FREE delivery April 4 - 19. Details

Only 1 left in stock - order soon.

$$26.34 () Includes selected options. Includes initial monthly payment and selected options. Details

Ships from

GrandEagleRetail

Ships from

GrandEagleRetail

Sold by

GrandEagleRetail

Sold by

GrandEagleRetail

Returns

Eligible for Return, Refund or Replacement within 30 days of receipt

Returns

Eligible for Return, Refund or Replacement within 30 days of receipt

This item can be returned in its original condition for a full refund or replacement within 30 days of receipt. You may receive a partial or no refund on used, damaged or materially different returns.

Read full return policy

Payment

Secure transaction

Payment

Secure transaction

We work hard to protect your security and privacy. Our payment security system encrypts your information during transmission. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Learn more

Details

FREE delivery March 28 - April 3. Details

Or fastest delivery March 22 - 26. Details

Select delivery location

Used: Like New | Details

Sold by ThriftBooks-Baltimore

Access codes and supplements are not guaranteed with used items.

Other Sellers on Amazon

Added

Not added

$22.36
+ $3.99 shipping

Sold by: ---SuperBookDeals

Added

Not added

$32.01
FREE Shipping on orders over $35.00 shipped by Amazon.

Sold by: BiBi RiRi

Added

Not added

$36.34
& FREE Shipping. Details

Sold by: Pro Reads

Follow the author

Peter Strom Rudman

Follow

How Mathematics Happened: The First 50,000 Years Hardcover – Illustrated, February 5, 2007

by Peter S. Rudman (Author)

4.1 24 ratings

See all formats and editions

{"desktop_buybox_group_1":[{"displayPrice":"$26.34","priceAmount":26.34,"currencySymbol":"$","integerValue":"26","decimalSeparator":".","fractionalValue":"34","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"Vu%2F6qyozWJF2JA94mKtsm39KdPHVHAJWEj25CxsXmcC51e4R81Ls%2BN%2Bbz9lM5A%2FoIpIEKSqlFHQ4aX%2BDrMF2KBuozJCsOW6g%2BSuobVYL6FPIZSffT142ebZl3nJduYAbj3vPAa5%2BVabx8of%2FofpaM11rZMCH9ggztyLCsQrgakinkDN%2FIEIJZDq92SwDDe7t","locale":"en-US","buyingOptionType":"NEW","aapiBuyingOptionIndex":0}, {"displayPrice":"$6.32","priceAmount":6.32,"currencySymbol":"$","integerValue":"6","decimalSeparator":".","fractionalValue":"32","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"Vu%2F6qyozWJF2JA94mKtsm39KdPHVHAJWNjCzzHuGWgbdg7cp%2FZB3nyaXV3JX1l3VKFwFFkiDJaPVRVaYD%2FEGnuFzoAJChlIN6CclvG9tAY8lDlz33HZAfWQyj39idq7QlAuZ2XRIWvR6JaCgj%2FJTZsc1lAdKR3NTP3C7V4O22%2BBtbckMgsyoMpwtxZTtx3Ov","locale":"en-US","buyingOptionType":"USED","aapiBuyingOptionIndex":1}]}

Purchase options and add-ons

In this fascinating discussion of ancient mathematics, author Peter Rudman does not just chronicle the archeological record of what mathematics was done; he digs deeper into the more important question of why it was done in a particular way. Why did the Egyptians use a bizarre method of expressing fractions? Why did the Babylonians use an awkward number system based on multiples of 60? Rudman answers such intriguing questions, arguing that some mathematical thinking is universal and timeless. The similarity of the Babylonian and Mayan number systems, two cultures widely separated in time and space, illustrates the argument. He then traces the evolution of number systems from finger counting in hunter-gatherer cultures to pebble counting in herder-farmer cultures of the Nile and Tigris-Euphrates valleys, which defined the number systems that continued to be used even after the invention of writing. With separate chapters devoted to the remarkable Egyptian and Babylonian mathematics of the era from about 3500 to 2000 BCE, when all of the basic arithmetic operations and even quadratic algebra became doable, Rudman concludes his interpretation of the archeological record. Since some of the mathematics formerly credited to the Greeks is now known to be a prior Babylonian invention, Rudman adds a chapter that discusses the math used by Pythagoras, Eratosthenes, and Hippasus, which has Babylonian roots, illustrating the watershed difference in abstraction and rigor that the Greeks introduced. He also suggests that we might improve present-day teaching by taking note of how the Greeks taught math. Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history.

Print length

316 pages
Language

English
Publisher

Prometheus
Publication date

February 5, 2007
Reading age

14 - 17 years
Dimensions

6.39 x 1.03 x 9.13 inches
ISBN-10

9781591024774
ISBN-13

978-1591024774
See all details

David Reimer
66
Hardcover
26 offers from $14.59
Carl B. Boyer
213
Paperback
71 offers from $12.75

Editorial Reviews

From Booklist

Anyone who has ever wondered why an hour is divided into 60 minutes has much to learn from Rudman, student of the ancient mathematics of the Babylonians, Egyptians, and Mayans. Behind the base-60 number system that survives on a clock face, Rudman discerns the fascinating history of how numbers evolved beyond the finger- and stone-counting of hunter-gatherer societies. It all started with the Babylonians, who fit very old body-part measurements into a powerful new arithmetic of squares and square roots. Rudman also probes the physiological logic that equipped the Mayans with base-20 numbers for mapping the heavens, and he scrutinizes the brilliance of Egyptian mathematicians who calculated complex volumes without calculus. Readers can deepen their understanding of ancient feats by working out the numerous "Fun Questions" Rudman has embedded in his text to provide practical experience with key concepts. Such experience leads eventually to the conceptual threshold the Greeks crossed 2,500 years ago when they began developing proofs for their mathematical theories. Even readers casually interested in mathematics will enjoy traveling the road that leads to Pythagoras. Bryce Christensen
Copyright © American Library Association. All rights reserved

About the Author

Peter S. Rudman (Haifa, Israel) is professor (ret.) of solid-state physics at the Technion-Israel Institute of Technology and the author of more than 100 articles in physics.

Product details

ASIN ‏ : ‎ 1591024773
Publisher ‏ : ‎ Prometheus; Illustrated edition (February 5, 2007)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 316 pages
ISBN-10 ‏ : ‎ 9781591024774
ISBN-13 ‏ : ‎ 978-1591024774
Reading age ‏ : ‎ 14 - 17 years
Item Weight ‏ : ‎ 1.51 pounds
Dimensions ‏ : ‎ 6.39 x 1.03 x 9.13 inches

Best Sellers Rank: #1,091,391 in Books (See Top 100 in Books)
- #390 in Assyria, Babylonia & Sumer History
- #621 in Mathematics History
- #3,028 in Evolution (Books)

Customer Reviews:
4.1 24 ratings

Brief content visible, double tap to read full content.

Full content visible, double tap to read brief content.

Videos

Help others learn more about this product by uploading a video!

Upload your video

About the author

Follow authors to get new release updates, plus improved recommendations.

Peter Strom Rudman

Brief content visible, double tap to read full content.

Full content visible, double tap to read brief content.

Discover more of the author’s books, see similar authors, read author blogs and more

Customer reviews

4.1 out of 5

24 global ratings

How customer reviews and ratings work

Sort reviews by

Top reviews from the United States

There was a problem filtering reviews right now. Please try again later.

K. in Texas

Excellent book about the beginnings of mathematics

Reviewed in the United States on April 17, 2016

Verified Purchase

Excellent book about the beginnings of mathematics. The author evidently has studied that area in depth, and the book provides details I had not seen before.

Reviewed in the United States on June 2, 2019

Verified Purchase

Many books have been written on the history of mathematics, but much of what is written seems to focus almost entirely on the mathematical traditions beginning with the Greeks and extending into modernity with only passing mentions of the more ancient systems that existed in many parts of the world long before Pythagoras, Archimedes, or Euclid. It's refreshing to read a book that largely reverses this trend by devoting the majority of its attention to what I've seen described as the pre-history of mathematics. By the nature of this exercise, however, one can't simply trace the development of theorems through time but must instead focus equally on mathematical concepts and archaeological ones. Because the subjects of both mathematics and archaeology are so vast, it would be impossible to give even a cursory treatment to either topic in a single volume of only 314 pages. Instead, it's best to consider this book a very broad survey of the development of ancient mathematics, occasionally narrowing its focus to discuss a concept or result of particular interest but generally maintaining its position as a cursory overview of an entire field of inquiry.

Approximately the first half of the book is devoted to the origin of various number systems. Many readers are likely already familiar with the fact that our decimal system is not the only or even the oldest number system, but even those who already know a little bit about ancient mathematics will likely find it interesting to learn about Torres-Strait body-parts counting or the Babylonian sexagismal system. However, for the reader whose undergraduate mathematics education did not include (as mine did) significant time spent performing operations with unit fractions (sometimes written in Egyptian Hieroglyphics), this first part of the book might seem to drag on a bit longer than it needs to.

The book begins to obtain a broader general interest in the second half when it moves on from counting systems and the most basic concepts of arithmetic into the early history of algebra, spending a good amount of time discussing the algebraic problems from ancient Egypt recorded in the Rhind Papyrus. The author does an excellent job of communicating, in relatively few pages, the depth of mathematical understanding possessed by the ancient Egyptians, including concepts of geometric series, algebraic geometry, and precursors to integral calculus. The following chapter traces an alternate lineage of mathematics in Babylon covering similar but distinct mathematical territory including a rather stunning approximation of the square root of 2 and a special case of the Pythagorean theorem.

Arguably the most interesting mathematics is found in relatively few pages toward the end of the book where the author describes the development of rigorous proof. Illustrative examples include one of my own favorite stories from mathematical history: Eratosthenes, whose sieve can be used to locate prime numbers and whose knowledge of geometry allowed for a remarkably accurate calculation of the Earth's circumference as early as some 250 BCE. While this chapter does include a few of the "greatest hits" of early (Greek) mathematics, as well as a brief description of our own mathematical lineage (it can, after all, be argued that we are all the mathematical descendants of the Greeks), it's not the strongest point of the book because the description is, frankly, far too brief to allow for any real depth of understanding.

The book concludes with a brief but important plea for improved education in mathematics. While this certainly isn't the message you buy this book to hear, it remains a message that more people interested in mathematics need to start thinking about. The author's nine pages on the subject won't solve any problems, but I applaud him for devoting even a few pages to an attempt to start a conversation we desperately need to have.

The bottom line is that this book is a fascinating if somewhat superficial look at the early history of mathematics, culminating in a brief discussion of early "rigorous" mathematics. I recommend it for anyone with an interest in mathematics, OR anyone with an interest in history. The reader needn't be an expert mathematician to understand the vast majority of the book's material (a bit of high school algebra and geometry should easily suffice). If you're looking for a book that traces some of the famous proofs in mathematics, however, you'll be disappointed. That subject is taken up only at the very end of the book in a chapter I consider to be a bridge between this book and the many other works that have been written on Greek mathematics. If you find yourself looking for more of that kind of material after finishing this book, William Dunham's Journey Through Genius provides an excellent follow-up (conversely, if you read a book like Dunham's and want some more of the earlier history, this book would be perfect for you).

2 people found this helpful

Helpful

Dr. John

Five Stars

Reviewed in the United States on December 14, 2017

Verified Purchase

very good read=thank you

Reviewed in the United States on March 3, 2018

Not only does the author provide context, he also provides his rationale as to why he believes we should accept others theories as right or wrong so you can make up your own mind. I loved the fact that this book provides questions and gives more information than I have found in any other book about the origins of counting and math.

Others here seemed to critique him without an ounce of counter argument.

Helpful

flashgordon

Wonders of Ancient mathematics

Reviewed in the United States on December 11, 2014

Verified Purchase

Peter Rudman's "How mathematics happened" is more about the explaining Babylonian/Egyptian arithmetic, and some geometric algebra . . . then explaining the nature of mathematics. He doesn't talk about abtraction works. I just find the title a little off. His book explains some of the remarkably different arithmetic that the Babylonians and Egyptians came up with; explains it possibly better than even Van Der Waerden in his "Science Awakening."

Mr Rudman tries to disprove that there were cultures that only counted up to two, and then three, and so on . . . as explained in say Barrow's "Pi in the Sky", chapter 2. Point is that 'imprints' from previous number base cultures are in the number linguistics. For instance, three is tres which is 'beyond', and nine means 'new' number. He even mentions the point that one can say there's an equivalent amount of objects in say this sack, without actually knowing the number. For instance, if you have a theater(imagine an old Greek theater), and all the seats are filled; you can say that there's a theater of people without actually knowing the number. Archaeologists have found Babylonian pots with objects in them that were used in this fashion. They'd just put the objects in the pots as they matched one by one say the sheep they were going to move from one person to another. They wouldn't know the actual amount, but they'd know there's an equivalent container of sheep, or whatever. Yes, the the ancients really did go from such beginning understandings of number to a more systematic arithmetic. He even mentions this after argueing there were no two and three counter cultures. Let me put it another way.

People in general can only 'see' how many objects there are with five or less objects say on a table. Five or more, and they start counting. Mathematics, in this sense, is a kind of mental crutch to help us deal with things we can't normally see on first hand.

2 people found this helpful

Helpful

J C

Calling all Geeks (in a nice way)

Reviewed in the United States on January 1, 2015

Verified Purchase

Great book for the mathematically curious. The author has obviously done whole lot of work on the Egyptian and Baylonian mathematics. I was a bit disappointed in the lack of discussion that the lack of a "zero" for the Egyptians, Greeks, and the Romans really messes up the more complex mathematics. As an example, the Greeks mapped the constellations - by transforming the mathematics to Babylonian, doing the star mapping, and then transforming all the results back the Greek mathematics. Overall, a fascinating read.

Reviewed in the United States on December 23, 2014

Verified Purchase

Lots of interesting math info and lots of anti religious nonsense. The nonsense really takes away from the book. Knows math but not ancient religions

2 people found this helpful

Helpful

Amazon Customer

Good

Reviewed in the United States on June 29, 2013

Verified Purchase

An interesting book that explains some of the methods very clearly. Helped me to write a paper for my history of mathematics class.

Helpful

Top reviews from other countries

Translate all reviews to English

AFT

How maths happened

Reviewed in the United Kingdom on May 15, 2020

Verified Purchase

Not as interesting as his next book The Babylonian Theorem

L. Fini

Testo assai approfondito, ma un po' dispersivo

Reviewed in Italy on December 23, 2018

Verified Purchase

Il libro tratta ampiamente dello stato di sviluppo della matematica antica, in particolare di quella babilonese, egizia e greca, dando conto anche delle scoperte archeologiche degli ultimi anni. E' corredato da quesiti ed esercizi per il lettore che costituiscono sia il pregio che il difetto del libro. Possono infatti essere divertenti, ma ne appesantiscono la lettura.

Translate review to English

Gigi

Useless

Reviewed in Germany on October 5, 2018

Verified Purchase

It is just a chat about numbers with no real scientific background. Don't waste money on it.

See more reviews