuli I’ve had from my colleagues here at IAS. Here are a few vignettes.

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Curiosity and Persistence by Unknown Mathematician Leads to Fundamental Breakthrough

Member Yitang Zhang looking out at the Institute pond    (Photo: Amy Ramsey)
Member Yitang Zhang looking out at the Institute pond (Photo: Amy Ramsey)

A year ago April, the editors of the Annals of Mathematics, a journal published by the Institute and Princeton University, received an email with a submission by an unknown mathematician. “Bounded Gaps Between Primes” by Yitang Zhang, an adjunct professor at the University of New Hampshire, immediately caught the attention of the editors as well as Professors in the School of Mathematics. It was refereed by mathematicians who were visiting the Institute at the time and was accepted three weeks later, an unusually expedited pace.

“He is not a fellow who had done much before,” says Peter Sarnak, Professor in the School of Mathematics. “No-body knew him. Thanks to the refereeing process, there were a lot of vibes here at the Institute long before the newspapers heard of it. His result was spectacular.”

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by Vladimir Voevodsky

Diagram by Voevodsky
This three-dimensional diagram is an example of the kind of ­”formulas” that Voevodsky would have to use to support his arguments about 2-theories.

Professor Voevodsky’s Personal Mission to Develop Computer Proof Verification to Avoid Mathematical Mistakes

In January 1984, Alexander Grothendieck submitted to the French National Centre for Scientific Research his proposal “Esquisse d’un Programme.” Soon copies of this text started circulating among mathematicians. A few months later, as a first-year undergraduate at Moscow University, I was given a copy of it by George Shabat, my first scientific adviser. After learning some French with the sole purpose of being able to read this text, I started to work on some of the ideas outlined there.

In 1988 or 1989, I met Michael Kapranov who was equally fascinated by the perspectives of developing mathematics of new “higher-dimensional” objects inspired by the theory of categories and 2-categories.
The first paper that we published together was called “∞-Groupoids as a Model for a Homotopy Category.” In it, we claimed to provide a rigorous mathematical formulation and a proof of Grothendieck’s idea connecting two classes of mathematical objects: ∞-groupoids and homotopy types.

Later we decided that we could apply similar ideas to another top mathematical problem of that time: to construct motivic cohomology, conjectured to exist in a 1987 paper by Alexander Beilinson, Robert MacPherson (now Professor in the School of Mathematics), and Vadim Schechtman.

In the summer of 1990, Kapranov arranged for me to be accepted to graduate school at Harvard without applying. After a few months, while he was at Cornell and I was at Harvard, our mathematical paths diverged. I concentrated my efforts on motivic cohomology and later on motivic homotopy theory. My notes dated March 29, 1991, start with the question “What is a homotopy theory for algebraic varieties or schemes?”

The field of motivic cohomology was considered at that time to be highly speculative and lacking firm foundation. The groundbreaking 1986 paper “Algebraic Cycles and Higher K-theory” by Spencer Bloch was soon after publication found by Andrei Suslin to contain a mistake in the proof of Lemma 1.1. The proof could not be fixed, and almost all of the claims of the paper were left unsubstantiated.

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by Yvonne Chiu

A wounded German soldier lighting a cigarette for a wounded British soldier at a British field hospital during the Battle of Épehy, near the end of the First World War (1918)
A wounded German soldier lighting a cigarette for a wounded British soldier at a British field hospital during the Battle of Épehy, near the end of the First World War (1918) (Photo: Lt. Thomas K. Aitken, British Army photographer/Imperial War Museums)

‘Live and Let Live’ as a Representative Element of War

Images that convey the essence of war are more likely to resemble the frenzied, merciless, mutual slaughter between the Aegeans and the Trojans as told in The Iliad, the rapes depicted in Goya’s The Disasters of War, the torture portrayed in The Battle of Algiers, or the indiscriminate napalm bombing in Vietnam dramatized in Apocalypse Now. It is commonly believed—and for good reason—that morality and civilization are inevitably forgotten in war, as participants become desperate to survive, get caught up in the bloodlust, or lose touch with their humanity. There is truth to that, so it might be surprising to think of banning hollow point bullets (Hague Convention, 1899) or regulating prisoner-of-war treatment (from the 1648 Peace of Westphalia through the 1949 Geneva Conventions) as simultaneously capturing an essential element of warfare, but in fact they represent a significant component of war, which is cooperation between enemies.

Some of the more amazing stories of cooperation in warfare come from the trenches of World War I. During the Christmas truces in 1914, and to a lesser extent in 1915, not only did 100,000 British and German soldiers in WWI unofficially stop fighting, but in some places in Belgium, German soldiers who decorated their trenches with candles and trees and sang carols were met with British soldiers singing in kind; eventually, the two sides mingled in No Man’s Land, exchanging gifts, food, and souvenirs, and even engaging in short, casual football games.

In addition to ad hoc cooperation on a shared holy day, opposing trenches spontaneously developed a longer-lived system of timed shellings to allow the other side to anticipate and avoid their impact. While trench warfare was a large part of the WWI experience, it is not particularly interesting militarily. Rather, it is noteworthy for what fighting did not happen. This “live and let live” system has been recounted in marvelous detail by Tony Ashworth (Trench Warfare 1914–1918). That reciprocal exchange—of minimization of injury and death—took different forms during the war: truces lasted anywhere from a few minutes to several months; some were explicit agreements between fraternizing soldiers in close quarters, while others were indirect (due to legal sanctions), over long distances, and involving large numbers of people. There were numerous reports of people walking openly above trenches; unrestricted movement in and out of the trenches; Germans frying sausages and photos of Brits frying bacon in the trenches, despite the fact that smoke from the fires would have attracted gunfire on active fronts; and descriptions of “quiet” fronts, where there were no ammunition shortages. In some trenches, people hunted and retrieved small game, harvested vegetables, kept milking cows for fresh milk, and had pianos and books.

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