Sic Transit Crankus

Monday, September 26, 2005
One thing I have to concede to those people at the NYT is that they are performing a necessary cultural function by writing obituaries about important but obscure intellectual figures. They're not doing it out of their love of mankind of course, but to bolster their self-image as smarter-than-thou. That's extremely important to their readers' egos as well as to their ultimate goal of having the power to tell the country what's what, because their apparent intellectual superiority implies (in their minds) the superiority of their opinions on all other subjects.

But good things can be done for the wrong reasons, and so yesterday they published an obituary of Serge Lang, an iconic mathematician who ended up at Yale after a tumultuous history. He died at the age of 78.

Serge Lang was a first rate mathematician who became famous outside the field for two things unrelated to his mathematical talents: textbooks and politics. He wrote brilliant but unusable textbooks on all the standard undergraduate mathematics topics at a furious pace, literally cranking a new one out in the span of three or four weeks. They were brilliant because they incisively cut to the quick in each particular hackneyed undergraduate subject, lending it a freshness which it had lacked for some fifty years. They were unusable because they were written for other research mathematicians just like him, paying no homage whatsoever to the difficulties encountered by actual undergraduates. For one undergraduate in a million it was probably a great success. I was obligated to teach out of one such textbook during one semester. The exposition was superlative; the class was fine until we came to the first problem set, at which point it was a disaster.

A political tyro who matured in the Sixties, he got caught up, as did many academics of his day, in the anti-Vietnam War movement. He became famous as a crank or a gadfly, depending on which side of an issue one believed to be the "right" one. He opposed the Vietnam War (side of the angels, according to NYT), opposed apartheid (ditto), but also became infamous for arguing that AIDS was not caused by the Human Immunodeficiency Virus (big--and I mean big--no-no to the NYT).

There's a fine line between genius and crank. If you're going to go out on a limb and think for yourself, if you're going to go beyond the ordinary run of human thinking, you run the risk of going completely off the deep end. It requires a big ego, and ultimately you become accountable only to your own thoughts, which is dangerous. There's no in-built guidance mechanism. It is hard to tell the difference between genius and crank sometimes. When it was discovered in the late Nineteenth Century that the "principle of relativity" as stated by Galileo was inconsistent with Maxwell's laws, a solution was proposed: let's just say all the measuring rods get shorter when we move! It makes all the equations work out, but when it was proposed it was proposed at least half tongue-in-cheek. It was crazy; it was cranky. But Einstein took that idea and wove it into a magnificent theory which is now the single most accurate theory known to mankind. We celebrate Einstein as the acme of genius.

RIP Serge Lang, crank and genius.


terrye said...

I would say that most brilliant people are flawed in some other way.

It is as if nature decided to take away some social skill or poise or serenity to balance out the surplus of smarts.

Think about it, most really brilliant people are a tad eccentric.

Seneca the Younger said...

Serge Lang and Don Adams.

I loved both of their work.

I suppose this says something.

chuck said...

I think that the NYT has pretty good coverage of mathematics, and science in general. I thought their articles on Wiles' proof of Fermat Last Conjecture were excellent. Of course, the rot may spread to the science section at some point, it may even be inevitable.

I will miss Serge Lang. I thought his texts were quite wonderful. I remember learning multi-dimensional calculus at Columbia by dividing the book into halves and reading the first half the weekend before the first final. I didn't attend classes, so it was my best guess as to the material that had been covered ;) On a more serious note, when I later took analysis from Rudin's book I also got Lange's text and worked through it. My opinion was that it would have been a better text for applied mathematicians due to his selection of material. I also learned algebra from Lang's text, although I think for algebra it would be a toss up with Hungerford's book, which does a better job on some topics but tends to over generalize a bit. One of Lang's great virtues was to present the core of a subject while stripping away much that was extraneous. For instance, reserving the designation ring for what other's might call rings with identity. His choice of problems also showed great taste.

I was always amazed that Lang could produce so many books of such quality, and the later editions only got better -- something that can't be said of some authors. RIP.