One of the odd perks of getting old is that one can look back to the

distant past and wonder with cold detachment just who the hell we

were.

As a kid I was obsessed with cryptography and secret messages. I even

halfheartedly tried to create a language that only my friends and I

would understand. I wanted to build a robot. I also wanted to live in

a desert island and made endless plans in my head on how I would run

my life on it. Perhaps nothing of this is too surprising in a restless

kid, reader of Jules Verne (“La isla misteriosa/The mysterious

island”, “Viaje al centro de la Tierra/Voyage to the center of the

Earth”).

So how did I get from there to becoming a researcher in pure

mathematics? Not along a straight line for sure.

I started engineering at the Universidad de Buenos Aires, aiming for

electronics, the robot thing. I found myself not caring about the

specific answer to any exercise but was fascinated instead by the

solution process. In a basic physics class the lecturer casually

mentioned the exponential, even the cosine, of a matrix. What?

In the vaulted, vast, inspiring space of the Engineering central

library (Paseo Colón!) I discovered a book that described the “dual

numbers”. Just imagine this grotesque incarnation of the complex

numbers: you add to the reals a quantity whose square is zero! How

amazing, how beautiful.

I got a TI-99 programmable calculator, like all my classmates. We

carried it around hanging from our belts looking like some kind of

geeky cowboys. I spent hours playing with the built-in functions for

matrices. Computing, for example, the limiting value of the inverse

of x – A for x near an eigenvalue of A. You could program the

calculator using at most 50 steps. What a triumph to realize two

steps of your code could be combined to gain an extra line. It warped

my programming style for years.

In the hall of that imposing building, at a booth of the university

publishing house EUDEBA, I bought Kelley’s book “General Topology”,

convinced by its preface that the only requirement was a knowledge of

the real numbers. I couldn’t read past the first page.

About then I decided to switch to a degree in math, in the second year

of University; didn’t have any idea of what I was doing, didn’t know

you could make a living doing mathematics.

In my second year of high school in Buenos Aires, mathematics meant

solving problems about triangles using a slide rule or a log table. The

teacher would bring to class a huge slide rule he would hang from the

top of the blackboard and start sliding away. That year I devised an

encryption scheme involving permutations of the five vowels:

a,e,i,o,u. I kept some notes I wrote then on this scheme, written in

the standardized three-holed sheets (hojas de carpeta Rivadavia!) we

had for all our high-school work. I never actually ever used the

encryption scheme.

The all-male group marooned on the desert island is rescued at the

very end of “The mysterious island” by the cryptic Captain Nemo, the

main character of another Jules Verne book, with his

submarine. Anachronistically apparently but a fabulous coup de theatre

that impressed me immensely nevertheless.

I look at the stuff in these notes on permutations now, more than 45

years later, and don’t really understand any of it. But it sure looks

like mathematics.