Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
- Downloads：1943
- Type：Epub+TxT+PDF+Mobi
- Create Date：2021-07-23 03:19:06
- Update Date：2025-09-06
- Status：finish
- Author：Jordan Ellenberg
- ISBN：B08RRQS2MW
- Environment：PC/Android/iPhone/iPad/Kindle
Reviews
Kim Zinkowski
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Enjoyable， humorous， oftentimes a bit tough to parse。
Ron
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Mostly enjoyable， but like other reviewers I found that the title and subtitle of the book were not quite justified。 I did not find enough Geometry here， even if broadly conceived。
Bernard
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Informative and wildly readableLots of great stuff in here touching on topics ranging from card shuffling to saving democracy， presented in a witty manner that teaches - easy without being facile。
April
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Interesting， easy to follow， and very current and relevant。 I most enjoyed the sections about disease spread and gerrymandering。 I’d be interested to read more from the same author on other topics if he released them！
Michiel
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"Shape" is the successor of Ellenbergs' popular work "How Not to Be Wrong"。 Whereas the earlier book showed how to use mathematical thinking in everyday life （and win the lottery）， this book aims to show that geometry is absolutely everywhere。 I am no mathematician， but I have the feeling that Ellenberg considers absolutely everything geometry。 There is a chapter on Euclid， about Euclid， the topology of straws and pants， Gerrymandering but also about random walks， graphs game theory， the uncerta "Shape" is the successor of Ellenbergs' popular work "How Not to Be Wrong"。 Whereas the earlier book showed how to use mathematical thinking in everyday life （and win the lottery）， this book aims to show that geometry is absolutely everywhere。 I am no mathematician， but I have the feeling that Ellenberg considers absolutely everything geometry。 There is a chapter on Euclid， about Euclid， the topology of straws and pants， Gerrymandering but also about random walks， graphs game theory， the uncertainty principle， etc。 Nothing much connects the chapters， so the whole style felt meandering。Ellenberg is a charismatic writer with a talent for explaining complicated math to the layperson。 I felt that after the success of this previous book， this has hardly been edited。 I have read several interviews with the author that geometry is his least favourite branch of mathematics。 It shows。 Most chapters feel like a collection of brainstormed， vaguely connected ideas weaved into a text on an evening。 For example， consider one chapter。 It jumps from: a series of numbers， an epidemiological model， Fibonacci numbers， rational numbers， stocks， eigenvalues， page rank， eigensequences and the uncertainty principle。 Compare with Strogatz' "Infinite Powers"， which guides the reader over the wonders of calculus or Parker's "Things to Make in the Fourth Dimension"， in which each chapter is a delightful self-contained story about a math topic。 These are more enjoyable math books for laypersons， at least in my opinion。 。。。more
Melody
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Shape - Jordan Ellenberg （2021）2021 read #83Grade: ASynoposis: Jordan Ellenberg is a math professor at the University of Wisconsin - Madison。 In his book， Shape， he explores how geometry can be used to solve a variety of real-world problems， from board games to gerrymandering。 He describes the math behind a lot of the virus spread data we've been seeing on the news since 2020。 This book is written not just for professional mathematicians， but for everyone who desires to learn why geometry is imp Shape - Jordan Ellenberg （2021）2021 read #83Grade: ASynoposis: Jordan Ellenberg is a math professor at the University of Wisconsin - Madison。 In his book， Shape， he explores how geometry can be used to solve a variety of real-world problems， from board games to gerrymandering。 He describes the math behind a lot of the virus spread data we've been seeing on the news since 2020。 This book is written not just for professional mathematicians， but for everyone who desires to learn why geometry is important。Thoughts: This was a birthday gift from my boyfriend so I was so excited to read this！ I am getting my PhD in Math so this book was right up my alley。 I've found with a lot of similar books， the material is either too basic for my level and I learn nothing， or it's too advanced and I feel like I'm reading for work instead of pleasure。 Ellenberg has found a happy medium。 What you won't do while reading Shape is crunch numbers in formulas， instead you'll learn the concepts and applications of geometry。 If you read a lot of nonfiction and want to learn a little math， then I highly recommend this book！ 。。。more
Ann Hriciga
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I wanted to like this book but found it like a random walk through space。 I was not expecting so much discussion about the personalities of various mathematicians。 The discussion of how to analyze the spread of a virus was very well done and easy to understand， so kudos for that。
Lance Johnson
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This book has many excellent pieces but they are poorly linked together and surrounded by bloat。 In my opinion， it could be polished into another masterpiece （like his previous book "How Not to be Wrong"） if the theme was more concrete and topics were more carefully strung together。 Before I go through my criticisms， there are several positives。 Generally， I like Ellenberg's writing style and his humor。 He also has a knack for choosing good examples and historical tidbits。 I also appreciate that This book has many excellent pieces but they are poorly linked together and surrounded by bloat。 In my opinion， it could be polished into another masterpiece （like his previous book "How Not to be Wrong"） if the theme was more concrete and topics were more carefully strung together。 Before I go through my criticisms， there are several positives。 Generally， I like Ellenberg's writing style and his humor。 He also has a knack for choosing good examples and historical tidbits。 I also appreciate that he is not afraid to talk about advanced concepts and present them in a simple language。 There were many points in the book that caused me to think about something in a different light or see a connection I previously had not。 So if you are already interested in mathematics and are willing to wade through the book to find the gems， I would recommend it。 My first major criticism is that the overall theme is poorly defined。 Math is broad and densely interconnected but has several different fields: algebra， analysis， topology， probability， combinatorics， number theory， geometry， etc。 Most problems fall naturally into one or more fields but can benefit from the tools or perspectives of other fields as well。 The theme of this book is geometry but for many of the topics discussed the author does little to convince me that the topic is either naturally a geometric problem or that a particularly geometric lens is being applied to it。 He seems to lump anything that has a shape present or involves a distance under the umbrella of geometry， which is most of math。 He is not wrong exactly， but taking such a loose approach robs it of any particular significance。 It is a bit like classifying most of math as arithmetic since many areas involve the use of addition， subtraction， and multiplication。 The statement is not quite wrong， but it lacks any meaningful insights。 My second criticism is that the topics are poorly strung together。 Each chapter meanders from tangent to tangent until I had forgotten what the original point was。 Then suddenly it jumps back to a previous topic。 Many topics were split into pieces and scattered across several chapters。 For example， there is a particular subplot that is broken up across at least 5 chapters。 The division just makes it hard to follow。 My third criticism is there is a significant amount of bloat。 The book is over 400 pages long， but many pages felt redundant or tedious。 By the end， I really didn't want to keep reading。 Sometimes he would go out of his way to avoid a certain technical term or concept， but to avoid it would involve all these gymnastics that took longer and were more confusing than it would be to quickly introduce the term and explain it。 Other bits were fine， but did not feel like they had a good reason to be in the book。 Either they overlapped heavily with another section or seemed so tangential that they did not fit with the surrounding material。There are gems in here， you just have to dig for them。 Looking forward to his next book。 。。。more
Isaac
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Pretty sure I could not have correctly defined "geometry" prior to reading this book。 I still can't， but at least now I know it's more than just angles and flat shapes。This book was kind of all over the place。 I probably use the expression "dizzying intellect" a bit too much， but it seems particularly apt to describe Jordan Ellenberg here。 He seems to start accessibly with a topic and often spends a while there but seems to inevitably spiral off on tangents of increasing complexity， occasionally Pretty sure I could not have correctly defined "geometry" prior to reading this book。 I still can't， but at least now I know it's more than just angles and flat shapes。This book was kind of all over the place。 I probably use the expression "dizzying intellect" a bit too much， but it seems particularly apt to describe Jordan Ellenberg here。 He seems to start accessibly with a topic and often spends a while there but seems to inevitably spiral off on tangents of increasing complexity， occasionally spiraling back out， occasionally just lurching back to the initial topic。That's all part of the charm though， his enthusiasm for the subject is so unmistakably genuine that even when I wasn't following the math at all， I was still enjoying the book。 He's also got a great sense of humor， the book is really funny in places。As a bit of a Lincoln nerd I really loved the first section about Lincoln and Euclid， and as a Wisconsonite I really loved the final section on our recent history of Gerrymandering。 There was some really interesting pandemic geometry in there， but it was very "last summer"， almost dated given all that's transpired， and I think that will all be much better if it gets expanded and revised in a few years。 。。。more
Marcos
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Like many of the reviews here， I also loved Ellenberg's earlier book！ So maybe I was too hyped about this one。The problem is that the topics are so interesting but it's very hard to follow the common thread in the book。 We jump from subject to subject without any （at first） obvious connection。 This worked really well in his previous book， where concepts were beautifully woven together to make a coherent whole。Another issue I had with the book was that it felt like some concepts are dumbed down p Like many of the reviews here， I also loved Ellenberg's earlier book！ So maybe I was too hyped about this one。The problem is that the topics are so interesting but it's very hard to follow the common thread in the book。 We jump from subject to subject without any （at first） obvious connection。 This worked really well in his previous book， where concepts were beautifully woven together to make a coherent whole。Another issue I had with the book was that it felt like some concepts are dumbed down past the what could be reasonably expected。 For example， when explaining loss functions in machine learning， Ellenberg writes "。。。we can assign our strategy a 'wrongness function。'" and in a footnote says "*among actual computer scientists， usually called an error or a loss" （p。 169）。 Why？ Saying loss function is less confusing than saying wrongness function is also called loss or error function。There are quite a few tangents to tangents to tangents in the storyline。 For example， Simpson's paradox （p。 226）， which I find fascinating and enjoyable to explore， is mentioned in passing while explaining something else （Covid-related）。 This was a shame because in that specific setting， I got no wiser about Simpson's paradox or about the Covid-example。It also felt like the book could have been much more concise。 Then again， I didn't write any book。 So， good job Jordan！ It's so much easier for us to criticise a book than write one ourselves。 Looking forward to your reading your next book！ 👏 。。。more
Kumar Ayush
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Less technical than I expected it to be， but I enjoyed reading it very much。
Bowman Dickson
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Enjoyed！ Strangely wanted more geometry （he defines geometry loosely） but got a bunch of teaching ideas
Susan
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This is the geometry book that you didn't know that you wanted to read。 Let's be truthful--it's not a fast or easy read， and despite the reviews saying that you'll follow the math， there are probably places where you won't， unless you're a lot better at math than I am。 But Ellenberg is an entertaining writer and knows his stuff cold， so you're sure to learn a lot anyway。 The long chapter on redistricting--Ellenberg was involved in the efforts in Wisconsin， where he lives--is enlightening， enragi This is the geometry book that you didn't know that you wanted to read。 Let's be truthful--it's not a fast or easy read， and despite the reviews saying that you'll follow the math， there are probably places where you won't， unless you're a lot better at math than I am。 But Ellenberg is an entertaining writer and knows his stuff cold， so you're sure to learn a lot anyway。 The long chapter on redistricting--Ellenberg was involved in the efforts in Wisconsin， where he lives--is enlightening， enraging， and discouraging， but there are laughs along the way。 。。。more
Keven Wang
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Some parts of the book is quite entertaining。 A math major would probably enjoy it more。
Miguel
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It’s really hard for a writer to make math， let alone geometry， a fun and inviting subject。 Ellenberg does about as good a job as possible for those not well versed in this area （even after taking courses up to Calc V and diff equations in college I am not familiar with most of his topics in any sort of depth）。 His style keeps the reader engaged， although some of the concepts still get a bit tough to meticulously follow such as the larger portion near the end on jerrymandering。 The charts and fi It’s really hard for a writer to make math， let alone geometry， a fun and inviting subject。 Ellenberg does about as good a job as possible for those not well versed in this area （even after taking courses up to Calc V and diff equations in college I am not familiar with most of his topics in any sort of depth）。 His style keeps the reader engaged， although some of the concepts still get a bit tough to meticulously follow such as the larger portion near the end on jerrymandering。 The charts and figures in the book do help somewhat and would have been difficult to follow the audiobook alone for this particular one。 。。。more
michael o。 duffy
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A Broader View Of GeometryJordan Ellenberg has written a beautiful book about geometry。 He had me at “Geometry is the cilantro of mathematics” - I had to read the book。 I especially liked his discussion of democracy and map making。 If only our Supreme Court had been able to understand the argument。 The writing is a tribute to his combination of Ph。D。 and MFA。
Ravi Warrier
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This is an American political rant disguised as a maths book。 It starts out fine， but the latter half of the book is the author's explanation （albeit mathematical） of what's wrong with the American political system。 This is an American political rant disguised as a maths book。 It starts out fine， but the latter half of the book is the author's explanation （albeit mathematical） of what's wrong with the American political system。 。。。more
DivyaJyoti Rajdev
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On the book jacket Bill Gates calls this book "accessible" which has proven once and for all that intellectually， accessible means two very different things to me & Bill Gates。 That aside， it is a fun book if you enjoy semi-dense math reads， particularly applied math。 If I dare to say so， Jordan the wickedly funny author， has managed to give me the guilty pleasure of watching something trashy like Jersey Shore through a book about geometry by dishing out colorful bits about revered people。Did yo On the book jacket Bill Gates calls this book "accessible" which has proven once and for all that intellectually， accessible means two very different things to me & Bill Gates。 That aside， it is a fun book if you enjoy semi-dense math reads， particularly applied math。 If I dare to say so， Jordan the wickedly funny author， has managed to give me the guilty pleasure of watching something trashy like Jersey Shore through a book about geometry by dishing out colorful bits about revered people。Did you know Einstein played violin on the street for extra cash？ Or that Gauss was often only a few steps ahead of his debts？ Or that Wordsworth （the poet） and Lincoln （the politician） were excellent mathematicians？ Can you even imagine the last president read Euclid for fun！？ Oh and my favorite bit -- Karl Pearson， the correlations guy， apparently looked like a Greek God。 He also taught his class the law of large numbers by throwing 10，000 pennies on the floor and making students count the heads。 I remember the dreary day I was taught that theorem。 Yikes。 Maybe this is how we should teach math！Now that we've laughed at the gossip-y bits， the more serious topics covered include an examination of Euclid's geometry， encryption keys as bead bracelets， wall street stock movements as mosquito paths across bogs， AI as mountaineering， and finally gerrymandering。 Some topics I was more lost than others， but some places -- boy was the read worth it。 （Like finally truly intuitively understanding convex hull after 6years doing Machine Learning）。 Couple of the quotes made me audibly laugh out loud at how true they were:"Mathematicians have an imperial tendency - we often see other people's problems as consisting of a true mathematical core surrounded by an irritating amount of domain specific information""If my grandma had wheels， she'd be a wagon" -- comparing this to the hypothetical incorrect statistical practice of "if we only consider xyz then we find abc" Some bits I'd like to remember:- the distance a bond travels is about inverse of sqrt of time that has passed- wrong answers are bad but wrong questions are worse- a connected graph stays connected only if the connections at each point >=2， interesting to think what this says about friendships and networks- we teach geometry not to prove the exterior angles of a polygon add to 360 but rather to learn deductive reasoning with which to discern non-proofs。 Like young Lincoln breaking things into their first principles until they become simple enough for him to understand- Markov chains were discovered because and atheist Markov wanted to disprove the free-will proof that his super religious peer Nekrasov had formulated （the proof hinged on the assumption that to have stable long term probability the agents in the system must be independent） - the hilarious story of how the Electoral College came about as an exhausted compromise rather than the brilliant design we tout it to be- through gerrymandering， understanding that the opposite of something can just be not-that-something （counterfactual）， rather than an individual entity of its own。 This is important when being asked "okay if not this then what？ well， not-this"- understanding through the sorites paradox （at how many grains of wheat do you get a pile）， that even if you don't know when something bad starts， you can tell when it's VERY bad。 Draw the line there， might be arbitrary but still usefulFinally a wonderful thought to leave with:"complex computations can feel like blind groping until you discover the common mathematical understructure shared by the two， illuminating each in the light of the other" 。。。more
Bill Posters
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How Not to Be Wrong is an all-timer and this isn't as good， but nobody's out there writing about mathematics like Ellenberg。 This is still really good。 How Not to Be Wrong is an all-timer and this isn't as good， but nobody's out there writing about mathematics like Ellenberg。 This is still really good。 。。。more
Jordan
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Fun and （as a non-math person） I learned a lot！ Make sure to read the footnotes for great jokes。
Keith Klein
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Shape's about reason， logic， mathematics & much more。。。I love the scope of this book; from explaining the rigor of Abraham Lincoln immersing himself "till I could give any propositions in the six books of Euclid at sight" to applying the inherent reasoning and logic of demonstrating proof to far-flung human endeavors。Ellenberg is a math professor who can write。 His speaking style， while forthright， cannot fully contain his enthusiasm for his subject matter。 His narration is conversational and re Shape's about reason， logic， mathematics & much more。。。I love the scope of this book; from explaining the rigor of Abraham Lincoln immersing himself "till I could give any propositions in the six books of Euclid at sight" to applying the inherent reasoning and logic of demonstrating proof to far-flung human endeavors。Ellenberg is a math professor who can write。 His speaking style， while forthright， cannot fully contain his enthusiasm for his subject matter。 His narration is conversational and reminds me of the best of the Great Lectures books I've enjoyed。Rational thought and reasoning can be applied to everything from geometry to maps to politics， artificial intelligence to genealogy and biology。 The best arguments are "self-evident，" and Ellenberg weaves mathematical， cultural and political history into Shape， elucidating great advances in math and other endeavors， from Ancient Greece to the American Revolution; from the thinking of Abraham Lincoln， to gerrymandering today。Shape will make you think。。。without making your head hurt too much in the process。 What a treat！ I'll be up for a second， and perhaps a third listen。 And based on Shape， I'm up for trying Ellenberg's other work as well。 。。。more
Ergative Absolutive
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This was a little disappointing。 It was good for what it was， but I came in expecting it to be as superb as How Not to be Wrong， which blew my mind with the chains of connections that united many different real-world applications with the underlying mathematics。 Here， there were some real-world applications （Covid spread， gerrymandering）， and there were some real mathematical underpinnings， but the intermediate steps were not more math， or more real-world applications， but instead lots of toy sc This was a little disappointing。 It was good for what it was， but I came in expecting it to be as superb as How Not to be Wrong， which blew my mind with the chains of connections that united many different real-world applications with the underlying mathematics。 Here， there were some real-world applications （Covid spread， gerrymandering）， and there were some real mathematical underpinnings， but the intermediate steps were not more math， or more real-world applications， but instead lots of toy scenarios。 It subtracted a bit from the richness of the content to spend so much time learning about toy games and toy geometries。 。。。more
Kyle
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Another excellent popular math book by Ellenberg。 The book is a bit longer， but if you read the acknowledgements， you'll know that there's even more content that Ellenberg had to cut out！The book is loosely related by the theme of geometry。 It isn't only about plane geometry， though， and has fun explorations of topology， random walks （the mathematical kind）， neural networks via gradient descent， networks/graph theory， and even a chapter on the math of gerrymandering。 That was not an all-comprehe Another excellent popular math book by Ellenberg。 The book is a bit longer， but if you read the acknowledgements， you'll know that there's even more content that Ellenberg had to cut out！The book is loosely related by the theme of geometry。 It isn't only about plane geometry， though， and has fun explorations of topology， random walks （the mathematical kind）， neural networks via gradient descent， networks/graph theory， and even a chapter on the math of gerrymandering。 That was not an all-comprehensive list， either。I thoroughly enjoy Ellenberg's style （and his hand-drawn pictures/diagrams to aid with explanations）， which is friendly and not overly formal。 But he is also careful to state things in a way that aren't so simplified they are no longer true。 There's a difficult balance and I think Ellenberg manages it quite well。 I learn a lot from seeing his presentation of an issue， even if I was already somewhat familiar with it。 I'd certainly recommend this book to anyone who thinks they would be interested。 If you've read Ellenberg's "How Not to be Wrong" and liked it， then I would think you'd like this one。 。。。more
Fraser Kinnear
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Fabulous read！ Most fun is all of the Wikipedia reading that follows， including:euler characteristics，homology groups，Homorphisms，Lorentz contraction，Minkowski space，Markov chains，DAGs，gradient descent，neurla nets，Multidimensional scaling，Parity problem，Simpson’s paradox，Dirichlet’s approximation，Eigenvalues，Agent-based model，Flajolet-Martin algorithm，invariance，efficiency gap，Spanning tree， andSorites paradox Fabulous read！ Most fun is all of the Wikipedia reading that follows， including:euler characteristics，homology groups，Homorphisms，Lorentz contraction，Minkowski space，Markov chains，DAGs，gradient descent，neurla nets，Multidimensional scaling，Parity problem，Simpson’s paradox，Dirichlet’s approximation，Eigenvalues，Agent-based model，Flajolet-Martin algorithm，invariance，efficiency gap，Spanning tree， andSorites paradox 。。。more
Rebekah Franklin
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Interesting look at math and society。
Matthew Whyndham
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Fantastic。 Learned a lot （I am numerate but firmly outside the set of people with an Erdös number）， laughed more， and scratched my head even more。 As well as maths， it has stories， jokes， explanations， wonky drawings and maps of all dimensions。 And poems！ Not the ideal book by any means， but a good enough sketch， actually。
Michael Reilly
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This hit my sweet spot for popular science books。 High school geometry was the last math course I understood and I don't remember much from that。 Ellenberg starts from basic Euclid stuff and traces it to artificial intelligence， Gerrymandering， Covid-19 plus games， magic tricks and logic problems。 I was able to follow him down most of the rabbit holes。 A few times I couldn't follow him all the way。 That is perfect。 I want this kind of book to push me right to the edge of what I can understand。 E This hit my sweet spot for popular science books。 High school geometry was the last math course I understood and I don't remember much from that。 Ellenberg starts from basic Euclid stuff and traces it to artificial intelligence， Gerrymandering， Covid-19 plus games， magic tricks and logic problems。 I was able to follow him down most of the rabbit holes。 A few times I couldn't follow him all the way。 That is perfect。 I want this kind of book to push me right to the edge of what I can understand。 Ellenberg likes to start by taking simple models of simple problems， what move to make in a tic-tac-toe game？ or， how many holes are there in a pair of pants？。 Next he explains a way to solve the problem。 He then shows how that explanation can be used to solve big problems like how to be the world's best chess computer or how to solve the hardest topological problems。 He has a relaxed writing style。 He mocks his own nerdiness and likes to drop in wisecracks but， at the same time， this is a serious and successful attempt to explain some very sophisticated applications of geometry to neural networks， cryptography， epidemiology， planetary physics and a bunch more。 Ellenberg throws in big chunks of history， mini-biographies and puzzles as he goes along。 I would have been helped by a discussion of what geometry is。 At several points I was interested in what he was explaining， but I didn't really understand why it was part of geometry。 。。。more
Brian Clegg
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I really enjoyed Jordan Ellenberg’s earlier book How Not to be Wrong， so looked forward to Shape with some anticipation。 In principle what we have here is a book about geometry - but not seen from the direction of the （dare I say it） rather boring， Euclid-based geometry textbooks some of us suffered at school。 Instead Ellenberg sets out to show how geometry underlies pretty much everything。Along the way， we are given some nice turns of phrase。 I enjoyed， for example， Ellenberg’s remark on the ph I really enjoyed Jordan Ellenberg’s earlier book How Not to be Wrong， so looked forward to Shape with some anticipation。 In principle what we have here is a book about geometry - but not seen from the direction of the （dare I say it） rather boring， Euclid-based geometry textbooks some of us suffered at school。 Instead Ellenberg sets out to show how geometry underlies pretty much everything。Along the way， we are given some nice turns of phrase。 I enjoyed， for example， Ellenberg’s remark on the philosopher Thomas Hobbes， where Ellenberg remarks Hobbes was ‘a man whose confidence in his own mental powers is not fully captured by the prefix “over”’。 Whether or not what we read about here is really all geometry is a matter of labelling （as is the ‘number of holes in a straw’ question that Ellenberg entertainingly covers）。 Arguably， for example， there is some material that is probability that can be looked at in a geometric fashion， rather than geometry that produces probabilistic results - I find the probability viewpoint a lot simpler and more interesting。 In the end， despite his efforts， unless you are a mathematician， some aspects of geometry （and maths in general） feel laboured and uninteresting。 But the marvel of this book is that he does make a surprising amount of it quite the opposite。 Unfortunately， Ellenberg can go into far too much detail sometimes （which may be why the book is a bit of a doorstop at 463 pages） - for example， a story that starts with the mosquito’s random walk seems to go on and on for ever and I rather lost the will to continue， in a topic that interests me a lot more than geometry does。 In a different way， I struggled to get my head around the lengthy section on US electoral district gerrymandering which seemed only of interest to someone with in-depth enthusiasm for US politics， while some of the final meandering final chapter should certainly have been lost in the edit。I do wonder if the success of the earlier book meant this one was not given the editorial scrutiny it needed。 Although Ellenberg failed to convince me that geometry is the foundation of many of the topics he discusses， there is material to interest the reader here - and it’s certainly a far cry from those laborious proofs and QEDs。 。。。more
Mike Wagner
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Terrific book， accessible， funny， thought-provoking and informative。 This book is helping to 。。。 reshape 。。。 my thinking。
Miranda
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