# Books by and about Julio Cesar de Mello e Souza

In 1934 Julio Cesar de Mello e Souza published

Amusing and curious mathematics

The Man Who Counted: A Collection of Mathematical Adventures

The Great Fantasies of Mathematics

The Problem of Definitions in Mathematics

The Art of Being a Perfect Bad Teacher

Malba Tahan and the magazine Al-Karismi (1946-1951)

*Matemática Divertida e Curiosa*(Amusing and curious mathematics) under the pseudonym Malba Tahan. Amazingly the book is still in print with the 29th edition being published in 2014. We give below an English translation of the Preface to the book and an example from the text. In 1937 Mello e Souza published*O homem que calculava*(The man who counted). We give some extracts from the book and three reviews. After brief looks at other works by Malba Tahan, finally we give extracts from the Preface from the 2016 book*Malba Tahan e a revista Al-Karismi (1946-1951)*(Malba Tahan and the magazine Al-Karismi (1946-1951)) (Paco Editorial, 2016).**Click on a link below to go to information on that work**Amusing and curious mathematics

The Man Who Counted: A Collection of Mathematical Adventures

The Great Fantasies of Mathematics

The Problem of Definitions in Mathematics

The Art of Being a Perfect Bad Teacher

Malba Tahan and the magazine Al-Karismi (1946-1951)

**1. Amusing and curious mathematics, by Malba Tahan.**

**1.1. Publisher's description of the author in a recent edition.**

Malba Tahan was born in 1885 in the village of Muzalit, Arabian Peninsula, near the city of Mecca, one of the holy places of the Muslim religion, Islam. He was mayor of the Arab city of El-Medina, studied in Cairo and Constantinople. At the age of 27 he received a large inheritance from his father, starting a long journey through Japan, Russia and India. He died in 1921, fighting for the liberation of a tribe in Central Arabia. The story is pretty convincing, isn't it? But in fact, Malba Tahan never existed. Pseudonym and biography were invented by Júlio César de Mello e Souza, a Brazilian professor, educator, pedagogue, writer and lecturer. Júlio César was born on 6 May 1895 and spent most of his life in Rio de Janeiro. He died in 1974, at the age of 79. The idea of creating a pseudonym was born when the writer was 23 years old and was a contributor to the Rio de Janeiro newspaper

*O Imparcial*. He handed over five short stories he had written to the editor and the papers lay on a newsroom table for several days. Without commenting, Julius took the work back. The next day he took the same stories to the paper, but with the signature of R S Slade, a fictional American writer. He told the editor that he had just translated them and that they were a big hit in New York. The first of them was published the very next day, on the front page. The other four had the same prominence later on. Julius learned his lesson and decided to become Malba Tahan. He produced 69 books of short stories and 51 of mathematics. His most famous work,

*The Man Who Calculated*, has been translated into more than 12 languages. Among other books by the author published by Editora Record are

*Salim, the magician*,

*Legends of the desert*,

*The box of the future*and

*Thousand stories without end*.

**1.2. Preface.**

The present volume contains exclusively recreations and curiosities relating to Elementary Mathematics. Therefore, descriptions and problems involving transcendental numbers, algebraic functions, logarithms, imaginary expressions, trigonometric curves, non-Euclidean geometries, modular functions, etc., are not included in this work.

We thought it would be more interesting not to divide the material that makes up this book into distinct parts according to the nature of the subjects - Arithmetic, Algebra, Geometry, etc. Thus, readers will find intertwined - without this arrangement obeying any law - numerical problems, anecdotes, sums, tales, famous phrases, etc.

We completely abolished complicated algebraic proofs and questions that required laborious numerical calculations. Certain chapters of Mathematics are approached here in an elementary and intuitive way; studies on magic squares, friendly numbers or the golden division would not even be appropriate in a book of this nature.

Mathematics teachers - with few exceptions - have, in general, a marked tendency towards dry and boring algebraism. In practical, interesting and simple problems, they systematically demand from their students real riddles whose meaning the student does not manage to penetrate. The phrase of the famous geometer is well known who, after a class at the Polytechnic School, exclaimed radiantly: "Today, yes, I'm satisfied! I taught a class and nobody understood!"

The greatest enemy of Mathematics is, without a doubt, the algebraist - who does nothing but sow in the minds of young people this unjustified aversion to the study of the simplest, most beautiful and most useful science. The general culture of the people would benefit if the students, plagiarising Plato's famous demand, wrote on the doors of their schools: "Don't come to teach us anyone who is an algebraist."

This demand, however, should not be... platonic!

**1.3. Mathematical sorcerers.**

Rebière tells us that Tsar Ivan IV, nicknamed the Terrible, once posed a problem to a geometer at his court. It was a question of determining how many bricks would be needed to construct a regular building, whose dimensions were indicated. The response was quick and the construction made came later to demonstrate the accuracy of the calculations. Ivan, impressed by this fact, had the mathematician burned, convinced that by doing so he would rid the Russian people of a dangerous sorcerer.

François Viète - the founder of Modern Algebra - was also accused of cultivating witchcraft.

Here is how historians narrate this curious episode:

"During the civil wars in France, the Spaniards used, for secret correspondence, a code in which there were about 600 different symbols, periodically exchanged according to a certain rule that only the most intimate subjects of Philip II knew. A secret dispatch from Spain, however, having been intercepted, Henry IV, King of France, resolved to hand over its decipherment to the marvellous genius of Viète. And the geometer not only deciphered the stolen document, but also discovered the way words were written in the Spanish code. And the French used this discovery to incalculable advantage for two years.

When Philip II learned that his enemies had discovered the secret of the code, which until then had been indecipherable, he was struck with great astonishment and rancour, hastening to ask Pope Gregory XIII to make the denunciation that the French, 'contrary to the practice of the Christian faith', they had resorted to the diabolical spells of witchcraft, a denunciation to which the supreme pontiff paid no heed.

However, it is curious that it was because of his mathematical talent that Viète was included among the magicians and sorcerers of his time."

**2. The Man Who Counted: A Collection of Mathematical Adventures, by Malba Tahan.**

**2.1. From the Publisher.**

Malba Tahan is the creation of a celebrated Brazilian mathematician looking for a way to bring some of the mysteries and pleasures of mathematics to a wider public. The adventures of Beremiz Samir, The Man Who Counted, take the reader on a journey in which, time and again, Samir summons his extraordinary mathematical powers to settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame, fortune, and rich rewards. We learn of previous mathematicians and come to admire Samir's wisdom and patience. In the grace of Tahan's telling, these stories hold unusual delights for the reader.

**2.2. Dedication.**

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, descended from the Prophetdedicate these pages of legend and fantasy.

Ali Iezid Izz-Edim ibn-Salim Hanak

Malba Tahan

believer in Allah

and in Muhammad, his sacred Prophet

- Baghdad, nineteenth day of the moon of Ramadan, 1321.

**2.3. On the amusing circumstances of my encounter with a strange traveller on the road from Samarra to Baghdad.**

In the name of Allah, the All-Merciful!

My name is Hanak Tade Maia. Once I was returning at my camel's 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 traveller who was seated on a rock, apparently resting from the fatigue of the journey.

I was about to offer the perfunctory salaam of travellers when, to my great surprise, he rose and said ceremoniously, "One million, four hundred and twenty-three 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.

A few moments later, the man again rose to his feet and, in a clear, deliberate voice, called out another, equally fabulous number, "Two million, three hundred and twenty-one thousand, eight hundred and sixty-six."

Several times more the strange traveller 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 these 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.

"My name is Beremiz Samir. I was born in the little village of Khoi, in Persia, in the shadow of the huge pyramid of Mount Ararat. While still very young, I began work as a shepherd in the service of a rich gentleman from Khamat.

"Every day, at first light, I took the vast flock of sheep to graze and was required to bring them back to their fold before nightfall. For fear of losing a stray lamb and being severely punished as a consequence, I counted them several times a day.

"I became so good at counting that I could sometimes count the whole flock correctly at a glance. I went on to count, for practice, flights of birds in the sky. Little by little, I began to develop a great skill in this art. After a few months - thanks to new and continuing practice counting ants and other insects - I performed the remarkable feat of counting all the bees in a swarm. This prodigious calculation, however, was as nothing compared with the many others I later achieved. My generous master owned, in two or three far-of oases, huge date plantations, and, informed of my mathematical agility, he charged me with overseeing the sale of his fruit, which I counted in clusters. one by one. I worked thus, under the date palms, for almost ten years. Pleased with the profits I secured for him, my good master rewarded me with four months of rest, and I am now on my way to Baghdad to visit some of my family and to see the beautiful mosques and sumptuous palaces of the famous city. And, so as not to waste time, I have practiced throughout my journey counting the trees in this region, the flowers that perfume it, and the birds that fly among its clouds."

And, pointing to an old fig tree quite close, he went on, "That tree, for example, has two hundred and eighty-four branches. Given that each branch has, on the average, three hundred and forty-seven leaves, it is easy to conclude that that tree has a total of ninety-eight thousand, five hundred and forty-eight leaves. Well, my friend?"

"Wonderful!" I cried in astonishment. "It is incredible that a man can count, at a glance, all the branches in a tree, all the flowers in a garden. That skill can bring immense riches to anyone."

"Do you think so?" exclaimed Beremiz. "It has never occurred to me that counting millions of leaves and swarms of bees could make money. Who could possibly be interested in how many branches there are in a tree, how many birds in a flight that crosses the sky?"

"Your wondrous skill," I explained, "could be used in twenty thousand different ways. In a great capital like Constantinople, or even in Baghdad, you would be of invaluable help to the government. You could count populations, armies, and flocks. It would be easy for you to sum up the resources of the country, the value of its harvest, its taxes, its commodities, all the wealth of the state. Through my connections - for I am from Baghdad - I assure you that it will not be difficult to find some distinguished post in the service of Caliph al-Mutasim, our lord and master. Perhaps you might become treasurer, or fulfil the function of secretary to the Muslim household."

"If that is truly so, then my mind is made up," replied the counting man. "I am going to Baghdad."

And without more ado, he mounted behind me on my camel - the only one we had - and we set out on the long road to the splendid city. From that point on, united by that casual meeting on a country road, we became friends and inseparable companions.

Beremiz was a man of happy and talkative disposition. Still young (he was not yet twenty-six), he was blessed with a most lively intelligence and a remarkable aptitude for the science of numbers. From the most trivial of happenings, he would make unlikely analogies that demonstrated his mathematical acuity. He also knew how to tell stories and anecdotes that illustrated his conversation, already odd and attractive in itself.

At times, he would not speak for several hours, wrapped in an impenetrable silence, pondering prodigious calculations. On those occasions, I took pains not to disturb him. I left him in peace, to make, in his exceptional mind, fascinating discoveries in the arcane mysteries of mathematics, the science that the Arab race so developed and extended.

**2.4. The tale of the 35 Camels.**

We had been travelling for a few hours without stopping when there occurred an episode worth retelling, wherein my companion Beremiz put to use his talents as an esteemed cultivator of algebra.

Close to an old, half-abandoned inn, we saw three men arguing heatedly beside a herd of camels. Amid the shouts and insults, the men gestured wildly in fierce debate, and we could hear their angry cries:

"It cannot be!"

"That is robbery!"

"But I do not agree! "

The intelligent Beremiz asked them why they were quarrelling.

"We are brothers" the oldest explained, "and we received these 35 camels as our inheritance. According to the express wishes of my father, half of them belong to me, one-third to my brother Hamed, and one-ninth to Harim, the youngest. Nevertheless, we do not know how to make the division, and whatever one of us suggests. the other two dispute. Of the solutions tried so far, none have been acceptable. If half of 35 is $17\large\frac{1}{2}\normalsize$, if neither one-third nor one-ninth of this amount is a precise number, then how can we make the division?"

"Very simple," said the Man Who Counted. "I promise to make the division fairly, but let me add to the inheritance of 35 camels this splendid beast that brought us here at such an opportune moment."

At this point I intervened.

"But I cannot permit such madness. How are we going to continue on our journey if we arc left without a camel?"

"Do not worry, my Baghdad friend," Beremiz said in a whisper. "I know exactly what I am doing. Give me your camel, and you will see what results."

And such was the tone of confidence in his voice that, without the slightest hesitation, I gave over my beautiful Jamal, which was then added to the number that had to be divided between the three brothers.

"My friends," he said. "I am going to make a fair and accurate division of the camels, which, as you can see, now number 36."

Turning to the eldest of the brothers, he spoke thus: "You would have received half of 35 - that is, $17\large\frac{1}{2}\normalsize$. Now you will receive half of 36 - that is, 18. You have nothing to complain about, because you gain by this division."

Turning to the second heir, he continued, "And you, Hamed, you would have received one-third of 35 that is, 11 and some. Now you will receive one-third of 36 - that is, 12. You cannot protest, as you too gain by this division."

Finally, he spoke to the youngest: "And you, young Harim Namir, according to your father's last wishes, you were to receive one-ninth of 35. or 3 camels and part of another. Nevertheless, I will give you one-ninth of 36, or 4. You have benefited substantially and should be grateful to me for it."

And he concluded with the greatest confidence, "By this advantageous division, which has benefited everyone, 18 camels belong to the oldest, 12 to the next, and 4 to the youngest, which comes out to - 18 + 12 + 4 = 34 camels. Of the 36 camels, therefore, there are 2 extra. One, as you know, belongs to my friend from Baghdad. The other rightly belongs to me for having resolved the complicated problem of the inheritance to everyone's satisfaction."

"Stranger, you are a most intelligent man," exclaimed the oldest of the three brothers, "and we accept your solution with the confidence that it was achieved with justice and equity."

The clever Beremiz, the Man Who Counted, took possession of one of the finest animals in the herd and, handing me the reins of my own animal, said, "Now, dear friend, you can continue the journey on your camel, comfortable and content. I have one of my own to carry me."

And we travelled on toward Baghdad.

**2.5. Review by: Lewis Hammond Stone.**

*Harvard Review*

**5**(Fall, 1993), 236-237.

I have never liked numbers. I have never liked mathematics. That is until I became enchanted with Brazilian mathematician Julio Cesar de Mello e Souza's

*The Man Who Counted*. I never thought of the world of numbers as an exotic adventure. Now I know that numbers can and will produce their own wonderful stories. At least Mello e Souza can, writing under the pseudonym Malba Tahan.

Beremiz Samir is our mathematical guide on the caravan trails and roads from Samarra to Baghdad during the year 1258. He is a Muslim and a true believer in Allah and in Muhammed, his sacred Prophet. Samir is a searcher for truth through the functions and history of numbers. On the way to his destiny with the Princess Telassim, Beremiz Samir overcomes problems and obstacles through his amazing ability to count and use numbers. Because of his wonderful talent, Samir is addressed by all as The Man Who Counted.

The plot of this refreshing adventure into numbers and thought is that Samir's fame and facility with mathematical solutions precedes him. Everyone has a puzzle or problem that they wish The Man Who Counted to solve. On one occasion Samir is confronted with a seemingly impossible conundrum. The Grand Vizier Maluf of Baghdad has asked The Man Who Counted to solve the riddle that will enable him to arrange ten soldiers in five rows in such a way that each row has four soldiers. The problem looks impossible. But it has a simple solution as explained by Samir once the reader and the Vizier learn to think non-linearly. (I shouldn't be telling you the answers because that takes away from the joy of the book, but this is just one, so this solution is a five-pointed star with a pentagon in its middle.)

The stories are really not just stories or problems to be solved but slices of Muslim life and character. In a Damascus coffee house a merchant presents to Samir "a problem to which a solution has never been found." A man has three daughters of which he has boasted about their intelligence. A "qadi" or a judge (for all these vignettes have a moral that relates to the Islamic way of life and thought in much the same way that Conan-Doyle's Sherlock Holmes exemplified a broader view of late 19th/early 20th century English social habits and customs) becomes annoyed at what appears as the man's excessive pride in his daughters' abilities. The qadi sets a test to see whether the daughters are as clever as the father claims. "Take 90 apples," the qadi says "and have your three daughters go to the market and sell them. The oldest girl will take 50, the middle 30, and the youngest 10. Whatever the oldest girl sells her apples for, the other two will sell at the same price. But no matter what, each daughter must end up with the same amount of money from your different numbers of apples!" Of course Samir shows us how the girls eventually achieved this amazing result and the impact on their father and the qadi.

From the magic squares to assassins stalking Samir in the marketplace to the wonders of using four fours to produce any number in the universe,

*The Man Who Counted*leads readers on paths that should enlighten and enliven even the most committed anti-algorist and hold the attention of the most discriminating fiction devotee. Even if Mello e Souza's book was around when I was younger, I doubt it could have gotten me to lovingly embrace quadrilateral equations. But I'm sure after reading it now,

*The Man Who Counted*would have caused me to give them at least a quick hug.

**2.6. Review by: Agnes Rocha de Oliveira and Miguel Chaquiam.**

*Boletim Cearense de Educação e História da Matemática*

**5**(14) (2018), 27-40.

The records show us that Malba Tahan wrote several books that intertwine stories and mathematical knowledge, among his works the book

*The Man Who Counted*is the most famous, with the first edition in 1938, and has already been translated into about twelve languages.

The book tells the story of Beremiz Samir, a young Arab who discovers an enormous mathematical skill in herding sheep and calculating leaves of trees. Upon meeting the Bagdali (from Baghdad) Hank Tade-Maia, they set off on a trip to Baghdad. Along the journey, Beremiz gets to know people and places and solves different situations through his mathematical skills.

*The Man Who Counted*is distinguished by covering several elements in a single work: curiosity, logic and mathematical arithmetic, philosophy, culture and Arab religion, romance with adventure and the pedagogical appeal of teaching experienced in an alternative and pleasurable way. Thus, this work is not only suitable for mathematics teachers, but also for those who are interested in knowing another culture, in appreciating stories and expanding their knowledge of the world.

**2.7. Review by: David Fernandes.**

*Mathematical Intelligencer*

**41**(2) (2019), 80-81.

A hero, the dictionary tells us, is a person who is admired for great achievements or noble qualities. In classical myth and legend, a hero was a man, often of divine descent, who exhibited extraordinary strength, cunning, or courage. In modern representations, many heroes are admirable in but a single facet of their lives, though in other aspects they may be all too human. Their interest lies in that inherent contradiction: perfection has become boring, because it is unnatural. We admire, for instance, the deductive gifts of the unforgettable Sherlock Holmes, his ability to solve seemingly perfect crimes, but within that machine of deduction and observation, we perceive a dark and threatening psyche that Holmes tries to soothe with a seven-per-cent solution of cocaine.

At the beginning of the thirteenth century, while travelling to Baghdad on his beautiful camel Jamal after visiting the historic city of Samarra, Hanak Tade Maia came across a modestly dressed traveller seated on a rock, resting from the fatigue of his journey. In salutation, interrupting Tade Maia's thoughts, the mysterious wayfarer started reciting fabulous numbers, such as 1423745 and 2321866. Surprisingly, these were not random numbers, as he informed his interlocutor, but the number of trees in the region and the number of flowers that perfumed it. Beremiz Samir - for that was his name - had discovered his gift while he was working as a shepherd in the service of a rich gentleman from Khamat and was required to count his flock several times a day, which he soon learned to do at a glance. Little by little, he began to develop a great skill in this art by counting colonies of ants, swarms of bees, and the branches of a tree. Tade Maia easily convinced Beremiz that his talent to reduce a multiplicity of objects to its numerical essence could be used in twenty different ways by the government in Constantinople or Baghdad, and as a consequence, he would be able to obtain a distinguished post in the service of Caliph al-Mutasim. His remarkable aptitude for al-Khwarizmi's science and his ability to tell illustrative stories and anecdotes made Beremiz a delightful traveling companion, and Beremiz and Tade Maia became inseparable friends. Whereas Don Quixote and Sancho Panza righted wrongs and brought justice to the world, Beremiz and Tade Maia intervened in a series of arguments (usually problematic divisions of objects) that they were able to solve fairly through the application of Beremiz's mathematical skills; in the process, the duo obtained recognition and profit (camels, coins, medals) in a magical and shining Baghdad, pervaded with fountains and gardens, a city smelling of jasmine and inhabited by colourful characters.

In the 244 pages of this book we learn nothing about the physical aspect or the circumstances and desires of Beremiz, quickly renamed the Man who Counted, beyond his job and his birth in the sad, stony village of Khoi twenty-six years earlier. We learn even less about his companion Tade Maia. I think it is a pity that the author has not endowed his characters with a degree of humanity, desires, and contradictions. Of course, Beremiz is something of a hero according to the dictionary definition, but he awakens no emotional response in the reader. I am afraid that comparison with the three-dimensional Sherlock Holmes is inevitable, and that this singular duo will not earn a place in our collective memory along with such other famous duos as Don Quixote and Sancho Panza, Asterix and Obelix, or Holmes and Watson. Beremiz behaves like an emotionless automaton. Allah seems to whisper the solutions and speeches in his ear. Beremiz shows emotion only in Chapter 25 (of 34), when he receives a present from his pupil Telassim, who is learning the workings of algebra and the secrets of geometry, attending the lessons from behind a curtain with her face veiled.

Throughout the book, Baghdad is described as a dreamlike city where the future can be read from clouds and stars, and an astrologer's predictions may chart the course of a person's life. According to a famous astrologer, the brilliant Telassim was doomed to misfortune unless she mastered the properties of numbers. But the court scholars refused to teach mathematics to a woman, because, as they said, no one can teach a giraffe to sing. Indeed, they claimed that it is easier for a whale to make a pilgrimage to Mecca than for a woman to learn mathematics. Then the Man who Counted recalled the illuminating example of Hypatia of Alexandria to show that the female intelligence can perfectly grasp the beauties and secrets of science. The truth of this is obvious to a twenty-first-century reader, but we should recall that this book was written in Brazil in 1938, where, for example, a woman's right to vote was granted only in 1932.

This book includes many numerical curiosities and problems of equitable division to be performed under certain constraints, which Beremiz solves, such as the assertion that 8 and 27 are the only numbers greater than 1 that equal the sum of the digits of their cubes ($8^{3} = 512$ and 8 = 5 + 1 + 2). More interestingly, our curious duo chances upon a shop called the Four Fours, in which everything for sale (turbans, boxes, daggers, bracelets) costs only four dinars. Beremiz then states that "using four fours, we can get any number whatsoever.'' For instance, the number 7 is obtained as $\large\frac{44}{4}\normalsize - 4$, and $\large\frac{44-4}{4}\normalsize$ is equal to 10. To solve the problem for the number 113, the assertion has to be rephrased as follows: given no more than four instances of the digit 4, represent all integers using a finite number of mathematical symbols and operators in common use (square roots, factorials, decimal points, repeating decimals or double factorials). In fact, using the double factorial (e.g., 4!! = 4 × 2, 7!! = 7 × 5 × 3), Jim Millar gave the following remarkable solution for 113: $113 = (4!! - \large\frac{4}{4}\normalsize )!! + 4!!$. Another curious example is the riddle of the 35 camels, an excellent example of thinking outside the box. Three brothers received thirty-five camels as their father's inheritance. In his will, he bequeathed half of his camels to the eldest son, a third to the second, and a ninth to the youngest. With the loan of his own camel, Beremiz easily solves the problem, recovering his beautiful Jamal and obtaining a camel as profit (i.e., $36 = \large\frac{36}{2}\normalsize + \large\frac{36}{3}\normalsize + \large\frac{36}{9}\normalsize$ + Jamal + 1). This is an instance of the famous one-half, one-third, one-ninth problem. This riddle had already appeared in the literature with 17 animals to divide - some authors claim that it can be found in Niccolò Fontana Tartaglia's 1556 work

*General Trattato di Numeri et Misure*, and it is usually attributed to Ali Ibn Talib (ca. 600-661). To the best of my knowledge, the author of the book under review was the first to propose the division of 35 animals.

In my opinion, the most interesting parts of the book are those in which Beremiz introduces and explains mathematical concepts such as perfect numbers (those equal to the sum of their divisors, such as 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14). These arouse the reader's curiosity: Is there an infinite number of perfect numbers? Is there an odd perfect number? Today, fifty perfect numbers are known, and it is known that there is no odd perfect number below $10^{1500}$. Also, Beremiz's lessons are beautiful and eloquent, and the reader is certain to enjoy them.

Finally, a word about the author of the book. It is said that Malba Tahan was born in 1885 near Mecca, lived in Manchester for twelve years, was mayor of the city of Medina, traveled to Russia, India, China, and Japan, and died in 1921 fighting for the freedom of a group of Bedouins in the desert near Riyadh. But as is all too often the case, the truth is rather more prosaic. Ali Iezid Izz-Edim Ibn-Salim Hanak Malba Tahan was the pen name of the Brazilian mathematics teacher Júlio Céar de Mello e Sousa (1895-1974), who realized that he would benefit from an exotic pseudonym in publishing his stories in the local newspapers. Years later, to complete the hoax, Mello e Sousa confirmed that in 1954, the former Brazilian president Getúlio Vargas had authorised him to add "Malba Tahan" to his identity card (

*Carteira de identidade*) as part of his name. Paradoxically, the author's travels took him only to Buenos Aires, Montevideo, and Lisbon, so the vivid descriptions of the legendary and fantastic Arab world are nothing more than the constructions of his fertile imagination.

I should add that Mello e Sousa was a devotee of Christianity. This is not a minor detail, because at the end of his book (both in the original Portuguese edition and in the Spanish translation) he wrote that Beremiz lived in a state of happiness due to his Christian faith; in fact, Beremiz claims that "real happiness can only exist in the shadow of the Christian religion." But in this English edition (translated by Leslie Clark and Alastair Reid in 1993), all such references to Christianity have been deleted, and consequently, Chapter 34 has been drastically modified. Two questions arise: Why such a significant omission? Is the omission a betrayal of Mello e Sousa's creation? Otherwise, W W Norton offers us a polished book. Patricia Reid Baquero's illustrations are splendid, and they help make this book a perfect present for a teenager to awaken his or her interest in science and mathematics.

After the publication of

*The Man Who Counted*, Mello e Sousa became as famous as an international football star, and he gave an endless number of talks in Brazil to demonstrate the beauty of mathematics and to fight against those who love making mathematical education as complicated as possible. He was undoubtedly an influential figure in the development of mathematics in Brazil, which has been carried out brilliantly by the Instituto de Matemática Pura e Aplicada (IMPA), and especially by the charismatic Elon Lages Lima, who sought out mathematical talent via the mathematical Olympiads and worked for continuous improvement in the skills of primary- and secondary-school teachers. Joyful books like the book under review here are a way to awaken vocation in our youth. I hope that

*The Man Who Counted*will inspire other authors to explore novel narratives and alternative perspectives.

**3. The Great Fantasies of Mathematics, by Malba Tahan.**

**3.1. Malba Tahan's Family and Fans Official Website.**

https://malbatahan.com.br/portfolio/as-grandes-fantasias-da-matematica/

The origin of numbers. The glory of an irrational. Golden Division. The bee problem. The Prophet, the Antichrist and Mathematics. Derivative Lady smiled at you. Curious and delusional curves and many other cases.

**3.2. Quick Description.**

Contents:

The origin of numbers.

The glory of an irrational.

Golden Division.

The bee problem.

The Prophet, the Antichrist and Mathematics.

Derivative Lady smiled at you.

Curious and delirious curves, etc. ...

Mathematical topics discussed:

- Value and importance of this science;

- Dislike for mathematics;

- The enemies of mathematics;

- The geometry of the supernatural;

- The way of the hunting dog;

- Educational action of mathematics and its philosophical value;

- Anatomy of infinity ;-

- The idea of number;

- Circles;

- Mathematics and other sciences;

- Mathematical symbolism;

- Mathematics teaching;

- Aptitude for mathematics;

- Zero is number;

- A famous curve in history;

**3.3. Review by: Agnes Rocha de Oliveira and Miguel Chaquiam.**

*Boletim Cearense de Educação e História da Matemática*

**5**(14) (2018), 27-40.

This work is divided into chapters, where initially Malba Tahan talks about the value and importance of Mathematics, as well as its role in the progress of humanity. The chapter dedicated to Geometry addresses the concept of the fourth dimension, entitled "The Geometry of the supernatural", in addition to having the following chapter called "The path of the hunting dog" that introduces the attempt, by the geometers, to define straight lines, straight lines and the plane, postulates of the line, as well as curious definitions of the line. In its fourth chapter we have the theory of sets, until reaching finite and infinite sets and showing "The anatomy of infinity".

The following chapter "The idea of number", considers the evolution of the idea of number, number and magnitude, quantity, measure of a magnitude, among others. Finally, we have "Squaring the circle", showing what the problem of squaring the circle is and what attempts and dreams of the squarers consist of.

**4. The Problem of Definitions in Mathematics, by Malba Tahan.**

**4.1. Malba Tahan's Family and Fans Official Website.**

https://malbatahan.com.br/portfolio/o-problema-das-definicoes-em-matematica/

Author's preface. Errors, doubts and curiosities. Concepts that we cannot define. How to define time? Pascal's principles. The definitions and their modalities. Problems related to definitions.

**4.2. Quick description.**

Exact sciences: Mathematics. Logic. Definitions and concepts. Problems related to definitions and concepts. The geometric point. The line and its concept. Straight concept. Study of lines. Study of angles. Polygonal line. Plane geometry. Analysis of definitions in mathematics. Axiomatic method. Deductive system. Theorems. Mathematical research and investigation. Inductive method. Calculation. Mathematical language. Didactics. Pascal. Euclid. Gergonne. Archimedes. Lobachevsky. Le Roy. Aristotle. Poincaré.

**4.3. Review by: Agnes Rocha de Oliveira and Miguel Chaquiam.**

*Boletim Cearense de Educação e História da Matemática*

**5**(14) (2018), 27-40.

Once again, the author seeks not only to teach Mathematics in a pleasant and fun way, but also to demonstrate the usefulness and attractive objectives of Mathematics. It is an eminently logical work, which aims to place on solid foundations the problem of formulating concepts and definitions in Mathematics.

The language presented in the book is made in a didactic and evident way, seeking, primarily, clarity, coherence and total understanding on the part of its countless readers. In this work, the author analyses, explains and comments on several definitions by renowned masters and seeks to extract from them the essence that is useful to him in discussing and establishing his own, conclusive and absolute, definitions.

**5. The Art of Being a Perfect Bad Teacher, by Malba Tahan.**

**5.1. Malba Tahan's Family and Fans Official Website.**

https://malbatahan.com.br/portfolio/a-arte-de-ser-um-perfeito-mau-professor/

The book is inspired by the wise precept of Saint Augustine: "To condemn sin with intransigence, but to do everything to enlighten and save the sinner."

**5.1. Review by: Agnes Rocha de Oliveira and Miguel Chaquiam.**

*Boletim Cearense de Educação e História da Matemática*

**5**(14) (2018), 27-40.

Malba Tahan surprises us, once again, by presenting a differentiated work that was heavily criticised mainly because of its title. However, this did not cause the author to rethink and make any changes to the title.

The author defends his idea and makes it clear when he states in the book that 'The perfect bad professor', with his uneducated and undignified attitude, without composure and without modesty, cannot assess the harm he does to society, the damage he causes to Brazil. Throughout the book, Malba Tahan warns teachers, stating that the teaching at that time was inefficient. He was always attentive to the smallest details, so that the class was pleasant. Thus, he said that "The perfect bad teacher should figure in the immense gallery of criminals and be condemned to the absolute repudiation of all educators and all good patriots."

**6. Malba Tahan and the magazine Al-Karismi (1946-1951).**

**6.1. The research team.**

The book C Coppe, M M Andrade, O A Viana and V Marim (eds.), Malba Tahan e a revista Al-Karismi (1946-1951) (Paco Editorial, 2016) was the result of a five year project by the NUPEm (Núcleo de Pesquisa e Estudos em Educação Matemática) research group at the Universidade Federal de Uberlândia.

**6.2. Preface by Ubiratan D'Ambrosio, São Paulo, July 2015.**

The focus of this book, which I am pleased to preface, is the analysis of the personality and work of Júlio Cesar de Mello e Souza, a prolific and enigmatic writer, mathematician and educator of the 20th century. Among the many achievements of Júlio Cesar de Mello e Souza are scientific works, works of fiction. didactic works, three magazines with national circulation, Al-Karizmi (1946-1951), the subject of Part II of this book, Lilavári (1957) and Damião (1951-1963), the latter dedicated to supporting people with Hansen's Disease. The most notable work of Júlio Cesar de Mello e Souza is the creation, in 1925, of a fictional character, el-hadj sheriff Ali Ielid Izz-Edim ibn Salim Hank Malba Tahan (believer of Allah and his holy prophet Mohammed), who would have been born in 1885, having been mayor of El Medina and killed in 1921 in combat for the freedom of his people. This character came to be known simply as Malba Tahan. The personalities of the creator and the creature are confused throughout the career of Júlio Cesar de Mello e Souza.

The book is organised in two parts, in a total of nine chapters, in which the personality of Júlio César de Mello e Souza and the theoretical, historical and philosophical bases that are present in his works and in his various activities are recognised as a great contribution to the Brazilian intelligentsia. In the voice of his creature Malba Tahan, Mello e Souza transmitted to countless generations of Brazilians the message of peace and wisdom intrinsic to Arab culture. Particularly interesting is the case of Mathematics. Mathematical narratives in the Euclidean style, typical of schools and academia, start from first ideas, definitions, axioms and, following a logic of conclusions step by step, arrive at theorems, they have the character of truth. But this concept of truth is considered by many to be insufficient for a broad view of material and psychic reality. Mello e Souza goes beyond the traditional concept of mathematical truth and incorporates considerations of an intuitive and moral nature into the narratives of the creature Malba Tahan. In these narratives, particularly in the wisdom of Beremiz Sarnir,

*The Man who Calculated*, a broader statement of truth is found, questioning what is more general and what is specific, especially when specificities result from individual and collective responses to different cultural, ethical, linguistic and even physical factors. In different traditions, we observe differences in the behaviour of individuals and in the narratives, the result of different perceptions of space and time, of mythologies and cosmic visions, of cultural and ethical, linguistic and social variations. The analysis of the works of Júlio César de Mello e Souza highlights these differences.

The book begins with a Presentation, by Cristiane Coppe, Mirian Maria Andrade, Odaléa Aparecida Viana and Vlademir Marim, editors of the book. The first author devoted part of her academic life to the work of Malba Tahan. I had the privilege of being her advisor in the Master's Degree and Doctorate and I keep grateful memories of this guidance as one of the moments of great accomplishment in my long career as an educator. It was a happy opportunity to have been invited by Cristiane to accompany her on the brilliant trajectory of her training as a researcher.

Júlio César created Malba Tahan, saying that this character was an Arabic-language writer who synthesised wisdom and political activism in his books, and also created another fictional character, Breno Alencar Bianco, who appears as a translator of the "Arabic original" written by Malba Tahan. Thus, several works by Malba Tahan were published, with translation by Breno Alencar Bianco. The name Júlio Cesar de Mello e Souza does not appear in these works, in fact written in Portuguese by himself, which relate folk tales and stories from Eastern antiquity, some of which are featured in the medieval classic

*One Thousand and One Nights*. Central to the production of Malba Tahan/Júlio Cesar is the book

*The Man who Calculated*, which has achieved great popularity, having had several editions and being translated and published in several countries.

What is Júlio Cesar de Mello e Souza's objective when creating Malba Tahan? How do creator and creature relate? The creator's complex personality, a life that since childhood revealed intense curiosity and a lot of creativity, is presented and very well discussed in the first chapter of Part I of this book, written by Pedro Paulo Salles and André Pereira Faria Neto, respectively his great-nephew, and grandson. I see as a great goal of the creator, Julius Caesar, his great devotion as an educator, which is expressed by the creature, Malba Tahan, when dedicating his book

*The Man Who Calculated*"to all those who study, teach or admire the prodigious science of magnitudes, forms, numbers, measures, functions, motions and forces." In this dedication, Júlio César expresses what he considers his mission as a mathematician educator.

Chapter 2 of Part I is an analysis of the popular repercussion of the work of Mello e Souza, made by Augusto Cesar Aguiar Pimentel, who I also had the pleasure of supervising in graduate school. From this orientation, bonds of friendship developed between us. Pimenta, as he is known to his friends, wrote an exquisite chapter on the history of mathematics for this book. As we know, monuments and museums already existed in antiquity, but they were frequented only by the ruling elite. Today these works are intended for the public and are essential for the dissemination of scientific and technological knowledge. This diffusion is exemplified by the monument Praça da Matemática in Itaocara, a small community in the State of Rio de Janeiro. Pimenta recapitulates the history of this monument, from its conception, in 1943, by a young mayor, until its listing as Historical and Cultural Heritage of the Municipality of Itaocara, in 2007. The monument project was the result of a public competition, whose jury was chaired by Júlio César de Mello e Souza. On the monument there are phrases from great figures in the history of mathematics and, among them, the phrase "Mathematics is the great poetry of form", by the fictional Malba Tahan. Pimenta shows how Praça da Matemática was integrated into activities promoting the improvement of Mathematics Education, going beyond the small community of Itaocara and being nationally recognised.

Part II of the book consists of theoretical studies on Mathematics Education, guided by analyses from the magazine Al-Karizmi and indications of how Mello e Souza's contribution is current and can be applied in basic education. The magazine was one of the numerous achievements of Júlio César de Mello e Souza and circulated from 1946 to 1951, distributed throughout the country. In seven chapters, authored by the four editors and guest authors, various facets of the journal are analysed. Chapter titles are explicit about their goals. This book is facilitated by the very comprehensive Presentation and the choice of chapter titles. This facilitates the non-linear reading of the book, which is a characteristic of Júlio Cesar de Mello e Souza's pedagogical proposal.

The first two chapters deal with Durand's in-depth hermeneutics and myth-criticism, which are the theoretical frameworks used in the analysis and interpretations of the journal Al-Karizmi, the subject of this Part II. The other chapters address topics that are treated in the magazine in an attractive and thought-provoking way, arousing interest and vocation for further deepening in mathematics studies. There is a didactic concern in these chapters, discussing specific issues of Geometry, an interesting approach to Problem Solving and proposing a very attractive approach to the History of Mathematics, with resources proposed in the magazine Al-Karizmi. The History of Mathematics is one of the most important aids in improving the teaching of Mathematics. The last chapter, which deals with the interdisciplinary implications for the organisation of the journal, is very important. It is very clear how Mello e Souza was a pioneer in the interdisciplinarity approach in Basic Education.

I congratulate the editors and authors for this important contribution to Mathematics Education, aimed at researchers and teachers in the classroom. The book brings theoretical and methodological aspects that are very important for research and also gives many suggestions to improve the teaching of Mathematics in Basic Education.

Last Updated November 2022