Malba Tahan: The Man Who Counted (Norton 1993) [IBR2022]

…[T]he book is set in Arabia as a mixture of One Thousand and One Nights and a maths book – it’s coming out of the most populous Catholic country in the world and yet it’s as much a love story to Arab culture as to maths itself…. It is composed of lovely little stories and, with each chapter of a few pages, it introduces a mathematical idea along with a story about travelling through the Arab world. ….[I]n Brazil when I told friends, ‘I’m now working on maths,’ they all said, ‘Oh, you must read Malba Tahan.’ And friends who were kids during that era said, ‘Oh, I remember my parents reading it to me’ – it’s almost like Alice in Wonderland in that it is one of the things that makes people feel nostalgic about their childhood. My Brazilian copy is the 74th edition.

Alex Bellos, FiveBooks Best Books on Math

I love goofy math books; I even have my own list of Best Math Books for People Who Don’t Do Math in the user archives of FiveBooks. I think I may have to rotate one of them out, because this one has completely charmed me. It was originally published in Portuguese in Brazil in 1972; the English edition I have, dated 1993,  is translated from the Portuguese by Leslie Clark and Alastair Reid. The beautiful color image on the cover, as well as the black-and-white drawings that begin each chapter, are by Patricia Reid Baquero.

Within the book we encounter, in short vignettes set in 13th century Baghdad, several numerical tricks and puzzles, a little history of mathematics, and some introduction to various concepts in understandable, practical terms. How can three brothers divide the 35 camels inherited from their father so that, according to the testament, the oldest receives half, the middle brother receives one-third, and the youngest gets one-ninth? How can a merchant discover which of eight pearls is lighter than the others, given a balancing scale that can be used only twice? Perfect numbers are defined by releasing three birds from a cage of 499; amicable numbers are demonstrated by poems written on a wall in red and black letters.

But it isn’t all about such concepts. Myths about the origin of chess, about the death of Archimedes and Eratosthenes, and passages on ethical issues and the wonder of math, apart from its usefulness, appear as well.

There is an overall plot:

My name is Hanak Tade Maia. Once I was returning, at my camels slow pace, along the road to Baghdad after an excursion to the famous city of Samarra, on the banks of the Tigris, when I saw a modestly dressed traveler who was seated on a rock, apparently resting from the fatigue of the journey.
I was about to offer the perfunctory salaam of travelers when, to my great surprise, he rose and said ceremoniously, “One million, four hundred and twenty-thee thousand, seven hundred and forty-five.” He quickly sat down and lapsed into silence, his head resting in his hands, as if he were absorbed in profound meditation. I stopped at some distance and stood watching him, as if he were a historic monument to the legendary past.
…. Several times more the strange traveler rose and uttered a number in the millions, before sinking down again on the rough stone by the roadside. Unable to restrain my curiosity, I approached the stranger and, after greeting him in the name of Allah, asked him the meaning of those fantastic sums.
“Stranger,” replied The Man Who Counted, “I do not disapprove of this curiosity that disturbs the peace of my thoughts and calculations. And now that you have spoken to me with such courtesy and graciousness, I am going to accede to your wishes. But first I must tell you the story of my life.”
And he told me the following, which, for your entertainment, I transcribe exactly as I heard it.

From there, Hanak and Berezim, The Man Who Counted, run into various people with mathematical or logical problems. Berezim solves the problems and, at each encounter, comes away with more than he entered with: a second camel, a turban, a ring, a job as secretary to a Vizier in Baghdad (with Hanak appointed as scribe). He continues to offer advice to various people they encounter in Baghdad, where a Vizier, skeptical at first but finally convinced of the man’s abilities, asks Berezim to teach his seventeen-year-old daughter mathematics to assure her happy future:

When Telassim was born, I consulted a famous astrologer who knew how to read the future by observing clouds and stars. He told me my daughter would be happy for her first eighteen years. From that age on, she would be threatened by a series of tragic misfortunes. He, however, had a way of keeping her bad luck from deeply affecting her destiny. Telassim, he said, ought to learn the properties of numbers and their many working possibilities. But to master numbers and calculation, it is essential to know the science of al Khwarizmi, that is, mathematics. So I decided to provide a happy future for Telassim by making her study the mysteries of calculus and geometry.”

This becomes a fateful request that impacts the rest of the overall story. Some philosophers have ridiculed the idea of teaching a woman mathematics, but Berezim passionately approves of the idea and takes on the assignment. It’s in these meetings, the girl modestly hidden behind screens and fabrics, that Berezim delivers his most eloquent defenses of mathematics:

Geometry is everywhere. Consider the ordinary and perfect forms of many bodies. Flowers, leaves, and innumerable animals reveal admirable symmetries that lighten the spirit. Geometry, I repeat, exists everywhere: in the sun’s disk, in leaves, in the rainbow, in butterflies, in diamonds, in starfish, in the tiniest grain of sand. There is an infinite variety of geometric forms throughout nature. A crow flying slowly through the air traces wondrous figures with its sooty body. The blood circulating in the veins of a camel also obeys strict geometric principles; its humps, unique among mammals, show a singular elliptical form; the stone thrown at an intruding jackal describes a perfect curve in the air, known as a parabola: the bee makes its cells in the form of hexagonal prisms and uses that geometrical form to build its house with the greatest possible economy of material.
“Geometry exists everywhere. It is necessary, to have the eyes to see it, intelligence to understand it, and spirit to wonder at it….”

By the end of the book, Berezim is brought before a council of seven wise men who put questions to him to determine if he is truly as brilliant as he seems. He passes the tests, of course, but we suddenly find ourselves with a love story that rises above the historical Mongol conquest of Baghdad that occurred in 1258.

The dedication that opens the book at first had me a bit puzzled:

To the memory of seven great geometrists, Christian or agnostic:
Descartes, Pascal, Newton
Leibniz, Euler, Lagrange, Comte

Allah take pity on these infidels!

and to the memory of the unforgettable mathematician, astronomer, and Muslim philosopher
Abu Jafar Muhammad ibn-Musa al-Khwarizmi

Allah preserve him in his glory!

and also to all who study, teach, or admire the prodigious science of scale, form, numbers, measures, functions, movement, and the laws of nature.

I, pilgrim, descend from the Prophet
Ali Iezid Izz-Edim ibn-Salim Hanak
Malba Tahan

believer in Allah and in Muhammad, his sacred Prophet

dedicate these pages of legend and fantasy.

– Baghdad, nineteenth day of the moon of Ramadan, 1321

I recognized the names of the mathematicians (and am so honored to be included as one who studies and admires, however poorly, the arts to which he refers) but was puzzled because of the date: many of them lived long after 1321. Then I remembered: the Muslim calendar begins with the Hejira of 622, so 1321 is the Gregorian year 1903.

However, there’s more to it than that.

The publication history of the book is almost as delightful as the text itself. Malban Tahan is a pen name of Brazilian mathematician Júlio César (who is, unfortunately, deceased) which gives this story an extra level: a fictional character (Beremiz) chronicled by a fictional companion (Maia) finally discovered and published by a fictional author (Tahan). The Guardian tells me that César had tried to interest newspapers in publishing some of his earlier stories to no avail, so made up the pseudonym R. S. Slade, a New York translator. That worked, so he eventually took on the persona of Malban Tahan for a series of newspaper columns which became books, including this one.

I wish someone would do a math class – for adults, for children (because the book is, as all those Brazilians will tell you, very suitable for kids), for everyone – using this book as a text. It keeps the surprise of math up front (you mean you really can create any integer using four fours? Is there a proof for this?) while introducing real concepts. And generosity, morality, and kindness are always in the picture. Spread all that over the plot that rewards our good guy heroes, and you’ve got better than Scheherazade if she were a mathematician: you’ve got the perfect goofy little math book.

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