Steven M. Bellovin gave a fascinating talk yesterday on a subject he knows nothing about. Okay, I should rephrase that. Bellovin knows everything you can know about his subject without actually knowing anything, but he’s careful to point out that he doesn’t really know, or else he couldn’t have given the talk. This conundrum will […]

Among children of a certain age, everyone has a best friend—and exactly one. Ideally, the best-friend relationship is symmetric: If I am your best friend, then you are my best friend, too. But symmetry is not guaranteed, and it can happen that I like you best, but you have someone else you like better than […]

In the game of Chomp, the player who moves first always has a guaranteed winning strategy. This fact might seem to take all the suspense out of the game, but it doesn’t. Except in the smallest and simplest games, no one knows which first move will lead to the guaranteed victory. For me, this situation […]

I went to the Joint Mathematics Meetings two weeks ago with the idea that I would post reports live and on location from San Antonio. I was dazzled by the mere possibility of doing this. Sitting in a lecture hall, listening to a talk, connected to the Net via the invisible magic of WiFi, I […]

Graph Limits and Graph Homomorphisms. Laszlo Lovasz (Microsoft). The field of graph theory has been transformed by recent interest in understanding properties of very large graphs, most notably those that describe communications networks such as the Internet and the Web. But the same thing that makes those graphs interesting makes them very hard to study: […]

Small Gaps between Prime Numbers: The Work of Goldston-Pintz-Yildirim. Kannan Soundarajan (University of Michigan, Ann Arbor). Soundarajan began by pointing out that it’s been quite a good millennium, so far, for work on prime numbers. In the first few years we’ve had a proof that testing primality can be done in polynomial time, we’ve had […]

Longest alternating subsequences of permutations. Richard P. Stanley (MIT). In the past decade or so, there’s been a surprisingly big fuss over what might seem to be a very small question: What is the distribution of the longest increasing subsequence in a random permutation of integers? Here’s an example of such a permutation—a random ordering […]

“It would have been a very enjoyable ride altogether, that evening’s spin along the banks of the Rhine, if I had not been haunted at the time by the idea that I should have to write an account of it next day in my diary. As it was, I enjoyed it as a man enjoys […]

I am at gate C21 at Houston Intercontinental, en route to San Antonio. The flight is late and overbooked; there’s a crowd of hopeful standbys at the podium. The first-class plutocrats are already aboard, and now the rest of us are filing on, one section at a time. “Passengers in rows 25 to 29 are […]

Ask any molecule what it thinks about the second law of thermodynamics and it will laugh at the question. All the same the molecules, collectively, uphold the second law.
—John Archibald Wheeler, At Home in the Universe, 1994, p. 283.