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.

Internal Work III: Cultivating the Three Treasures

In my last post on the Internal Work I mentioned the san bao (三寶, three treasures), namely jing, qi, shen, and their progressive transmutations at different stages of the work. Their collective name, three treasures, is far from accidental, as they are the basis of the elixir. They must be preserved and cultivated at all cost, as life and well-being depend on them.

But, how?

I know no better advice than the one given in Chapter IV of Taoist Yoga, a translation by Charles Luk of a treatise on internal development by the Daoist Master Chao Pi Chen. Here it is:

• The essence (jing) changes into vitality (qi) when the body is immobile,
• The vitality (qi) changes into spirit (shen) when the heart is not agitated,
• The spirit (shen) turns into Void (xu) as a result of the Immutable Thought.

So, now you have it. Notice that in all three case immobility plays the pivotal role. Immobility, not death: the conscious outcome of letting go, immobility that is the very height of awareness.

Not easy to come by, of course (just try to keep your body relaxed and immobile for a few minutes). But think of this: every moment you reach this immobility in the midst of ordinary life, the san bao are cultivated.

The Three Treasures are our true inborn treasure. We can be wealthy beyond our wildest dreams, if we use them judiciously.