Your first option is in Portuguese.
A fascinating property of mathematics is that it is totally international and never goes out of style. so if you write a math classic, it’s a classic forever, everywhere. this brazilian book links my past life in brazil with mathematics. the literal translation of the Portuguese title is “the man who calculated”, but the English version is called the man who counted. there are also editions in many other languages.
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the author malba tahan is a fictional character, the pseudonym of júlio césar de mello e sousa, and the book is set in arabia as a mixture of the thousand and one nights and a math book – it is coming out of the most country most populous Catholic in the world, and yet it is as much a love story for Arab culture as it is for mathematics itself. there were a lot of arab immigrants in brazil and they love the arabian culture: one of the most popular fast food chains is called habib’s. The story here is presented as if the author, who I believe only went to Lisbon once and practically never left Brazil, had come across or discovered this Arabic text.
A bit like omar khayyam’s rubaiyat?
exactly. It is made up of delightful little stories and, with each chapter only a few pages long, introduces a mathematical idea along with a story about travels in the Arab world. for example, one chapter shows you how to make all the numbers between one and 10 just by using four fours because the narrator knows someone who shows him this trick.
It’s also a brilliant piece of international cultural history because Brazil is a country where very few people read books, where everyone is obsessed with sports. However, when this book came out in the 1950s, Malba Tahan became as famous as any of the footballers. he was huge so in brazil when i told my friends, ‘now i’m working on math’, they all said, ‘oh, you should read malba tahan’ and friends who were kids at that time said, ‘oh, i remember my parents read to me’ – it’s almost like alice in wonderland in that it’s one of the things that makes people nostalgic for their childhood. my brazilian copy is edition 74.
It’s easy and fun, but any adult would love it. an international classic.
however, your other options are not fictitious.
my next book is by georges ifrah, who could be said to be the real “man who counted”. The French have what is probably the best tradition of popular mathematics in the world: they love their science, their mathematics, their engineering, and their philosophy. And from 1650 to 1850 probably the largest percentage of the great mathematicians were French: Pascal, Fermat, Laplace, Lagrange, and the rest.
ifrah was a school teacher who was constantly asked by his students: “where do numbers come from?”. he began to investigate and, strangely, it turned out that no one had bothered to ask this question in the same way. he’s not an academic, nor is he a writer: he’s a hugely mission-obsessed schoolteacher. so the book is a bit long and doesn’t have a lot of narrative, but it’s absolutely amazing. walks through each culture and describes why they thought about numbers and how they counted. so we’ve got it explained here exactly how the Mayans counted, the Sumerians counted, the Hebrews counted, exactly how the ancient Chinese counted, all the different types of counting systems, manual systems, how the abacus works.
then halfway through it changes and becomes largely india because ifrah realizes that our own number system actually originated in india. our number system is what we call arabic numbers and they are actually indian numbers. what you realize when reading the universal history of numbers is that everything before india is really just a curiosity.
The three things that define our number system are: 10 digits only, zero through nine; a place value system, which does not apply to Roman numerals; and the use of zero, because with a zero it allows for easy multiplication and then becomes feasible for the layman to calculate, which was not really possible with Roman numerals.
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Then the book becomes an encyclopedia of all things Indian: a little wacky, but so packed with information that when I was writing my book, I was at my desk all the time to refer to it. is the bible of counting and where numbers come from.
it is a huge rectangular format.
It’s worth having among any other odd shaped books you might own. Ifrah has never really done anything since then, and is described here as “an independent scholar” who was “the despair of his own math teacher”. he financed his worldwide research on the project for 10 years doing jobs as a waiter and a taxi driver.
your next choice seems less unusual, although it is an unusual topic, zero.
unlike ifrah, charles seife is a brilliant popular science writer who has written the “biography” here from scratch. and although he doesn’t talk much about india, it works well as a primer for the ifrah sections on india. because seife talks about zero being mathematically very close to the idea of infinity, which is another mathematical idea that the Indians thought differently. seife gives you the context and explains why, really, without zero, you can’t do anything. the difficulty of understanding zero is similar to the difficulty of understanding infinity. the Greeks did not have a zero, the Roman numerals did not have a zero, and they did not have infinity. he plays with this idea that we were afraid of infinity and then gradually learned not to be afraid of it.
there is an energy in the way seife writes about mathematics, using a strong narrative, that is very difficult to achieve: but he knows exactly how to do it. you finish each chapter and really want to move on to the next one and ‘find out what happens’.
Why were we afraid of infinity?
There were different reasons, but the fear of mathematical infinity is probably best expressed in Zeno’s paradoxes, the most famous of which is probably that of Achilles and the tortoise.
Imagine Achilles in a race with a tortoise, with Achilles starting behind. by the time Achilles reaches the tortoise, the tortoise has gone a little further. this happens the next time he catches up with the tortoise and again and again, so he will never beat the tortoise. how can it be? To understand this paradox you have to be able to deal with infinity, because you are counting an infinite number of time units and you are assuming that an infinite number of time units goes on forever. but in fact it can be finite. only with calculus and newton did mathematicians harness the power of infinity instead of running from it.
but seife says that the other reason, spiritual or religious, why we were afraid of infinity and zero, and why india got zero, was that western religions thought there had to be a god everywhere. nothingness, or emptiness, is scary, because it is a world without god. while in Indian religious thought, that is nirvana.
that, in fact, we all strive towards a state of nothingness.
yeah, so this religious thinking sparked mathematical thinking. the seife is an exciting page turner on the history of zero, but it’s great to read it with ifrah so you can see all the beautiful information about india next door.
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your next choice is pi, another number.
petr beckmann was a czech electrical engineer who lived in czechoslovakia until the age of 39 in 1963, when he went to the united states as a visiting professor and stayed there.
The history of pi is very well written. he’s really funny, really witty and charming, full of weird one-liners, but also incredibly opinionated. he says, ‘not being a historian I am not obliged to wear the mask of dispassionate aloofness.’
this guy was a teenager in prague who later escaped the regime, and there’s a lot of brilliant anti-communist stuff here. For example, when he talks about the death of Archimedes at the hands of the Romans, he obviously hates the Romans very much, whom he sees as totalitarians. it’s quite rare in mathematical writing that you find someone who is such a good stylist and who is cultured, so he puts it in context. it is an absolute joy to read, although some of the math is quite difficult. I would probably recommend it to someone who is already interested in math, maybe even a teenager.
You only have one more option from that pile.
well, this is the triumph of numbers for ib cohen, who is a scholar, an eminent historian of science and has written many academic books. but this, very brief, was only published after his death. Again, the difficulty in math writing is often that mathematicians don’t know how to write and non-mathematicians don’t really understand math. but cohen is an amazing historian, so even though what he has chosen is a huge topic, he only has nine chapters which are nine moments in the history of numbers.
It’s pretty hard to write a good history of science because there’s a lot going on at different times and you want to pick something that explains science but also has a bit of personality, but doesn’t demean it. the kind of mind that understands how to write history is very different from the mind that understands how to do math, which is highly structured. so most math writers tend to be incredibly structured and a bit obvious. for example, they tend to do the story very chronologically and can’t really do it any other way. but you can tell that cohen has this breadth of knowledge and that he picks the right moments and then puts them in the right context.
historians may synthesize knowledge differently.
yes, and this is an absolutely brilliant history book – you really feel like you’re in good hands. Often with the history of science, you feel like the writer only really knows about the limited topic he’s writing about because he’s too specialized. here, however, it is noted that the other knowledge of him is filtered. That is why he talks about Napoleon, who was a great mathematician and surrounded himself with the best mathematicians. There is a great anecdote where Napoleon had just defeated the Berbers in the Battle of the Pyramids. while his generals were climbing the pyramids, he sat at the bottom and resolved that, using the stone of the great pyramid, a wall three meters high and, I think, a third of a meter wide could be built, which more or less exactly coincides with the perimeter of france. and then he had the best mathematician of the day review his calculation, which was correct.
Wouldn’t you tell him he was fine even if he wasn’t?
The emperor was right! or, in fact, he was not an emperor at the time; I think it was just the man who came. It’s a great story anyway. but the book is essentially about the time in the 18th and 19th century where, thanks to Indian numerals coming into common use, suddenly everyone could use them. Nobody really used numbers to begin with; Now, in the modern world, we all use numbers all the time. and this book, through a few episodes, explains the birth of statistics, the birth of graphics, of measurement. there’s a lot of stuff about how rising numbers created a lot of backlash, using the example of charles dickens’ character, gradgrind on hard times, who only cares about measuring.
tells the story of the obscenity case against the publication of james joyce’s ulysses in the united states, which was based on the idea of the “average man”. the judge referred to “the eyes of the average man”, but had no idea that it was a mathematical concept that had come to prominence in the 19th century with the numerical analysis of social phenomena. And that leads us into a discussion of statistics and how the bell curve that plots social data was used as an argument for eugenics, which was of course very much in vogue until hitler came along.
This interview was first published in 2010.
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