کاکل طاووس: ریشه های غیر اروپایی ریاضیات

by George Gheverghese Joseph, غلامحسین صدری افشار (Translator), شیرین حکمی (Editor)

این کتاب گزارشی است از یک پژوهش عالمانه و فراگیر از میراث علمی ملت های غیر اروپایی در زمینه ریاضیات.

برگرفته از یادداشت مترجم

Genres: History, Mathematics, Nonfiction, Science, India, History Of Science, Stem

553 pages, Paperback

First published May 1, 1991

Reviews

[Koen Crolla · Rating 1 out of 5]

The problem of Eurocentrism is grossly overstated, particularly when it comes to histories of mathematics, but attacking it is an easy way to get people to think of you as sophisticated and brave, I guess.
If Joseph set out, as he claims at various points, to show that non-Europeans contributed far more to modern mathematics than is commonly assumed, he failed. If he merely wanted to show that people outside of Europe and the Islamic world also had very sophisticated mathematical traditions, I'm not even sure he succeeded at that.

A big problem seems to be that Joseph wasn't motivated to write this book by knowledge (either knowledge that he already had and wanted to share or just a love of the pursuit of knowledge), but spite. He covers a lot of ground with which I'm not incredibly familiar, but in the areas where I do have the ability to call him on bullshit, he shows himself more than willing to take liberties with the truth.
A particularly egregious example (which I understand to be a bit of a hobby horse of his) is the Kerala school, which he doesn't just credit with independently discovering some clever concepts in proto-calculus and infinite series (which is probably already too generous; there are good reasons to believe they got quite a lot of help from Islamic scholars), but with actually being responsible for all of the accomplishments of Newton and Leibniz a few decades later, who he claims would have had access to the work of the Kerala school through Jesuit missionaries—something for which there is absolutely no evidence, and which no credible historian believes.
Kerala, incidentally, is also Joseph's birthplace. Not that I'm suggesting bias or anything.

This crap is typical of the entire book, though; when facts disagree with you, just appeal to a ``sophisticated understanding'' of those facts, or manufacture them outright. Add a good quantity of condescending racism aimed at most the people you claim to be defending (Egyptians, Mesoamericans, the Chinese), and voilà! you have a book for which you can apparently charge €27.
The orthodoxy it purports to challenge is a tired straw man, and Joseph does nothing to refute the stereotype of Indian historical revisionaries as jealous obscurantists and petty cultural relativists.

[Salem Salem · Rating 5 out of 5]

I've had this book for years. I flipped through it once in awhile and kept it around because I was interested in the multiple histories of math origins. To counter another review here, the author does not propose a thesis of the European inheritance of math from elsewhere nor does he glorify Indian mathematicians. He suggests there may be some paths of that nature but they are clearly loose hypotheses. Mostly he focuses on math and eventually we get to the real inheritance of our dominant decimal system.

What worked the best for me were the alternating passages on history embedded with the somewhat clear breakdown, usually side by side with contemporary algebra, of some ancient method of performing a calculation. These were very interesting for me to work out. I expect to revisit some of the math in the book here and there to work through more of the problems he invites the reader to try.

This is a very even-handed book. Where the author does not have enough time to go deeper into a subject, he offers up other avenues in the text. I will be taking him up on that offer.

[Hannah Thomas · Rating 4 out of 5]

This is a book that will keep you going! There are chapters in here that will compare mathematics of Egyptians and Mesopotamians and the comparison between the Indians and Chinese. I would say that it also depends on what culture interests you: Are you interested in the repeative kind or are you more interested in the "wide-spread" of mathematical history

[Jeff · Rating 3 out of 5]

This is an important book in the history of mathematics, but unfortunately it’s usefulness is more as a reference than as a readable narrative.

Joseph lays out in a clear and well documented argument how the cultures of Egypt, ancient Mesopotamia, China, India, and the Islamic world all contributed to the development of modern mathematics. His argument acts as a corrective to the Eurocentric view that all meaningful mathematics originated with the work of the Greeks. As if between the Greek work and the European Renaissance nothing of meaning occurred and all developments originated out of European minds.

By providing this valuable compendium of mathematical achievements from other parts of the world and honestly exploring the transmission of these ideas out of the cultures in which they originated, Joseph has produced a work that holds a lot of value.

Unfortunately the writing is dry and utilitarian when it could be more engaging. It feels like there is ample space here for a stronger writer to take any number of the stories outlined here to create the compelling narrative that the grand story of mathematical discovery and invention deserves.

[Sas Vijay · Rating 5 out of 5]

This is an excellent book. Especially in terms of a historical perspective of looking at how Mathematical concepts evolved in various civilizations at a similar time. It also gives a revival to many civilizations forgot under the influence of Eurocentrism. It is an interesting perspective to learn history aside Mathematics. How ideas travelled all theway from Africa, Middle East, India, China and vice versa is also an indication of how connected scientific network was even back then.

Regarding criticisms, If taken just as a treasure of historical Maths, there is not really much to criticize. Maybe Europeans might take certain aspects targeting Eurocentric approach to Maths as a personal attack. But it is not. This very book is aimed at exploring Non-European mathematics. SO it would be good if one proceeds to read keeping that title in mind.

[Hannah · Rating 4 out of 5]

I read this in my history of math class this semester, and although we didn't read the entire book we read most of it and treated as one of our textbooks. It was really interesting learning about the different historical roots of math which don't usually tend to be discussed. Parts of it were hard to understand, but for the most part it was readable. I especially liked his diagrams depicting the interconnections between civilizations' influences on the development of math.

[Sam Kelly · Rating 3 out of 5]

I found this book to be quite interesting. I had to read the first 5 chapters for an independent study class and I am glad it was just those 5. I don’t mean to say that the rest of the book was bad because it really wasn’t, it was just that there was something quite different about the way the first halfish of the book was written compared to the rest of it. Hit was all very interesting to read about though. And contrary to at least one or two reviews I saw, I don’t think this book had an unnecessarily pushyness against the Eurocentric view of mathematics, I think it was completely on par with what was expected from a book of this nature.

[Cheryl V · Rating 5 out of 5]

My best friend sent this book to me, and I’m so glad she did. I was going through a bunch of Newton documentaries and found a few things peculiar:
- why did he destroy the work for his proofs of calculus and how he discovered it. It was tradition even in the time of Kepler before him to keep the work to show others the process of discovery and ignite discussion
- why did he wait 40 years to publish the full works (a year after Hook died)… I know dead men don’t argue but why not publish right away?
- how did this amazing man in his early twenties discover all this in just one year and then nothing else in the field of mathematics for his long life? Seems strange to drop it all for alchemy/religion
- what is contained in his notebooks that were bought at auction by Keynes and another man who gave them to the state of Israel
- how brave of him to perform the test poking a needle into his eye and then writing down the results of the experiment. That seems to me like a very brutal form of torturer that one might perform on prisoners in the name of “science” and carried out by not just a bored 20-something in college
- how is it that the folks who invented Arabic numberals, algebra, the number zero, etc just stopped after the fall of the Ottoman Empire and suddenly the folks who were so bad at astronomy/navigation that they thought North America was Asia, that they took centuries to adopt zero after being introduced to it (China adopted it nearly as they heard about it), and invented Roman numerals (at least we can all agree that’s an inferior numeric system for math) suddenly got this genius in his 20s who had some great ideas when an apple fell on his head.

This book helps show the proof that I’m sure many will ignore like the guy who gave it 1 star. Oh well… math belongs to everyone, it really doesn’t matter but it is pretty sad to see some ppl get so bothered with the truth of history is presented in a way that doesn’t (for once) have a bias toward the people in power today.

Let’s all just enjoy math and pursue truth. Nothing else really matters.

[Hillary Clayton · Rating 4 out of 5]

A bit dense, it reads more like a math textbook than a history most of the time. What bothers me is that it seems to be written for the sole purpose of convincing euro-centric mathematicians that non-white people *did* math. Anyone who’s studied history outside of Europe knows that almost every culture in history had math and numeracy and organizational systems that required counting and, in many cases, applications of counting. It seems obvious from that perspective that Greek/European mathematicians therefore only compiled other culture’s methods and strategies and created theorems and proofs from thousands of years of practices from places like Egypt and India and China.
That being said, this book does a beautiful job of highlighting the original practices of calculation and paralleling them with their algebraic cousins. It also does a great job contextualizing the societal and cultural demands for the ancient mathematical practices (like... Egyptians invented fractions to equitably distribute resources and payment). If you’re like me and you definitely did not study math history in college, this does a great job of bringing you up to speed on origins and modern applications!

[Michael · Rating 3 out of 5]

For a book about the history of mathematics there isn't very much historical or mathematical context.

I read the 2nd edition where the "Reflections" afterword was much better written than the body. Judging only by the table of contents, the third edition appears to have been rewritten, so maybe it reads better.

[Ardyth]

More an in-depth math text than a history text. Not quite what I was seeking, which is why I have set it aside.

The good news is that much of what I read here is also discussed (and in a more layperson-friendly style) in How Not to Be Wrong: The Power of Mathematical Thinking. Joseph's proposed cultural exchange diagram is new to me, though the ideas it suggests are not.

Crest of the Peacock is thirty years old at this point, and I can say with some confidence (being a high school student at the time) that his opening salvos were fair: he was correct that non-European mathematics were not mentioned in my twelve years of school. Ever.

No idea whether schools have adjusted their history / math coverage, but in the grown-up world that bizarre quiet about developments and possible (not declared, not proven, but possible) reciprocal influences is fading.

Most casual-interest readers will prefer How Not to Be Wrong for its low barrier to entry, but that doesn't devalue Joseph's effort. "Break ground so we may follow" etc

[John · Rating 4 out of 5]

This book’s reputation preceded my reading of it. Opinions fall into two broad categories: fans and haters. The fans delight in using Crest as ammunition in their holy war against Eurocentric white male whatever and the haters take pains to point out that many of Joseph’s suggestions that Western mathematics owes an unacknowledged debt to other civilizations and traditions are, in most cases, not supported by actual physical evidence. Relax people! Mathematics is unique among human pursuits in that its results are often independently rediscovered by different people at different times. Even I “discovered” Markov chains before I learned they were well-known. The idea that brilliant people, pursuing ideas in the most objective and structured domain of knowledge, might come up with identical results is hardly surprising. I don’t know what alien mathematics will look like, but I’ll bet big bucks you’ll find the Pythagorean Theorem somewhere in it. Of course, aliens won’t call it the Pythagorean Theorem. I found the third edition of Crest balanced and useful. Never pay attention to hysterics praising or damming books. Read them and judge for yourself.

[Justin Leroux · Rating 5 out of 5]

A definitive text for all math nerds

[धनंजय · Rating 4 out of 5]

This is a bit overwhelming at times but a fantastic read for those interested in history of mathematics out of India.

[Jafar S Pulpally · Rating 3 out of 5]

Excellent

[Nacho · Rating 4 out of 5]

Un libro más que leí hace años en español y que la Ediciones Pirámide (edicionespiramide.es) tiene secuestrado sin reimprimirlo desde hace una década, protegiendo así la cultura para que nadie pueda acceder a ella. Así que lo he conseguido en inglés y lo he releído.

Es un buen libro sobre matemáticas, ameno y lleno de anécdotas que aligeran la lectura de un tema tan, a priori, árido como pueden ser las matemáticas. Lo recomiendo.

[Bill Ward]

I read this in college (UC Santa Cruz) in a class on the History of Mathematics, and I just recently found it and started rereading it.

[Miguel Ángel Moreno · Rating 3 out of 5]

Un repaso detallado de las matemáticas de las culturas no occidentales.