Aldo Andreotti's Math Lesson

It was long ago in Pisa. Scuola Normale Superiore, Science Division. The students were waiting anxiously for the famous geometer, Aldo Andreotti, a legend of modern day italian mathematics.

The place: a lecture room, in the old Palazzo dei Cavalieri. Time: evening, before dark.

November, perhaps. Perhaps not.

At a certain point, a clumsy, chubby fellow shows up and announces that Prof. Andreotti will be late, and that he will start the lecture in his stead. There was nothing remarkable about it, the fellow writes formulae monotonously, one after the other, on the wide chalky blackboard.

Time passes, endless, tedious time.

Then, suddenly, as if materializing out of thin air, Professor A. shows up. He stares at the formulae, dismisses briskly the chubby and clumsy fellow, and begins writing, as if talking to himself.

He may have continued for a few minutes, he may have asked a few questions, I have no clear recollection.

Once again, as suddenly as he had appeared, he stops.

He sits on his chair, his jaws contracted, and looks at all of us, with a deep, almost annoyed, penetrating eye.

There is a sense of oppression, of thick clouds gathering, a palpable mute tension.

Professor A. finally open his mouth and utters the following words, in a strong tuscan accent (how strange it sounded in that momentous event):

- Let me tell you one thing. Math is hard, very hard. I worked all my life to understand it, and it is still hard. Each day. You must be prepared to work just as hard, or you better not waste your time, better go out and work in the fields-

(the last sentence, -andate a lavorar' ne' campi - echoes in my mind like a harsh, ironic mantra)

Then he pauses, an unfathomable pain engraved in his face, he toils with something on the desk, perhaps a cheap packet of cigarettes:

-The lesson is over-

I will never forget that class, Professor Andreotti, as long as I live. It took me so many years to understand it, but now I know. You were right, math is hard, and so is everything worth while in this world.You better be prepared to do your best, or let it go, before it is too late to regret it.

PS For the cognoscenti, Aldo Andreotti appears in the monumental and very idiosyncratic mathematical autobiography of Alexander Grothendieck, Recoltes et Semailles. Andreotti is one of the rare individuals whom AG seems to remember with affections, from his previous academic life.

Mathematician and Art Collector

In the aftermath of his passing (January 30th 1998), two tight and a bit idiosyncratic communities independently mourned Professor Samuel Eilenberg: mathematicians and art collectors said goodbye to one of their brightest stars.

For several decades this remarkable man had shifted, with no apparent effort, back and forth between two worlds as far apart as our modern compartmentalized culture would permit: in the first one, populated with commutative diagrams, abelian groups, towers of topological spaces, he was simply and only Sammy to everyone. In the other he painstakingly bought, sold, exchanged, assessed Burmese statuettes, Chinese ceramic, south east Asia religious artifacts of all kinds and sorts, all the while being known as the Professor. And professor he certainly was, but of what? Of math, of course, but I bet you that most of his fellow dealers wouldn't know, and wouldn't care either. He was The Professor, a darn good dealer.

I hear a voice rising:- What is the big deal? Aren't there thousands of individuals out there having a career and a hobby? - Well, sure there are, but there is a difference, a big difference, in fact two big differences.

First, Eilenberg was extremely successful at both. As a mathematician he literally changed the course of many fields of research, not to mention the fact that he was also at the very heart of countless initiatives and relentlessly promoting a mathematical enterprise of gargantuan proportions. In art, starting from virtually nothing (he immigrated in a rush from his native Poland, fleeing the Nazis), he built a unique collection worth several millions at the time of his donation to the Metropolitan Museum of Art in NYC.

Second, he tried (and apparently succeeded remarkably well) to keep his two identities as separated as he could. He was two-in-one-body: a Mathematician and an Art Collector.

How did he manage to handle his dual life? What was the hidden thread between the two passions that ruled his life? What kind of mind shift (if any) did he need in sliding from one world to the next? Why did he keep his two roles so far apart?

So many questions....

Few weeks ago I called one of his students, asking for answers. There was only one: -I am afraid I cannot help. Sammy did not volunteer any information- To be sure I expected it, but I have to confess I was a bit disappointed. Somehow, I was still clinging to the tenuous hope that the veil would be lifted and I could peep inside Sammy's mysterious life...

In the last few years, after a long neglect, laymen books on mathematicians and outstanding math problems have cropped up at a steady pace (who hasn't heard of A beautiful Mind? ). I hope that someone, with a lot of time available and a good deal of patience (a bit of detective skills wouldn't hurt), will inquire into Sammy's story and write it down for the rest of us.

Till then, we are left with a great mathematical legacy, and a treasure trove at the Metropolitan Museum. Till then, we can just think one more time of a truly enigmatic man:

Sammy Eilenberg, Mathematician & Art Collector.


PS The photo of Sammy with his penetrating & pensive eyes at the top of this post renders full justice to the man (I know, as I was under his scrutiny for 30 very long seconds). However, there was another side of him, lighter, brighter, and a bit ironic too, as marvellously witnessed by this great pic at a Math Conference, in 1992 (please notice the big cigar & the exotic ring).