Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else

Jordan Ellenberg has this incredible knack for making you see the world through a completely different lens. This isn't the dusty, formula-heavy geometry you suffered through in ninth grade with your braces and pop-star crushes. Instead, Ellenberg shows how shapes and spatial logic underpin everything from the spread of a pandemic to the way computers learn to play Go. The chapter on the geometry of gerrymandering was a revelation for me, specifically because I never realized how mathematical fairness could be so complex. To be fair, he does wander off into the weeds occasionally, but his charismatic writing keeps things engaging. If you want to understand how the hidden structures of our world actually function, this is essential reading. It manages to bridge the gap between abstract algebra and our daily lives with genuine humor and wit.

The way Ellenberg bridges the gap between abstract algebra and the physical world is nothing short of masterful. I was particularly gripped by his explanation of the SIR model during the pandemic discussion; it turned a terrifying reality into a logical puzzle. This book is a far cry from the laborious proofs and QEDs that most of us remember from high school. Each chapter introduces a new way of thinking, whether it’s through game theory or the geometry of representation in democracy. Not gonna lie, some of the math toward the end gets pretty heavy, especially regarding eigenvectors and neural networks. But even if you don't grasp every single technical detail, the overarching narrative about human curiosity is beautiful. It is an informative and accessible exploration of a subject I thought I hated. I highly recommend it to anyone who likes their science with a side of humor.

After hearing so many good things about this, I was thrilled to find that the reality lived up to the hype. Ellenberg argues that geometry isn't just a school subject; it is a way of measuring and explaining the world we live in. His deep dive into the issue of fairness in voting districts was eye-opening and showed how math can solve real-world political problems. I loved the way he wove together history, philosophy, and high-level statistics into something that actually felt readable. Some of the meandering chapters actually felt like a conversation with a very smart friend who keeps finding cool things to tell you. It is a big, ambitious book that makes you feel smarter for having read it. Even the sections that were a bit over my head were fascinating enough to keep me engaged. This is definitely a five-star read for anyone who enjoys popular science.

As someone who usually finds math textbooks incredibly dry, I was surprised by how much this book pulled me in. Ellenberg uses geometry to explain some of the most pressing scientific and philosophical problems we face today. I particularly enjoyed the section on how computers have been taught to play chess and the inherent difficulties in machine learning. The diagrams are actually helpful rather than being just filler, which I appreciated. Truth is, I did get lost during some of the more technical explanations of the uncertainty principle and random walks. Despite those moments of confusion, the author’s enthusiasm for the subject is infectious and kept me moving forward. It’s a broad, ambitious work that succeeds more often than it fails. Definitely worth your time if you enjoyed his previous work.

Finally got around to reading this, and I have to say, Ellenberg’s wit is what keeps the pages turning. He has a way of phrasing things—like his comments on Thomas Hobbes—that made me laugh out loud in a book about math. The book does an excellent job of showing that geometry isn't just about triangles, but about how things are near each other and how they connect. I was especially impressed by the explanation of the mosquito’s random walk, even if it did go on for a few pages too many. Personally, I think this book is a bit less polished than 'How Not to Be Wrong,' but it still offers a lot of value. The clever examples of mathematical proof in Chapter 5 were a highlight for me. It’s a great choice for anyone looking to broaden their scientific horizons without feeling like they're back in a classroom.

While I absolutely loved 'How Not to Be Wrong', this follow-up felt like it needed a much firmer editorial hand. Ellenberg is a brilliant communicator, but this book feels a bit like a collection of late-night brainstorms rather than a cohesive narrative. One moment you are learning about Euclid, and the next you are plunged into the deep end of eigenvalues and page rank. Frankly, the transition between topics can be jarring and the pacing feels inconsistent throughout the middle sections. Some parts, like the discussion on the topology of straws and pants, are genuinely delightful and easy to follow. However, other chapters, especially the deep dive into US political redistricting, go on for far too long. It is a dense 400-plus pages that might leave casual readers feeling slightly exhausted by the end.

Picking this up after reading Strogatz’s 'Infinite Powers' was an interesting experience in contrasts. While Strogatz guides you gently through calculus, Ellenberg takes you on a wild, sometimes confusing ride through the entire landscape of modern geometry. I found the 'number of holes in a straw' debate to be a funny and approachable way to introduce topology. However, the author seems to think that absolutely everything is geometry, which leads to some very long-winded sections. In my experience, the chapters on probability felt a bit laboured compared to the more visual elements of the book. The section on Abraham Lincoln’s obsession with Euclid was fascinating, yet it felt disconnected from the modern technical bits. It's a bit of a doorstop, and I think a shorter, more focused version would have been more effective for laypeople.

Ever wonder how many holes are actually in a straw? That is just one of the many quirky questions Jordan Ellenberg tackles in this massive book about geometry. It is clear that the author is a charismatic writer who truly loves his field, but I found the structure a bit too rambling for my taste. One chapter jumps from Fibonacci numbers to stocks and then suddenly into the uncertainty principle without much of a breather. For an audiobook listener like me, these quick shifts made it very easy to lose the thread of the argument. I did find the discussion on gerrymandering incredibly detailed, perhaps a bit too detailed for anyone not obsessed with US politics. It’s an interesting read for sure, but be prepared for a lot of tangents that don't always feel necessary. I might need a second pass to truly absorb everything.

Maybe I’m just not a 'math person,' but I found large sections of this book nearly impossible to get through. The description promised a look at how geometry explains the world, but it felt more like a disorganized history lecture. There are so many names and dates thrown at you that it becomes difficult to keep track of the actual mathematical concepts. For example, the extended discussion on irrational numbers like pi and phi seemed to meander without a clear point or payoff. I was hoping for something as structured as Strogatz’s 'Infinite Powers,' where each chapter builds on the last. Instead, this felt like jumping into a series of vaguely connected essays. It’s certainly well-written in terms of prose, but the lack of focus made it a chore to finish.

Look, I appreciate the author's passion for the subject, but this book is a bit of a doorstop and quite unfocused. I struggled significantly with the middle section, which seemed to dwell on the history of certain mathematicians for ages without explaining the concepts clearly. The discussion on eigenvalues was particularly opaque to me, and I felt like I needed a degree in physics to understand the connection to the uncertainty principle. To be fair, there are some gems here, like the section on computer programming and the game of Go, which were quite interesting. However, the overall experience felt like wading through a collection of brainstormed ideas that hadn't been properly woven together. If you aren't already a math enthusiast, you might find yourself skimming a lot of the denser material. It just didn't click for me.