So I learned from the interesting historical sketch of the big personalities of Italian algebraic geometry in this month’s *Notices of the AMS. *After Severi’s death, Roth wrote of him:

Personal relationships with Severi, however complicated in appearance, were always reducible to two basically simple situations: either he had just taken offence or else he was in the process of giving it.

He also made a point of jumping to the top of the academic ladder in Mussolini’s Italy, taking advantage of the barring of his Jewish colleagues from the highest positions. And the Notices article excerpts a magnificently peevish letter he wrote to his student Beniamino Segre, commanding him to add more about Severi’s work to his survey article on the history of algebraic geometry in Italy.

I predict only Steve will know the reason for the title of this post, or at least that it will please no one else so much as him.

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Severi’s politics and personal demeanor are well-known. What I found most interesting about the article is that Judith Goodstein, the wife of the host of the TV physics series “The Mechanical Universe” (one of the highlights of my school days), is now a historian of mathematics.

Dear Jordan,

I wondered why the cadence of the title was familiar; haven’t read those stories in a long time!

Best wishes,

Matt

Hopefully it wouldn’t be too off topic to mention some mathematical facts related to the Notices article, which might be of interest to some of your readers (and not known to all of them):

The irregularity of a surface (which in the article is defined as the difference of the geometric and arithmetic genus) is also equal to the dimension of H^1(X,O), and so the theorem relating Picard integrals of the first kind to the irregularity can (in modern terms) be thought of as an instance of the Hodge symmetry:

dim H^1(X,O) = dim H^0(X,Omega^1)

Also, for a surface in projective space, the irregularity vanishes. My understanding is that in the traditional theory of surfaces, surfaces that couldn’t be smoothly embedded in space were studied by means of a singular projection into space (like studying a hyperelliptic curve via its singular plane model y^2 = f(x) ), and this made them seem perhaps more mysterious than they might have otherwise, and also made them late-comers to the theory. Thus theorems proved in the early part of the theory of surfaces, which applied to surfaces in space only, had to be modified by this quantity (the irregularity) when applied in a more general context.

The theorem relating Picard integrals of the second kind to twice the irregularity can, in modern terms (when combined with the above case of Hodge symmetry), be interpreted as something like the equality

dim of the algebraic de Rham H^1 = dim H^1(X,O) + dim H^0(X,Omega^1)

which is a part of the degeneration of the Hodge-to-de-Rham spectral sequence.

I think it’s interesting to see how these formulas,which are so basic for us now, and are tools we use in passing when solving other problems, loomed so large in the geometric life of those who came before us, and stood out as fundamental problems in their own right. It would be nice to read history of mathematics which really came to grip with the history of the ideas like this, but I don’t know that terribly much of it exists.

I always hear great stories secondhand about mathematicians who are assholes, but I have yet to actually meet someone who fits the description.

Could Professor Severi read minds?

Regarding Matt’s comment about history of mathematics, I totally agree. But for issues having to do with the Picard scheme, Abelian integrals, etc., I think a nice, mathematically-sophisticated historical introduction does exist (probably more than one). Steve Kleiman has a 12-page historical survey in his article at the following URL.

http://arxiv.org/abs/math/0504020

Kleiman also has many other nice historical surveys on other topics in algebraic geometry.

Dear Jason,

Thanks for the reference to Kleiman’s article.

Best wishes,

Matt