Ars Mathematica

Famously, the economist Gerard Debreu was close to the Bourbaki circle of mathematicians. This gives his book-length treatment of general equilibrium, Theory of Value, the reputation of being economics the way Bourbaki would write it.

I’ve been looking over Theory of Value, and while it is very abstract for an economics book, but anyone who thinks that the book could have been written by Bourbaki has never had the pleasure of the real thing. Debreu’s book has picture and everything. I would put it at the same abstraction level as Herstein’s Topic in Algebra.

Guest posting at the n-Category Café, Tom Leinster drew everyone’s attention to Sheldon Axler’s manifesto, Down With Determinants! Axler argues when teaching linear algebra, determinants should be avoided almost completely.

This has led to a surprisingly wide-ranging discussion. Lieven Le Bruyn and more recently Masoud Khalkhali have weighed in with defences of the determinant.

The mysterious figure known only as “Robbie” upgraded our WordPress installation. Let us know if anything has broken. The only noncosmetic difference is that we are experimenting with captchas. Now, I hate captchas with the white hot fury of a thousand suns, but the amount of spam that was getting through the Akismet filter and requiring manual deletion was making me yearn for death, so I’ll leave captchas enabled to see how they work out.

Lieven Le Bruyn has relaunched his weblog under the new name Moonshine Math. The planned focus is monstrous moonshine.

Lieven converted some of the posts from the blog’s former life to PDF. You can find a links to the listings here.

Via Scott Aaronson and Peter Woit, I learn the story of Elizabeth Okazaki, who apparently has been hanging around the Stanford physics department for the past four years posing as a visiting scholar working on an interdisciplinary project. She has also apparently been using office space and even sleeping in the building. The range of reactions I’ve seen have been from shock and fear to pity, to amusement, but I haven’t seen anyone express my reaction: admiration. Assuming, as many people have suggested, that Okazaki is someone down on her luck looking for a place to stay, I have to admire her ingenuity in solving her problem. Physics departments have a high tolerance for personal idiosyncracy, and someone who keeps weird hours would never stand out in one. Physicists are a little vague on they do in humanities departments, so sprinkle a little interdisciplinarity on your project, and presto!, instant credibility. Her whole plan was practically scientifically designed to succeed for years. Maybe the NSF should give her a grant.

Stanford had another case of an interloper which in some ways is even more interesting. Azia Kim actually moved into the dorms and successfully posed as a college student for eight months. Okazaki’s plan only required the ingenuity of coming up with the cover story, and then sticking to it. Kim had to actually pretend to take classes to keep up her pretense. She also had to sneak into the dining halls to eat, and to climb back up into her dorm room window every night. I can’t even imagine the chutzpah it took to trick her way into dorm room, knowing how easy it would have been for her to get caught. It all required considerable courage.

In late May, Peter Woit posted that Lucien Szpiro had announced a proof of the abc conjecture at the Goldfeld conference. In comments here, commenter Z passes along a rumor (with emphasis on rumor) that Szpiro’s proof has a significant flaw. Peter has updated his post to mention he’s hearing similar things.

Peter links to a couple of resources on the conjecture, which implies several other results (including most famously Fermat’s Last Theorem): The abc conjecture home page, and a survey article by Dorian Goldfeld.

The tenth Carnival of Mathematics is up at Math Notations. The next carnival will appear at Grey Matters.

I was doing some more reading on general equilibrium, when I came across On the Fundamental Theorems of General Equilibrium by Maskin and Roberts, which gives a succinct proof of the existence of general equilibrium, as well as the two subsidiary results known as the first and second welfare theorems. It’s particuarly good in spelling out the mathematical relationship between the different results. (Be warned, though. It’s completely unintelligible if you don’t have a separate description of the model handy, though.)

I found the paper via this post by Michael Greinecker on his weblog Yet Another Sheep.

Elsevier, one of the major commercial academic publishers, had the curious side business of hosting arms fairs. After pressure from customers and authors, they have decided to exit the business.

Via Crooked Timber.

Bernhard Krötz has added another update on Tribikram Pati’s preprint. He now reports that the paper does not in fact disprove the Riemann hypothesis. Details provided by a colleague.