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Encounters with Euclid: How an Ancient Greek Geometry Text Shaped the World
A sweeping cultural history of one of the most influential mathematical books ever written
Euclid's Elements of Geometry is one of the fountainheads of mathematics―and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today.
In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space.
Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.
Euclid's Elements of Geometry is one of the fountainheads of mathematics―and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today.
In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space.
Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.
416 pages, Hardcover
Published July 6, 2021
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434 people want to read
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Displaying 1 - 28 of 28 reviews
December 29, 2021
More than anything else this is a global cultural history of a book — but don’t let that put you off. Wardhaugh does a rather wonderful job of writing clearly and easily for the reader: rarely have I encountered such a comforting and rewarding treatment of its subject matter and the extensive range it covers; one does not need to have a deep sense of mathematics to appreciate it. It is a book to relish at ease, and as such it is a considerable achievement.
Some time about 300 BCE in Alexandria the Greek geometer Euclid systematised and composed his tome, the Elements of Geometry in 13 books. This is the work which has influenced just about every culture in human history in one way or another for the last 2,300 years (and still counting). How this has been achieved is a rather astonishing yet wonderful tale, and beautifully brought to fruition by Wardhaugh.
Some time about 300 BCE in Alexandria the Greek geometer Euclid systematised and composed his tome, the Elements of Geometry in 13 books. This is the work which has influenced just about every culture in human history in one way or another for the last 2,300 years (and still counting). How this has been achieved is a rather astonishing yet wonderful tale, and beautifully brought to fruition by Wardhaugh.
May 28, 2024
I'm very glad to have picked up this book on a whim.
Euclid's Elements was written around 300BC, and is a book that would come to impact the teaching (and learning) of mathematics for the next 2300 years. There's a copy of Newton's Elements that can be viewed at Trinity College, which contains Newton's small, neat handwriting in the margins converting the Euclidean proofs into their Cartesian, algebraic equivalents.
Particularly interesting to me where the chapters set in Ancient Greece and Rome, as they painted a picture of what intellectual life (both geometrical and philosophical) looked during those periods. Tracing the various languages into which the Elements was translated also gives you a history of not just the book, but of mathematical thinking in general, and you learn what cultures were undergoing a golden age at what times.
Less interesting to me were the sections involving how Euclid impacted the ordinary person post-Renaissance (some schoolchildren were tormented by it, others found solace in it, etc.), as the stories seemed a little too familiar (and consequently less interesting). I mostly skimmed these sections (and also the ones talking about Euclid's impact on the arts - both visual and literary).
Euclid's Elements was written around 300BC, and is a book that would come to impact the teaching (and learning) of mathematics for the next 2300 years. There's a copy of Newton's Elements that can be viewed at Trinity College, which contains Newton's small, neat handwriting in the margins converting the Euclidean proofs into their Cartesian, algebraic equivalents.
Particularly interesting to me where the chapters set in Ancient Greece and Rome, as they painted a picture of what intellectual life (both geometrical and philosophical) looked during those periods. Tracing the various languages into which the Elements was translated also gives you a history of not just the book, but of mathematical thinking in general, and you learn what cultures were undergoing a golden age at what times.
Less interesting to me were the sections involving how Euclid impacted the ordinary person post-Renaissance (some schoolchildren were tormented by it, others found solace in it, etc.), as the stories seemed a little too familiar (and consequently less interesting). I mostly skimmed these sections (and also the ones talking about Euclid's impact on the arts - both visual and literary).
May 22, 2023
If you are witty, love mathematics and history, don’t die before reading this book.
At its core, Encounter with Euclid is a book review, long review, book by an obscure character in history, but his influence is enormous.
At the same time it is also a detective story: Finding Euclid, searching him through his Elements, across the globe and through the millennium.
His crime: equally influencing geometricians, mathematicians, logicians, scientists, artists, astronomers, musicians, philosophers, theologians, and as well as sociologists and even dramatists.
A historical bestseller.
Shrouded in the countless versions and commentaries of his books, Elements, Euclid sometimes appears a philosopher, at time a mathematician and often sage.
It was my first ‘Encounter with Benjamin Wardhaugh’. a historian of mathematics. I’ll see his other books as well.
November 7, 2022
Great fun! Wardhaugh had a bit of a stiff way to introduce his subjects. Over all I enjoyed the book, especially the chapters in Al-Buzjani and Thomas Little Heath.
May 27, 2023
M'han obligat al cole però està interessant per una lectura relaxada. Es una mica fun facts el llibre però cada capítol tracta sobre la vida de un personatge de èpoques molt diverses.
August 25, 2023
Acabado y recomendable al máximo. Una historia de las matemáticas centrada en el libro "Elementos" de Euclides. Parece denso, pero es una lectura amena e interesante, muy bien traducida y editada.
April 1, 2024
A pesar de lo que nos podría sugerir el título, Las infinitas vidas de Euclides no pretenden ser una biografía del genio de Alejandría, sino del legado que dejó a la humanidad en su famoso libro de Los Elementos, y lo mucho que influyó en las culturas de las civilizaciones y de sus grandes pensadores. En un viaje de 23 siglos, podemos ver desde el punto de vista de un libro, como viaja a lo largo y ancho del planeta, es traducido a todos los idiomas, y la enorme huella que ha dejado no sólo en la enseñanza de la matemáticas, sino también en la filosofía, el arte y la ciencia.
El autor está muy documentado y lleva investigando sobre Los Elementos toda su vida. La enorme bibliografía que nos proporciona al final del libro nos da una idea de su enorme pasión por la materia. La lectura es agradable y los capítulos cortos invitan a devorar el libro.
El autor está muy documentado y lleva investigando sobre Los Elementos toda su vida. La enorme bibliografía que nos proporciona al final del libro nos da una idea de su enorme pasión por la materia. La lectura es agradable y los capítulos cortos invitan a devorar el libro.
June 19, 2024
Un libro sobre los Elementos de Euclides y su amplísima influencia histórica. Para reflejar la importancia de esta obra en la historia de la humanidad en cada capítulo se presenta un personaje histórico relacionado en cierta forma con la obra, desde editores del libro hasta matemáticos. La estructura del libro hace que cada capítulo sea una isla que no tiene nada que ver con el resto del libro. Un compendio de anécdotas sobre Los Elementos que se hace muy tedioso de leer y de muy poco interés por carecer de un hilo conductor lo suficientemente definido. Quizá las aspiraciones del autor sean demasiado faraónicas al intentar crear un libro que recoja toda la influencia de la obra de Euclides de manera interesante y amena a la lectura. No lo recomiendo.
January 6, 2025
(4.0 stars) An excellently written history of Euclid’s Elements throughout history. The author has a really playful writing style that I very much enjoyed. He helped bring a lot of the historical information to life and give voice to its characters. I learned a ton from this book, and the history of the Elements is in a lot of ways parallel with the history of math as a whole. It was really fascinating to see how such a strangely bare but beautiful document from 3000 years ago travelled through time, influencing generation after generation. I highly recommend this book for anybody interested in the history of mathematics. I only wish there was more of a discussion of Euclid’s influence on the USA and education.
July 19, 2025
Fascinante de principio a fin. Un apasionante viaje a través de la Historia con libro icónico como brújula. La diversidad de gentes y culturas que ha entrado en contacto con el texto de Euclides a través de los siglos, es la diversidad de la Humanidad, ni más ni menos. Un libro de fácil lectura, sin tecnicismos, pero con muchas enseñanzas y mucho en lo que pensar.
June 18, 2024
Lo más infumable que recuerdo haber leído. Las infinitas vidas que necesitas para acabarlo. Yo solo necesité unos meses. Hurra por mi.
Como punto positivo, es muy riguroso ( o lo parece) a nivel histórico y matemático.
Como punto positivo, es muy riguroso ( o lo parece) a nivel histórico y matemático.
September 12, 2021
Comprehensive
February 28, 2024
Un libro que me hace reflexionar del proceso requerido para la formación y formulación de la ciencia actual, específicamente las matemáticas
September 3, 2024
Las matemáticas son lo mejor y este libro lo confirma 🔵🟩🔺💛.
La estructura y lo bonito que está escrito lo hacen fácil de leer y muy disfrutable.
La estructura y lo bonito que está escrito lo hacen fácil de leer y muy disfrutable.
November 14, 2024
Un triángulo se hace de dos circunferencias de una desde las puntas de una recta.
(Shut yo bitch ass up God damn)
(Shut yo bitch ass up God damn)
May 23, 2025
no lo leí entero porque no tuve tiempo. Este libro trata de la historia de un libro, no es el libro en sí...
June 1, 2024
One of the most interesting books I’ve read in quite some time. I’ve been fascinated with geometry since high school but I never pursued it until I discovered Euclid’s Elements about five years ago. I really enjoy history, especially mathematical history Wardhough’s book really filled in a lot of gaps that I wondered about. I’m not good at math, particularly if it involves algebra, but the simple compass and straight edge on a plane of paper not only to create reproducible shapes, but to describe the proof through deductions seems to have lifted humanity out of the blind belief systems of myths and into the more scientific understanding of our universe.
Because the chapters are short, I interspersed actually coping all the definitions, axioms and common notions of the Elements in a plane notebook and then doing each proposition in Book One. Not even half way through and I have come to a deeper understanding of how important this document is to education and it is somewhat sad to see how many people have no idea who Euclid is and what the Elements are. I think that I would have really appreciated a classical liberal arts education with the first six books of Euclid’s Elements rather than the modern filters of “mechanical geometry “.
I won’t spoil the details of the book, but suffice to say that the book of Elements was apparently the most reproduced book in the world behind the Bible.
Secondly, although not described in Wardhaugh’s book, the story of Abraham Lincoln as a young lawyer before his Presidency, was apparently not very convincing or successful. So he reasoned that what he lacked was his ability to demonstrate his logic to the courts, so he self taught himself and actually memorized the first six books of Euclid’s Elements Propositions in order to better demonstrate his proofs through the deductive logic that they conclusively demonstrated. I am no lawyer but that has always been a great analogy for how we can come closer to the truth that we seek in the physical and abstract world.
Because the chapters are short, I interspersed actually coping all the definitions, axioms and common notions of the Elements in a plane notebook and then doing each proposition in Book One. Not even half way through and I have come to a deeper understanding of how important this document is to education and it is somewhat sad to see how many people have no idea who Euclid is and what the Elements are. I think that I would have really appreciated a classical liberal arts education with the first six books of Euclid’s Elements rather than the modern filters of “mechanical geometry “.
I won’t spoil the details of the book, but suffice to say that the book of Elements was apparently the most reproduced book in the world behind the Bible.
Secondly, although not described in Wardhaugh’s book, the story of Abraham Lincoln as a young lawyer before his Presidency, was apparently not very convincing or successful. So he reasoned that what he lacked was his ability to demonstrate his logic to the courts, so he self taught himself and actually memorized the first six books of Euclid’s Elements Propositions in order to better demonstrate his proofs through the deductive logic that they conclusively demonstrated. I am no lawyer but that has always been a great analogy for how we can come closer to the truth that we seek in the physical and abstract world.
May 1, 2022
The survival of Euclid's Elements over 2,300 years is in itself a remarkable story which Wardhaugh recounts in a way that is entertaining and interesting but like the ship of Theseus it has been dismantled and reconstructed many times and from the outset there has been discussion about its accuracy, its adequacy, its utility and its significance. In spite of many attempts to improve upon Euclid's work, there is a persistent drive to revert back to something closer to the original. It is often held up as a model of elegant reasoning and has even inspired creative art. It has tormented countless schoolchildren on whom it has been inflicted since ancient times, yet it has enabled self-teaching for many individuals otherwise unable to access formal education, including some remarkable women. Its more inflated claims to excellence whether as a textbook or even as a rare example of a true and accurate description of the world have been severely dampened, especially since the 19th Century, and Wardhaugh suggests that Euclid's (perhaps now declining) popularity with British educators is not matched in other European countries. Yet Euclidean geometry refuses to be dismissed and it seems that some cosmologists now think of the universe as a Euclidean space.
As a book, an artefact, as a mathematical model, as a systematic method of reasoning, as a creative inspiration and as an educational guide, Euclid's Elements really is a remarkable achievement. Its limitations may even be part of its value, because it is a book not to contemplate but to work with and its defects often act as grit to activate the creative potentials of its many acolytes. It is rare to find an old copy, however priceless and revered, that has no scribbled workings in its margins and white spaces, no irritated corrections and amendments to the text and its diagrams.
As a book, an artefact, as a mathematical model, as a systematic method of reasoning, as a creative inspiration and as an educational guide, Euclid's Elements really is a remarkable achievement. Its limitations may even be part of its value, because it is a book not to contemplate but to work with and its defects often act as grit to activate the creative potentials of its many acolytes. It is rare to find an old copy, however priceless and revered, that has no scribbled workings in its margins and white spaces, no irritated corrections and amendments to the text and its diagrams.
October 7, 2022
Un popurrí de historias ligadas, a veces por un hilo finísimo, con los Elementos de Euclides. El autor quiere expresar el gran impacto que ha tenido esta obra a lo largo de la historia a partir de una enumeración de hitos históricos de los que ha formado parte, y aunque a veces el libro cautiva y muestra cómo este libro ha sido parte esencial de la civilización occidental, la gran parte del tiempo parece un libro de curiosidades históricas sacadas de la revista muy interesante.
Por romper una lanza, diré que es indudable el trabajo de investigación que hay detrás de él, pero por eso mismo acaba pareciendo más un intento desesperado de trasladar investigaciones académicas al gran público que un libro con una historia sólida como hilo conductor. Me ha dejado muy frío en general, aunque he de decir que lo leía más por necesidad que por gusto.
Por romper una lanza, diré que es indudable el trabajo de investigación que hay detrás de él, pero por eso mismo acaba pareciendo más un intento desesperado de trasladar investigaciones académicas al gran público que un libro con una historia sólida como hilo conductor. Me ha dejado muy frío en general, aunque he de decir que lo leía más por necesidad que por gusto.
April 18, 2023
This is not a real review, just some thoughts I like to write down.
Das ist keine richtige Bewertung, nur ein paar Gedanken, die ich aufschreiben wollte.
An sich gute Übersicht über die "Elemente" und deren Einfluss in den verschiedenen Bereichen, nicht nur die Mathematik und Naturwissenschaften, sondern darüber hinaus in Philosophie, Kunst und Politik. Es ist erstaunlich, über wie viele Jahrhunderte dieses Werk in all seinen Form so präsent war und erst in den letzten hundert Jahren an Bedeutung abgenommen hat.
Es ist unterhaltsam und kurzweilig geschrieben, konnte mein Interesse aber nicht durchgängig halten. Dies ist vor allem dadurch geschuldet, dass das Buch aus verschiedenen Geschichten besteht, die manchmal interessant, aber auch eher langweilig sein können. Gerade der erste Teil, mit all den Aufzählungen über die Versionen, Anpassungen und Übersetzungen war eher zäh.
Das ist keine richtige Bewertung, nur ein paar Gedanken, die ich aufschreiben wollte.
An sich gute Übersicht über die "Elemente" und deren Einfluss in den verschiedenen Bereichen, nicht nur die Mathematik und Naturwissenschaften, sondern darüber hinaus in Philosophie, Kunst und Politik. Es ist erstaunlich, über wie viele Jahrhunderte dieses Werk in all seinen Form so präsent war und erst in den letzten hundert Jahren an Bedeutung abgenommen hat.
Es ist unterhaltsam und kurzweilig geschrieben, konnte mein Interesse aber nicht durchgängig halten. Dies ist vor allem dadurch geschuldet, dass das Buch aus verschiedenen Geschichten besteht, die manchmal interessant, aber auch eher langweilig sein können. Gerade der erste Teil, mit all den Aufzählungen über die Versionen, Anpassungen und Übersetzungen war eher zäh.
July 26, 2022
El libro está centrado en el libro "Elementos" (o Elementos de geometría) de Euclides, no es una biografía del personaje en sí, tal como se pensaría por su título en español tipo "clickbait".
Todo el principio del libro es muy interesante y divertido porque narra la influencia de los Elementos en las culturas antiguas, cómo se fue extendiendo, traduciendo, adaptando, y cómo muchos otros estudiosos lo fueron comentando y anotando.
Narra su paso por las culturas antiguas, por la Edad Media, su entrada al Renacimiento y las primeras impresiones, y finalmente a la edad moderna.
Pero los últimos capítulos del libro narran su influencia en muchos otros nichos culturales, además del académico: pintura, arquitectura y hasta la moda. No es que no sea interesante, ero es un poco pesado...
Todo el principio del libro es muy interesante y divertido porque narra la influencia de los Elementos en las culturas antiguas, cómo se fue extendiendo, traduciendo, adaptando, y cómo muchos otros estudiosos lo fueron comentando y anotando.
Narra su paso por las culturas antiguas, por la Edad Media, su entrada al Renacimiento y las primeras impresiones, y finalmente a la edad moderna.
Pero los últimos capítulos del libro narran su influencia en muchos otros nichos culturales, además del académico: pintura, arquitectura y hasta la moda. No es que no sea interesante, ero es un poco pesado...
April 5, 2023
Excelente libro, recopila de estupenda forma la magnífica trascendencia que ha tenido tanto Euclides como su obra, además de enriquecer con pequeños toques de historia, los cuales otorgan un contexto magnífico, al laborioso y fructuoso trabajo que nos ha dado tan bella obra como lo es "Los elementos de Euclides".
Quién quiera leerlo, tiene mi absoluta recomendación, el libro no divaga en conceptos matemáticos a profundidad, pero aún así, es capaz de profundizar en conceptos básicos y elementales de la geometría euclidiana y su progreso a lo largo de los dos mil trescientos años de historia con los que cuenta la obra.
Quién quiera leerlo, tiene mi absoluta recomendación, el libro no divaga en conceptos matemáticos a profundidad, pero aún así, es capaz de profundizar en conceptos básicos y elementales de la geometría euclidiana y su progreso a lo largo de los dos mil trescientos años de historia con los que cuenta la obra.
September 6, 2022
Más o menos interesante como anecdotario. De lectura ágil. Pero poco profundo y poco o nada comprometido con el verdadero desarrollo de una idea o interpretación sobre un hecho cultural (los Elementos de Euclides) que se sospecha bastante más relevante que una simplona fascinación por sus "infinitas vidas". Al final parece que se queda en el mero fetichismo, y no aporta demasiado. Se aprenden bastantes cosas para el Trivial, eso sí, o para un examen tipo test.
September 4, 2023
Buen libro; es de historia, no de matemáticas, y analiza la influencia de "Elementos", de Euclides. Puede servir para cultivar un interés en dicho libro y en la geometría clásica. Del mismo modo, recuerda cómo los intelectuales de siglos anteriores cultivaban múltiples ámbitos, cada vez más en decadencia hoy en día.
September 5, 2023
Se hace más largo que un discurso de Fidel Castro. Un ensayo aburrido incapaz de crear ningún aliciente para leer el próximo capítulo
Aún así, está bien documentado y tiene algunos puntos interesantes
Aún así, está bien documentado y tiene algunos puntos interesantes
November 22, 2022
The only math book to ever make me shed a tear of joy.
June 10, 2022
Es un libro entusiasta que cuenta la vida de otro libro de una manera divulgativa. Hay historias realmente emocionantes, otras más de relleno.
January 24, 2023
No tengo muy claro que esta idea diera para libro, la verdad.
Displaying 1 - 28 of 28 reviews