by Nicholas Neumann-Chun

AMS President George Andrews supports a number of initiatives for the AMS, including a Fellows program.  Long-standing secretary of the MAA Martha Siegel characterizes the various mathematical societies.

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by Diana Davis

Perfect Rigor, by Masha Gessen.

Before reading this book, I had only vague ideas about Grigori Perelman. I thought that, after being a postdoc in the US, he disappeared back to Russia, lived with his mother for a number of years, then suddenly uploaded his proof of the Poincaré Conjecture to the arXiv and then disappeared back into silence. However, this is not true! The story, as you might expect, is far richer than that. Masha Gessen’s book explains it all.

This book traces Perelman’s life from the age of 10, when he joined a math club, through high school and math competitions, through the university, his postdoc positions and proof of the Soul Conjecture, through his celebrated proof of the Poincaré and up to the present. Whatever you may have thought about math education under the USSR, it is probably far from the fertile reality that Perelman experienced: one-on-one attention with teachers and graduate assistants who listened to every student’s solution to every problem, and taught students to verbally explain their solutions to their classmates. Gessen describes how Perelman (universally known as “Grisha”) was not the outspoken star of the class, but he could solve every problem, and never made a mistake, never producing a false solution. If Grisha said he had solved the problem, then he had done it correctly. Many years later, this caused his colleagues to take his arXiv papers much more seriously than they had taken the other supposed “proofs” of the Poincaré that others had published over the years: they knew that he never had any false solutions, so if Grisha said it was true, then it was not a matter of verifying the proof, just of understanding it.

Though Gessen was not able to interview Perelman, she interviewed just about every important person in his life, and paints a complete portrait of him and his mathematics. Though it is true that Perelman eventually stopped communicating with the media, immediately following his posting preprints on the arXiv he embarked on a month-long lecture tour in the United States, speaking daily on his proof and answering mathematicians’ questions for hours. Gessen explains how Perelman was initially eager to give the mathematical community this rare gift, his proof of the Poincaré Conjecture. However, she argues that he experienced repeated slights (such as the Fields Medal committee refraining from claiming that he had proved the conjecture, instead just praising his “contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow”) from the mathematical community. Over the years, this caused Perelman to retract himself first from mathematics, and then from the rest of the world.

At this point, Gessen uses a wonderful mathematical metaphor (p. 172):

The more Perelman talked about his disappointment with the mathematical establishment, and the more his acquaintances decorated his stories with demonizing details, the more Perelman’s sense of betrayal deepened. His world, which had begun narrowing in his first university year and then broadened slightly both times he had traveled to the United States, was now headed for its final, disastrous narrowing. Like a rubber band slipping inexorably off a sphere, his world was about to shrink to a point.

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by Nicholas Neumann-Chun

The 2010 Joint Mathematics Meetings are coming up!  Next week the AMS (American Mathematical Society) and the MAA (Mathematical Association of America) will convene in San Francisco, CA.  From Wednesday, January 13 to Saturday, January 16, there will be nigh-constant paper presentations, colloquia, and addresses, as well as many social gatherings.  I want to attend as many of the talks as possible.  I hopefully will both write and read reports here.  I would also like to interview several of the speakers I see.  I will get more students involved with this blog; tell me if you’d be willing to help!  And last, but not least, I will present a poster in the undergraduate poster session.

It sounds like a busy week, and I’m looking forward to it – this is my first large math conference, so I’m naturally excited.

Who else is going?  What will you be up to?

By Soojung Shin

Soojung Shin is a Korean high school student and the newest member of the Graduate Student Editorial Board—FM

I never pondered whether or not I wanted to go to graduate school. I was too busy keeping my grades up so that I could even set foot in the college of my choice. After I found out about the AMS student blog however, I started doing some research on graduate schools and how it varies from graduate schools in Korea. In the US, the basic qualifications for attending graduate school is to have a GRE score; but that is not a requirement in Korea.  There isn’t a generalized test like the GRE so the qualifications differ depending on the graduate school you want to attend. Of course, US graduate schools also have different requirements. Moreover, you start medical school in Korea while you’re an undergraduate, but it is only available to you when you are a graduate student in the US. Despite these differences, I believe that the basic concept of graduate school is similar, if not the same, anywhere you go. I am glad to have done this research because it piqued my interest in graduate school.

by Brian Katz

A few days ago, Jo posted the following question (or anguished cry) under “To Post or Not to Post” below: “Is it normal to be in second year graduate school and about 30% of the time be utterly confused?”

In short, yes it is normal to be confused a fair amount as a graduate student. At the end of approximately 5 years the strongest claim you’ll really be able to make is that you’re the expert in a very narrow question and that you’re likely to understand nearby questions. The faculty with whom you interact have been doing this for much longer, and in that time they have learned far more than content. They have learned coping mechanisms for confusion, they have learned unrelated facts that support an entirely different kind of intuition, and they have changed their standards for what is appropriate to expect of themselves in terms of understanding others’ presentations.

I see two main reasons to expect graduate students to be confused. Continue reading →