[U.S.] Joseph Mazur: *Euclid in the Rainforest—A Storyed Short History of Mathematics*, translated by Wu Fei, Chongqing Publishing Group, Chongqing Publishing House, December 2006
A new installment of Xiaogu’s quarterly recommendations has appeared!
This is the most surprising, most unusual popular science book I have read in recent years! It is no exaggeration at all to say that the chair of Harvard’s mathematics department commented that the author “has pioneered a highly attractive way of writing”; at the very least, I have never read anything remotely like this style of popular science writing!
The subtitle and the review of this book may easily give one the wrong impression—that this is a book like “The Story of Mathematics” or “Mathematics in Everyday Life,” but in fact it is nothing of the sort. The author does not deliberately stuff mathematical knowledge into a story; instead, he seems to be writing a genuine “travelogue”—in South America, Turkey, New York… rather than a deliberately designed mathematical fable like a “travelogue to the village of liars.”
Let me casually quote a few passages:
“A thin mist rises above the wet Orinoco, and the vapor is mixed with the intoxicating fragrance given off by blooming yucca, violets, red jasmine, and jasmine flowers. It is the scent of the Venezuelan rainforest, where tobacco, bananas, and coffee grow wildly, and the calls of toucans are so loud that you can hardly hear the nearby rush of water.” (p. 1) “I lost her. Even when I lifted my head and floated to the surface, I could not find her anywhere. Panicked, I shouted her name, swam in circles, dived beneath the surface until I had to come up for air. I decided it would be better to search for her quietly with my underwater breathing tube. Just then, I felt an octopus tentacle winding around my throat. I dropped my spear gun, grabbed my fins with both hands, and turned around. It was Frederica. She had come up quietly from behind and suddenly held the dead octopus before my eyes. I was terrified, but soon realized that she was pulling me closer, and she kissed me. Her bare breasts pressed against my chest. She must have felt my heart pounding violently. I had never seen anyone more beautiful than she was. I no longer felt the octopus tentacle beside my neck, though it was still there. Until that moment, I had always thought she was Carl’s girlfriend, and thought I had no chance at all.” (p. 111) “Julian and I came to Figaro, the place I visited most often in Greenwich Village. In New York City in the mid-1960s, it was easier to get a bag of marijuana than a cup of authentic cappuccino. Figaro was a mile from my gym, yet it was one of the few decent places where you could see satisfying foam appear in your cup, where you could spend half an hour sipping until you saw the burnt brown sugar at the bottom, and where you could sit contentedly for several more hours, occasionally checking your empty cup and wondering when you had drunk it dry. Milk-white glass chandeliers, similar to those chandeliers in Professor Lide’s classroom, illuminated the high tinned ceiling, and the soft light was cast upon the walls through the smoke of rising cigarettes. The walls were covered with pasted-together yellowing copies of the French newspaper *Le Figaro*, mirrors, framed photographs of local poets, and menus like antiques, showing what a nickel could buy in the 1920s.” (p. 185)
If you only look at the passages above, what kind of book would you guess this is? In any case, I’m afraid no one would associate it with a popular mathematics book! What do these contents have to do with mathematics? Heaven knows! Hardly anything. You get the feeling that the author is by no means lecturing the reader as a scientist, but rather chatting with us. The theme of mathematics certainly keeps cropping up in the conversation, but everything is so natural and casual that it never feels as though he is trying to teach us anything on purpose.
The book makes extensive use of dialogue. At times the author speaks as a calculus teacher with his students; at times he is a listener talking with old professors or other friends; and more often he sounds like a traveler conversing with all sorts of people he meets along the way… Questions and reflections about the essence of mathematics run through these repeatedly insightful conversations.
The author’s discussion does indeed cover a wide range of material from the history of science, but rather than saying the theme of the book is a brief history of mathematics, it would be more accurate to say it is philosophy of mathematics. The book is divided into three parts—“Logic,” “Infinity,” and “Reality”—and deals with issues in the philosophy of mathematics such as logic and proof, intuition and faith, the finite and the infinite, induction and sets, probability and reality, truth and verification. The author develops these topics in dialogue form, but often does not provide definitive answers; instead, he provokes the reader’s thought and lets one feel the wonder of mathematics.
Let me quote a few more passages from the dialogues:
“There’s no problem with my speech. I just don’t understand the mathematics involved, though Jisu seems to. ‘Yes! Of course!’ Jisu said, ‘The little triangle is the first lump, the bigger one is the enlarged lump, and the initial triangle is the largest lump!’ ‘And yet,’ I said, thinking something had been left out, ‘you proved that if your lumps are right triangles, it works. But how do you know it works for anything else?’ ‘Aha!’ Roger exclaimed, ‘It has to do with ratios. Look at this.’…” (p. 28) “‘Here is where Gida was born. Do you know who he is?’ I thought he was talking about Zeno, so I answered, ‘Of course I do, he was a mathematician—no, a philosopher.’ I corrected myself, thinking there was a difference between the two. ‘No, no,’ he retorted, ‘he was the inventor of soccer! He made this town great!’” (p. 120) “Once again, I gave him a problem involving the square of √23. He did not notice that the answer was simply 23; instead, he turned to the TI-85 calculator he trusted, entered 23, pressed the ‘square root’ button, got 4.795831523, then pressed the ‘square’ button, and got 23. ‘See,’ he said proudly, ‘with my calculator I got the same answer as you did.’ I would not let it rest there, so I asked, ‘If you multiply 4.795831523 by itself, what happens? You would expect to get 23?’ ‘Yes, of course! Isn’t that what I just did?’ he said in a tone of surprise. He entered 4.795831523, then pressed the multiplication button, then entered 4.795831523 again. When he hit the ‘equals’ button, the number 23 appeared. ‘See, 4.795831523 times 4.795831523 equals 23!’ he said, wearing a puzzled smile. ‘But, but…’ I stammered, ‘how is that possible? You just multiplied two numbers whose last digit was 3? Shouldn’t you get a number whose last digit is 9?’ I asked, goading him with my unassailable argument. ‘Maybe that’s true when there are fewer digits, but you can find that it doesn’t hold when there are nine digits, like 4.795831523.’…” (pp. 130–131)
All of these conversations sound very real, as though they were truly the author’s own experiences. And in the author’s narration and reflections outside the dialogues, one can see even more clearly the breadth of his reading and the fluency of his thought. I won’t say any more here.
When reading this book, there is no need to approach it with the purpose of learning something from it. The best way is to read it as a genuine “travelogue,” as a work of literature; nor is there any need to force oneself to understand clearly the implications of all the many issues mentioned in the book. Looking out toward the rainforest veiled behind clouds and mist can be just as pleasurable and full of longing.
“At first glance, mathematics often inspires dread—not only in beginners, but even in trained scientists. Unfortunately, it is not always as lucid as the Indian proof of the Pythagorean theorem, which is only a diagram and the word ‘Behold’ (瞧). Yet in this book, I hope to cross mountains and valleys, to glimpse the rainforest of thought through slowly drifting clouds, and thereby reveal the beauty of mathematics and the delight that accompanies the long trek through the mathematical journey, just as Euclid did 2,300 years ago. And after completing a long journey deep into the abstract world, returning to the seemingly credible logic of the science that governs the natural world will feel wonderfully refreshing.” (p. VI)
The translation of this book is also quite good (although translating Zeno as Zino, Hume as Huum, and so on may be puzzling, that is not a mistranslation but another transliteration). The price of 26 yuan is also reasonable for a good book of 280,000 characters. I find that for the good books I “quarterly recommend,” I actually make very few notes—because I would rather copy out the whole book!
January 22, 2007, 1:07 p.m.
Latest comments
- unic
2007-01-22 22:45:56
Came to read your blog while eating zhajiangmian. When I first saw the title, I had a question: why was there a little star as a marker? Looking down, I understood.
I want to say: wow!!!
It really is a very distinctive writing style.
Maybe I should read it someday; for someone like me, who has read very few popular science books, it should be a pretty good start…
Today I went to the library and borrowed books for the winter vacation: three copies of *For People Who Hate Mathematics*—written by a Japanese scholar. I see that it talks about mathematics and theology, the role of logic, mathematics and capitalism… It seems to stand at a fairly high level, yet when you flip through each section, it is not very lengthy, MS not bad. *The Invisible Religion* and *One-Dimensional Man*—this one may be a bit deep for me, but skimming through it is still okay. - Gu
2007-01-22 23:19:55
I remember flipping through *For People Who Hate Mathematics* in a bookstore once, though I’ve forgotten the contents a bit. But roughly speaking, it introduces the importance of mathematics in human culture. Such books may help spark interest, but for you right now they probably do not have much significance. Learning that mathematics is “the language of God” may well make you revere it more—and thus perhaps fear it more, who knows. The only truly effective way to overcome fear of mathematics is to do problems, and you must be clear about that! Only by getting up where you fall can you truly cross the psychological shadow. So I suggest digging out your old problems and doing them again. Start from the point where your mathematics began to drag you down, and it is best to go back to elementary school. If you can’t find your elementary and middle school books anymore, try to borrow them. If you think those problems are too easy, imagine how you would explain the key points to children if you were teaching elementary school students. If you truly grasp the essentials, even high school material will be nothing more than that.
The reason mathematics is “nothing more than that” is precisely because it “opens all roads once one road is opened”; ever since third or fourth grade, I basically no longer needed to listen to class or use textbooks—just doing competition problems directly was enough to keep up all the way. Once you find the doorway, everything will move smoothly.
I have read *The Invisible Religion* in a cursory way: https://yilinhut.net/2006/01/28/249.html. This book does not seem to be a suitable introductory book to religious studies, though, come to think of it, I still have not found an introductory religious-studies book worth recommending. Anyway, if you are interested, reading it is best.
I have not read *One-Dimensional Man*, of course I know roughly what it is about. For things of this sort, it is better to read some lighter secondary literature first; if you are really interested, then reading the original work directly is of course better.
But… since you have time to read, why are you still complaining that you have no time to do mathematics? Hehe, hurry up~ - Gu
2007-01-22 23:32:04
I have always known the importance of English, but that is of absolutely no use! The only truly effective method is to pick up the book without hesitation and memorize it like crazy; without doing that, one can never overcome one’s laziness toward English.
Translated from the Chinese original with AI assistance. The original text is authoritative.
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