Articles from the Institute Letter
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On May 21, King Harald V of Norway presented the Abel Prize of the Norwegian Academy of Science and Letters to Pierre Deligne, Professor Emeritus in the School of Mathematics. In his acceptance speech, published here, Deligne articulates the essential role of freedom and curiosity in research––as the source of most of the important applications of sciences and as a powerful incentive to do the best work possible. The Institute is deeply grateful to Deligne, who has donated a portion of his monetary prize to support curiosity-driven research in the Institute’s School of Mathematics. His gift will be matched by the Simons/Simonyi $100 million challenge grant, which is the basis of the $200 million Campaign for the Institute.
Your Majesty, Minister, Excellencies, colleagues, family, friends, and guests,
I am very honored that this Abel Prize associates me with the luminaries who received it before me, amongst whom are my teachers and mentors Jacques Tits and Jean-Pierre Serre.
The past century has been a golden century for mathematics. When I look back, I am amazed at all the questions that in my youth seemed inaccessible, but which have now been solved. The last half-century has also been a golden time for mathematicians, but I worry that the prospects for young people are now far from being as good.
Throughout my life, I have received crucial help from many people and institutions. This for me is an occasion to give thanks.
By Christer Bruun
Besides Rome itself, there are principally two cities in Roman Italy that vie for the attention of both scholars and the public at large: Ostia and Pompeii. The latter is known for its tragic end in the volcanic eruption of 79 C.E., for fascinating wall paintings, and for millions of tourists who every year trample its sunbaked streets. Ostia suffers from relative neglect. Situated too close to the attractions of eternal Rome, the town draws many fewer visitors than its monuments and its overall importance would deserve, even though its green pine trees and the lush vegetation help make it into a peaceful historical oasis at the very mouth of the Tiber River.
From a historical perspective, Ostia was a more important settlement than Pompeii. With a population of perhaps as many as fifty thousand inhabitants, the town was much larger than its “rival.” More significantly, while Pompeii’s history was cut short when Rome’s imperial period was only in its infancy, Ostia, which was first settled in the fourth century B.C.E., still thrived during the third century C.E., and we have historical sources that allow us to follow its development well into the 400s.
In early April 1972, Hugh Montgomery, who had been a Member in the School of Mathematics the previous year, stopped by the Institute to share a new result with Atle Selberg, a Professor in the School. The discussion between Montgomery and Selberg involved Montgomery’s work on the zeros of the Riemann zeta function, which is connected to the pattern of the prime numbers in number theory. Generations of mathematicians at the Institute and elsewhere have tried to prove the Riemann Hypothesis, which conjectures that the non-trivial zeros (those that are not easy to find) of the Riemann zeta function lie on the critical line with real part equal to 1⁄2.
Montgomery had found that the statistical distribution of the zeros on the critical line of the Riemann zeta function has a certain property, now called Montgomery’s pair correlation conjecture. He explained that the zeros tend to repel between neighboring levels. At teatime, Montgomery mentioned his result to Freeman Dyson, Professor in the School of Natural Sciences.
In the 1960s, Dyson had worked on random matrix theory, which was proposed by physicist Eugene Wigner in 1951 to describe nuclear physics. The quantum mechanics of a heavy nucleus is complex and poorly understood. Wigner made a bold conjecture that the statistics of the energy levels could be captured by random matrices. Because of Dyson’s work on random matrices, the distribution or the statistical behavior of the eigenvalues of these matrices has been understood since the 1960s.
By Patrick Geary
Few historical questions have so fascinated historians as the fall of the Roman Empire or, in the more fashionable modern parlance, its “transformation” into something altogether different, namely independent kingdoms ruled by successors of barbarian commanders in the West and a Greek-speaking Byzantine Empire in the East. For over two centuries, historians have particularly debated the role of barbarian invasions in this process, but in reality we have very little hard data on the nature of the barbarian “peoples” that entered the Western provinces between the fourth and sixth centuries, their numbers, their composition, or the reality of their influence on the indigenous populations of the Empire.
Were these large ethnic populations moving across Europe from Scandinavia to Italy and Spain, as nineteenth-century romantics imagined? Or were they small heterogeneous military units employed by the Empire that settled, with a minimum of force and disruption, within the administrative and fiscal mechanisms of a still-functioning Empire, as has been suggested more recently? Did these groups long maintain their distinctiveness from the local population, eschewing intermarriage and holding fast to their distinctive legal and cultural traditions, or did they rapidly integrate themselves into local elites through intermarriage and cultural transformation? Were they really distinct population groups at all or merely provincial Romans and local “barbarians” who united under ethnic labels and took advantage of opportunities to seize power from a beleaguered empire? Traditional sources with which to answer these questions—highly rhetorical accounts of the period often written centuries later, sparse administrative documents surviving in scattered fragments, and ambiguous archaeological material showing changing patterns of burial custom and settlements—simply do not provide enough evidence to reach a consensus.
By Deva Woodly
I was in my final year of graduate school, writing a dissertation on the place of persuasion in the success of contemporary American social movements, when the nearly two-year-long campaign for the American president who would succeed George W. Bush began. As a student of politics, it was impossible not to be transfixed by the epic discursive battle being waged, first in the hard- fought democratic primary between Hillary Clinton and Barack Obama and finally during the general election campaign in which, Obama, having won against his formidable Democratic rival, entered a political contest with veteran politician John McCain. For the American public, this contest was the most closely followed election in decades. A Gallup poll taken in June 2008, early summer, when political attention is usually at its nadir, found that nearly two-thirds of Americans described the 2008 campaign as “exciting.” By September, Gallup found that a record 87 percent, almost nine in ten Americans, reported that they were following national politics closely. The astonished poll takers wrote, in the summary of their results, “This significantly exceeds anything Gallup has measured since it began asking this question in 1995.”*