Schons’ Elusive Manual: An Odyssey of Ink, Patience and Friendship

It all began with a maths exercise — one of those that lingers in memory like a timeless echo. I was sixteen when, among the pages of the textbook Introducción al análisis matemático by Luis Osin, problem number nine challenged me with its deceptive simplicity. Published in Buenos Aires in 1966, that Kapelusz manual, with its hard cover and austere ink, became my first companion through the labyrinth of numbers. But the true story wasn’t there — it lay in a fleeting reference: someone called Schons and his mysterious Exercices d’arithmologie.

The name echoed in me like a hidden constant. Years later, stumbling upon a mimeographed reference by Professor Adhemar Infantozzi, I knew I had to find it. “If Schons held treasures like the one Adhemar suggested, what other marvels might his Arithmologie contain?” I thought to myself.

In the pre-Internet era, seeking an out-of-print copy was a Quixotic endeavour. Montevideo — with its majestic libraries (the National Library, the Legislative Library, the Secondary School Library) — became my battleground. I walked dusty corridors, browsed gigantic catalogues, consulted attentive librarians. Nothing. Though I found other manuals by Schons, the Arithmologie remained a ghost.

But rather than deter me, the obstacles deepened my resolve. I mentioned it to colleagues — seasoned educators who had seen generations come and go. “Schons? Oh yes, a classic... but no, I never had it,” some said. “Did you check Brussels?” others joked. Then one day, in the staff room of Liceo No. 4 “Juan Zorrilla de San Martín,” a kind-eyed teacher — with the demeanour of someone you feel you’ve known forever — looked surprised when I uttered the forbidden name:

—Arithmologie by Schons? Of course I know it... but I don’t own it — she said, almost too quickly.

A few days later, when we met again, she said in a quiet voice:

—I owe you a confession...

She was a legendary teacher — one who had sown a love for mathematics over decades. “I lied. I do have Schons’ book. It’s... special.”

And then I understood. That copy of Arithmologie wasn’t just a book — it was a personal treasure, a study companion, a gift that had crossed oceans. She had ordered it from Belgium years earlier, through the mythical Ibana bookshop, waiting three or four months between hope and anticipation. “I couldn’t lend it,” she admitted, “but I’ll make an exception.”

Before handing me the photocopies, she shared the intimate dialogue that had changed her mind. That night, after my question, she had arrived home flustered. Her husband, a calm man of measured words, noticed. She confessed her lie — the burden of guarding that treasure like a secret.

—It’s just... it’s mine. I waited so long. If I lend it, I might lose it. If I photocopy it, the binding might get damaged...

Surely, her husband — with that knowing smile that only decades of complicity allow — helped those thoughts settle.

And to my great delight and surprise, the text I had chased for so long came into my hands in carefully bound photocopies. Schons’ pages opened before me a universe of elegant problems, ingenious proofs, challenges seemingly written to be solved under lamplight.

Luckily, French was our main foreign language in secondary school. For months, I immersed myself in the exercises, stealing hours from the night to decipher their secrets.

To this day, some of my lessons bear the mark of those pencil-and-coffee nights.

The teacher and I formed a friendship around Schons. She told me how, in her youth, those problems had rescued her from routine — had shown her that mathematics was not formulae, but rigorous poetry.

—Works like these aren’t lent... unless you find someone who loves them as you do — she told me one afternoon, certain she had made the right choice.

Today, decades later, every time I open my photocopied copy — now rusted and yellowed, filled with notes — I think of that invisible chain of passion linking seekers of lost books. Schons, Osin, Infantozzi, the teacher whose name I choose to withhold... we are all links in the same legacy — custodians of a fire that does not fade.

Because in the realm of ideas, true treasures are not the ones kept — but the ones shared, between accomplices, among those who know that knowledge only lives when it is passed on.

Much later, when Schons’ copy finally rested on my desk, I returned to the origin. The exercise that had started it all appeared on page 103, under number 684. Here it is, exactly as originally published — in French, with its elegant mathematical deduction. Despite its brevity, it holds a world of ideas:

Back to the exercise