So many brilliant minds pop up during that time: as Newton and Leibniz exit, Euler and Gauss enter. Later, Cauchy and Weierstrass formalize the concept of the limit , which does away with any need for infinity in calculus at all!

## Brief Histories Series | Awards | LibraryThing

There are plenty of names and plenty of stories—and this is where A Brief History of Infinity starts to lose its edge. The first few chapters of this book are fascinating. Clegg devotes a lot more space to the Greek philosophers than others might, going so far as to mention some of the more obscure ones, like Anaxagoras. Clegg lays the ground well for what will come in later chapters, all the while emphasizing the reluctance of the Greek philosophers to abandon the solidity of numbers found in the real world.

But as we get closer to those magical two centuries following the great Newton—Leibniz schism, the story of infinity gets more complicated as more people get involved.

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To be fair to Clegg, this book is almost as slim as Zero. And although he happens to go off on many a tangent, he at least has the ability to find his way back on track quickly enough—that is, his tangents are interesting and informative. He goes so far as to list and briefly elaborate upon each of the axioms of Zermelo-Fraenkel set theory! Rather, think of it like this: if you are not particularly mathematical and read this book, you will gain a wealth of knowledge. You will be fun at parties! If you are particularly mathematical, then depending on how much you like the history of math, you might already be familiar with most of these anecdotes.

But the book will still be fun to read, and chances are you will learn at least one or two new things. I hope this book, or at least my review of this book, demonstrates why I find math, as well as the history of math, so fascinating. Mathematics is a subject with a long and storied past, one that is fun to explore by looking at the humans who progressed—or regressed—throughout the centuries.

A Brief History of Infinity is a book in this mould. While its organization and its focus leaves something to be desired, its scope and ambition do not.

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View 2 comments. May 11, 4triplezed rated it really liked it Shelves: history , science , a-brief-history-of. I can find my way around a darts board rather well and have never had a problem with watching the runs tick over while watching the cricket. Other than that maths just is not my strong point.

But when a complete maths fool such as myself enjoys a book like this then there has to be something going for it. Of course, how could there not be. Read and enjoy! View all 4 comments. Jan 23, Peter Baran rated it liked it. Not a bad overview of the history of infinity, though it sits on the fence a lot, and is a little prone to classic pop science micro biographies to limp along hey here is Godel, he was brilliant but he was nuts Infinity is a subject I used to know a lot about, and since I have been out of the incomprehensible big stuff game I wondered if much new had come up.

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One bit of quantum computing aside, not really, and the book isn't strong on some of the philosophical implications, but it is a brie Not a bad overview of the history of infinity, though it sits on the fence a lot, and is a little prone to classic pop science micro biographies to limp along hey here is Godel, he was brilliant but he was nuts One bit of quantum computing aside, not really, and the book isn't strong on some of the philosophical implications, but it is a brief history.

Jun 03, Simona rated it liked it. Good book overall, but oftentimes the author manages to contradict himself in the same phrase or paragraph, and uses hopelessly confusing and sometimes inappropriate illustrations to get the point across. I wouldn't have understood him had I not encountered the concepts before, and he really lost me on the one thing I hadn't. And most annoyingly, mathematical concepts are so loosely used that would make serious mathematicians cringe - among many other things, calling irrational numbers "irration Good book overall, but oftentimes the author manages to contradict himself in the same phrase or paragraph, and uses hopelessly confusing and sometimes inappropriate illustrations to get the point across.

And most annoyingly, mathematical concepts are so loosely used that would make serious mathematicians cringe - among many other things, calling irrational numbers "irrational fractions" was maddening. While toning it down so it would be readable and accessible to any interested person, it shouldn't have been so hard to keep it rigorous and mathematically correct. Besides, introducing new people and relating the story of their lives was done in such a way that you were wondering what could possibly be their connection to the subject, which makes the reading anything but smooth.

Jun 14, Bennett Coles rated it really liked it. This was a very interesting exploration of a concept we bandy around every day but have no real understanding of.

By first exploring the philosophical and religious approaches through the millennia toward infinity, Mr. Clegg provided a surprisingly well-rounded view of humanity's quest to grasp the ungraspable. The mathematical and scientific approach to infinity eventually enters the story, and Mr. Clegg reveals that many today accept infinity as a useful tool in their calculations without real This was a very interesting exploration of a concept we bandy around every day but have no real understanding of. Clegg reveals that many today accept infinity as a useful tool in their calculations without really bothering to understand what it means.

Infinity in modern physics is often treated like the "weirdness" of quantum physics: it makes no sense, but it works. This book doesn't offer nor does it promise a true understanding of infinity, but it is a fascinating look at how great minds try to tackle one of the many concepts that may be forever beyond human understanding. Feb 17, Koen Crolla rated it it was ok Shelves: mathematics. Poorly written, both as regards actual language use and overall structure. Clegg seems to be confused about what he's actually trying to communicate, and doesn't appear to be able to distinguish actual mathematicians or proto-mathematicians exploring the concept of infinity from crackpots merely abusing language.

The result is something that lacks both a historical narrative and enough rigour to pass even as popular mathematics. And there's no shortage of better books on the same subject; just Poorly written, both as regards actual language use and overall structure. And there's no shortage of better books on the same subject; just read Taming the Infinite or The Infinite Book or something instead.

Apr 05, Aaron Humphrey rated it liked it Shelves: non-fiction. This book is more about the people who thought about infinity than it is about infinity itself. As such, it's sort of an orthogonal projection of the history of science onto one particular subject, so it includes Newton vs. Leibniz and the infinitesimals and limits of calculus, as well as the feud between Cantor and Kronecker over Cantor's infinite sets. For someone who doesn't know the theory I didn't run across anything I wasn't already familiar with--I can prove that the integers, whole numb This book is more about the people who thought about infinity than it is about infinity itself.

For someone who doesn't know the theory I didn't run across anything I wasn't already familiar with--I can prove that the integers, whole numbers, and rational numbers are smaller sets than the real numbers without working too hard , it should be fairly approachable. View 1 comment. Jun 05, Ellie Julio rated it did not like it. I wanted to like this book; I really did. Sadly, this isn't one of those. The author uses far too many swathes of other texts and then summarizes them and has an odd writing style that simply puts you to sleep. I gave it five chapters before I had to put it down.

Life's too short to read boring books. Apr 16, Shanmuganathan rated it did not like it. This book is a very boring read. The main problem is that some verses from other books are simply copy-pasted at various junctures. This makes the book very hard to read. One can read one, two, three Sep 13, Mark Schnitzius rated it it was ok. A largely tepid affair. Another history book masquerading as a math book, with all the usual fear of actually attempting to explain some harder concepts. That's a little harsh, I think; there were some decent bits, but nothing that isn't covered better elsewhere.

Oct 23, Marco Hokke rated it it was ok. Badly written and without a clear idea or point. Jan 09, Nick rated it really liked it. Infinity, or at least the idea of very big numbers, grips the mind at a tender age. But little did I know, until I read this book, that the numbers that go on forever are just one form of infinity, and that there is a 'bigger' infinity, one that is paradoxically compressed into the tiny gap between 0 and 1. This was the brilliant insight of Georg Cantor, whose pioneering work on infinity in the late nineteenth and early t "Do numbers go on forever?

This was the brilliant insight of Georg Cantor, whose pioneering work on infinity in the late nineteenth and early twentieth century helped drive the poor fellow mad. The proof is an elegant one: think of a list of every number between 0 and 1, such as 0. Now construct a new number, taking the first digit of the first number in the table, the second digit of the second number and so on. Then change every digit in this number for example by adding 1, shifting 9 up to 0. The number produced logically can't be the same as any number in the list - even though that infinitely long list included every number between 0 and 1.

It was as if Cantor had discovered a new 'dimension' of infinity. No wonder he lost his grip on sanity - although opposition from a vindictive rival, Leopold Kronecker, was perhaps what drove him over the edge. Cantor's story is just one of the fascinating episodes in this book, which tells of the mathematicians and philosophers who have pondered infinity and how perceptions of this impossible number have evolved over the centuries.

On the way, there are several interesting diversions, including one on how the Ancient Greeks managed without having a concept of fractions. Rather than thinking of a "half", they would visualise a shape that was smaller than another by a factor of 2, thinking of the relationship purely in terms of whole numbers. And though the concept of zero can be problematic, that of infinity is more mind-bending by far. There's something about infinity we can't get our head around, almost by definition, but in Brian Clegg's genial company, it is fun to try.

My only slight reservation was that while most of the mathematical concepts were excellently explained, other parts of the book made me painfully aware of the lacunae in my knowledge, especially the chapters which touched on calculus. That said, the non-mathematical reader shouldn't be scared of attempting this book, which is a fascinating journey for the mind. Then, quite unexpectedly, the magnificent animal stalks out into full view for a few, fleeting seconds Jul 21, Usman Baig rated it really liked it Shelves: mathematics.

The concept of infinity invariably comes up in countless places when one contemplates life, be it mathematical or otherwise.

## A Brief History of Infinity

What is the biggest number? What is the length of the longest line? These and other such questions have fascinated mathematicians for centuries but as Brian Clegg shows, infinity as a mathematical concept was not properly dealt with until very recently. Even though the infinitely small is essential to the working of calculus, there was a certain vagueness around the concep The concept of infinity invariably comes up in countless places when one contemplates life, be it mathematical or otherwise.

This book with its slow pace and engrossing style, treats this concept and its history in a way that will allow all readers , even the ones unfamiliar of basic calculus to enjoy the read. That is a tall task for a book that aims to explore the understanding of the infinite through the centuries. These pieces not only put those specific individuals into the academic context of their time but also provides us with tidbits of their personal lives so that we may appreciate their contributions on a higher level.

All in all, this is a highly readable book and a suitable primer to more advanced studies of the infinite in the mathematical world. Jul 12, Stephanie rated it it was amazing Shelves: mathematics. I was going to give this book 4 stars only because I thought there could've been more content, but when I thought about it, there really is so much to say about infinity.

But in order to maintain the audience's attention, and to attract a wider audience, I would have to say that this book did an excellent job. Virtually anyone can read it. It does help to have even a minimal understanding of calculus, but Clegg does a good job of explaining the concepts that involve infinity. It's truly so fasci I was going to give this book 4 stars only because I thought there could've been more content, but when I thought about it, there really is so much to say about infinity.

It's truly so fascinating how complex this topic is. I really enjoyed the different accounts of men who tried to tackle this concept, some had nervous breakdowns, some got into pretty intense encounters with other men doing the same thing.

It was really something to read about. Would recommend this book to anyone who wants to whet their appetite regarding infinity. Jun 30, Josemaria Valenciano rated it really liked it. An overall fun read. Oftentimes the book proved a struggle for me to comprehend, but that was due to the depth and difficulty of the subject matter involved rather than it being the fault of the author.

Besides sometimes straying unnecessarily off to other topics, Brian Clegg does an excellent job in explaining a variety of topics ranging from theology to number theory to the layman. May 27, Arun Babji rated it liked it. It presents an entertaining history along with the background motivation and life story of great people that contributed to our ideas of Infinity. Jul 04, Johnny T rated it it was amazing. A very entertaining blend of math and history. Jun 30, James Wheat rated it really liked it Shelves: storage , bookshelf , on-loan.

I was hoping for a socio-cultural history of the concept of infinity but this was very heavily mathematical. Jun 21, Anthony rated it liked it. Thought I was never going to finish this one I must admit that I was a little lost on occasion but overall an interesting, thought provoking and enjoyable read. Apr 06, Auceanne rated it did not like it. Jan 22, Marcus rated it really liked it. In his paper, Foucault outlines a brief history of space in the Western world, A Brief History of Infinity: The Quest to Think the Unthinkable engaging history Systeremarkably similar quest for the ultimate determinants of observed him the Western thought who imagined that mathe- matics ought.

Amidst all the Systems thinking is presented as the antithesis of "reductionism. Do you want to support owner of this site? Click here and donate to his account some amount, he will be able to use it to pay for any of our services, including removing this ad. Darmowy hosting CBA.

Contact Us name Please enter your name. A brief history of infinity the quest to think the unthinkable pdf Mind "Aczel tells of mathematicians struggling with absolute infinity and "Some contradiction The art historical quest unleashed by the idea of deserves comment. I think it might be useful to give a brief description of the ISBN pdf We are also keenly aware that we are globalization.

The origin of this now infamous heading is rather strange and socio-historical approach' Chapter 1 , which provides a brief historical and following, a brief description of the path followed by that research is given.