Weird Maths: At the Edge of Infinity and Beyond

by David Darling, Agnijo Banerjee

Is anything truly random?



Does infinity actually exist?



Could we ever see into other dimensions?



In this delightful journey of discovery, David Darling and extraordinary child prodigy Agnijo Banerjee draw connections between the cutting edge of modern maths and life as we understand it, delving into the strange – would we like alien music? – and venturing out on quests to consider the existence of free will and the fantastical future of quantum computers. Packed with puzzles and paradoxes, mind-bending concepts and surprising solutions, this is for anyone who wants life’s questions answered – even those you never thought to ask.

Genres: Mathematics, Nonfiction, Science, Popular Science, Stem

272 pages, Kindle Edition

Published February 1, 2018

About the author

There is more than one author in the database with this name. Not all books on this profile may belong to the same person.

David Darling is a science writer and astronomer. He is the author of many books, including the bestselling Equations of Eternity, and the popular online resource The Worlds of David Darling. He lives in Dundee, Scotland.

Reviews

[Lthmath · Rating 3 out of 5]

I have very mixed feelings about this book and it took me quite a while to finish it. I have found the book either very interesting or very boring. It was a strange combination of "OMG Sooo GOOOood!" and "Why am I reading this?". I don't really know why exactly why I have found it so inconsistent from this point of view.

Generally speaking, the book tackles a lot of topics from very basic easy to understand concepts such as prime numbers to quite hard to comprehend topics such as Continuum Hypothesis. Some chapters are full of high-level mathematics and a lot of interesting complex concepts are presented. On the other hand, some chapters seem more like random general knowledge on different topics and don't have a lot of mathematics in them.

If I would have to recommend this book to anyone, I would have to tell them to read specific chapters. I believe that some non-mathematicians will find some chapters really hard to understand or boring. On the other hand, mathematicians/ math-lovers will find some other chapters boring or just not that interesting. Considering this, I can also say that the book has something for everyone and this is quite hard to find in a book on weird aspects of mathematics.

[Swapna Peri ( Book Reviews Cafe ) · Rating 3 out of 5]

Book Title: Weird Maths
Author: David Darling & Agnijo Banerjee
Format: Paperback
Genre: Non-fiction

Book Title:
The title of the book is very striking and definitely intriguing.

Book Cover:
The cover of the book is simple with the title as a clip art image all around.

About the book:
'Maths', this subject is a nightmare to some kids and is also the favorite of others. Right from the age of primary school where we all learn numbers till Ph.D. in Mathematics, it's all just about numbers. But what really differentiates is the usage of these numbers in the real world to realize the very existence of life. Connecting the numbers and calculations to the world we live is the most enticing thing. And this forms the basis of this book ' Weird Maths '.

Jointly authored by David Darling, successful science writer, and Agnijo Banerjee, a teenage math wizard, this book helps the people understand the most complex matrices of numbers that are around us.

Since the times of evolution, human brains have assimilated arithmetic, geometry, and algebra in daily life. Our neural system evolved the potential to do advanced calculations, and understand such things as set theory and differential geometry, long before it was ever applied. In fact, it seems a bit of a mystery why we have this thirst for higher mathematics when it has no obvious survival value in the real world. Like all being, we effectively do a lot of difficult math in a lifetime. The simple act of catching a ball involves solving multiple equations simultaneously at high speed. While programming a robot the complexity of the calculations involved becomes clear. But the great strength of humans was their ability to move from the concrete to the abstract—to analyze situations, to ask if-then questions, to plan ahead.

The concept numbers and calculation is all present in the field of agriculture, astronomy, astrology, medicine, economics, commerce, entertainment, art, history and everything else. The connection between math and everyday reality is almost like a couple in love with agreements and disagreements included. Of all subjects, mathematics is the most precise and immutable. Mathematics exists, It's a fact that if a piece of math has been proven to be true, it will remain true for all time.

This book acts like a good and comprehensive reference guide to understand the concepts of Maths in the real world. The book is recommended to every Math lover and one of the books that have no age limit.

My Final Verdict:
An interesting read that draws an intersecting line of the world of Maths and the physical world.

Book Title: 3/5
Book Cover: 3/5
About the book: 3/5
Final Rating: 3/5

[Alice · Rating 2 out of 5]

I was deliberating between giving this book 2 or 3 stars and I decided on 2. I’m a math teacher and I wanted to read this book to possibly help answer the question “where will I ever use/see math again?” for my students. I will say that a few of the chapters held my interest but most did not. I was a math major in college and this book had a lot of proofs in it. I didn’t mind proofs when I was studying them but they shouldn’t have been used in this book. In order to make this book more accessible and readable to the average person they should have avoided mathematical vocabulary (like used in proofs). Overall I’m glad I finished it but I wouldn’t recommend it.

[Manikanta Avinash · Rating 3 out of 5]

While the book is enjoyable, it being written for people with zero maths background dilutes and limits a given concept to a very limited extent. I also didnt find proper flow between chapters and some chapters dont even talk about a mathematical concept or idea. It is a still a good book to read though! I atleast learned of existence of some very beautiful concepts and theorems in maths though this book didnt teach about each of them which is not the book is meant to do anyway.

[Melissa Dee · Rating 4 out of 5]

Strangely enough, I had a conversation with a teen-ager, the day before I started reading “Weird Math," about how to visualize 4 dimensions. I’ve been a math tutor for over twenty years, and “Weird Math” is *exactly* the math that appeals to the thinking student of mathematics. The questions in this book, “Can we see 4 dimensions?”, “What is randomness?” “Where is infinity?” are particularly compelling to the contemplative high school math student. I plan to add this book to my book shelf to supplement my students’ mathematical explorations.

[Miroslav Bicanic · Rating 4 out of 5]

A very interesting book by all means, but if you're like me and enjoy educational YouTube channels such as Veritasium, VSauce or Numberphile, you will have already known most of the mathematical quirks mentioned in the book.

[Willow Rankin · Rating 2 out of 5]

"DNF"

I wanted to love this book - the title and back blurb had me sold, but prior to purchasing I should of read some of the first chapter.
This book covers complex mathematical concepts - which having not studied maths formally for at least 10 years; I could've done with a more gentle tug, rather than feeling like I was thrown into the deep end.
I also didn't enjoy how the book was written - lots of maths language was used; it made it hard to understand the concepts.
I did learn from this book - especially the chapter on dimensions, but as a lot of the examples were highly theoretical I struggled greatly with this book.

[Sujan Bandyopadhyay · Rating 4 out of 5]

The book gives a succinct but really interesting overview of some large areas of mathematics. As a non-mathematician, I found the book really absorbing in most places; I especially enjoyed the chapters on dimensions, prime numbers, chaotic systems, types of infinities, and solving chess.

Some of the material is a bit technical/dry and can be a tad hard to understand. Admittedly, I knew some of the concepts (mostly through watching Numberphile videos on YouTube) so I probably didn’t find many parts of the book as hard as some other non-mathematicians may find. If you’re willing to go beyond the inevitable dry parts of the book, you will definitely come across some really interesting insights.

In order to truly appreciate the book, you probably should have at least a cursory interest in mathematics; otherwise you may question what the point of it all is. Some parts which truly blew my mind were: how 2-D beings view a 3-D world and then extrapolating that idea to how 3-D beings would view a 4-D world, the distribution of primes is not truly random, and computers being able to solve complex games like Poker (and not just Chess), and the different kind of infinities.

[Bartłomiej Falkowski · Rating 3 out of 5]

This is a book with big potential that has unfortunately remained unused.

What I liked:
- really good chapter about fourth dimension- time. Nice comparisons between one-, two- and three-dimensional objects. A step-by-step instruction that gave me the opportunity to understand the view of the particular item in 4D.
- enjoyable historical remarks. Many interesting stories - from Euclid and Archimedes, throughout entire the Middle Ages and the Renaissance, to the theories of Einstein and Hawking.

What I didn't like:
- I didnt' comprehend everything :) Some alghoritms / theorems were really complicated - even though the book is presented as a book for everyone.
- From time to time I felt that topic that we dive into is not relatively important to the amount of space and explanations it consumes. For example, there was an entire chapter about Big Numbers - with lots of alghoritms and detailed descriptions. It was quite interesting but conclusion of that chapter was - the whole topic is actually unimportant. It's just a "rooster" competition between institutes / mathemathicians to find the biggest possible number.

[Tracey · Rating 3 out of 5]

So, this limerick is a little misleading as to the intense level of mathematical thinking done in this book, but I enjoyed it, so here it is:
"A mathematician named Klein
Thought the Möbius band was divine.
Said he: "If you glue
The edges of two,
You'll get a weird bottle like mine." This is from the chapter on topology, which I found incredibly fascinating and well-written (The book has two authors, and I think that is why not all the chapters are equally well-written.) The chapters on chance, music, infinity, and proof were all well done, but I found a lot of places in the book as a whole were lacking in depth where I wanted more depth and overly detailed where it was unnecessary. I prefer Bellos' _Here's Looking at Euclid_ to this book, but this one had some topics/approaches not covered in that book.

[Erik Molnar · Rating 5 out of 5]

This book has a lot of the exact concepts that are covered in another book I just read, Alex's Adventure in Numberland. However, this also touches on some cool things that were not mentioned in that book, like large numbers. I have never even given the subject of large numbers any thought. We are talking insanely large numbers. Bigger than the mind can even comprehend. They are so big, computers can't even calculate them. That said, I can't say I really comprehended it all, but at least I know it is a thing and it can be conceptualized in a way if you try to wrap your head around it.

[Sarah Sarah Bo Barah]

title ~ Weird Math: A Teenage Genius & His Teacher Reveal the Strange Connections Between Math & Everyday Life
author(s) ~ David Darling & Agnijo Banerjee
pages ~ 278
chapters ~ 13
format ~ hardcover
ISBN ~ 978-1-5416-4478-6
classification ~ QA93 .D285 2018
started ~ June 9, 2025
finished ~ August 1, 2025

Anyone who reads this book, prepare to be wow-ed by the weird and wonderfully mystifying world of mathematics, and how it applies to everyday life. This subject matter tickles me pink! 😃

Fair warning, this book is not for the faint of heart… it’s for someone as geeky as I am, if not more so.
But this is not to say that you shouldn’t read it if you don’t consider yourself “the absolute greatest” at mathematics. It just might be a little more challenging.

A little challenge never hurt anyone. 😉

I have a bachelor’s degree in mathematics, which means I’m all too familiar with facing challenges. I know quite a bit already about what the book is talking about, but I wouldn’t be able to explain it as well as David Darling and Agnijo Banerjee did. My hats off to them!

Not only did they explain it well, but they also made it fun to read. Some of my favorite chapters talked about

• probability (Chapter 3: “Chance Is a Fine Thing”);
• prime numbers (Chapter 7: “Prime Mysteries”);
• paradoxes (Chapter 9: “What Is and What Should Never Be”);
• mathematical proofs (Chapter 13: “God, Gödel, and the Search for Proof”);
• and, surprisingly, topology (Chapter 12: “Bend It, Stretch It, Any Way You Want To”).

Topology was probably one of my least favorite classes in college, because the way it was taught made it seem so dull and repetitive, and I had trouble seeing how all the various theorems and definitions the professor threw at me could be applied to the real world. I still feel somewhat lightheaded thinking about it.

But David Darling and Agnijo Banerjee explained it in such a way that gives me more confidence, and makes me want to give it a second chance. Perhaps I’ll go and find a textbook on topology now from my alma mater’s library…

Yeah, I’m crazy.

[Tal · Rating 4 out of 5]

Beginners But Familiar
the first thing that you see as you go, that the authors don't assume a-priority knowledge but they do assume familiarity at some ground, the book is dense with both the past and the present ideas, some purely mathematical and some with high importance at the present-future reality that we live and will live.
throughout the book you:(a) will recognize patterns from reality,(b)will learn what mathematics is all about and how mathematicians get along with problems they encounter (c) will learn to appreciate the abstract and the importance of it and (d) realise how the structure came about from history(subfields,but understandable).

it has a really good flow, it got nice and not too many illustrations.
I recommend it for those who have some familiarity, to those who want to see the big picture about connections of mathematics and the ideas it brings.

[Özgür Takmaz · Rating 4 out of 5]

No two decks ordered same in the history of the world. If all the people presently alive were to have shuffled a card deck once every second since the universe began that would be amount to only about 3.10^27 shuffles, which is an incredibly tiny number by comparison. Because the probability is 1 in 8.10^67.
A lottery has a negative expected value, so it is a bad idea to play.
Sometimes an event can occur only once, so you need Bayesian probability. How confident are you?
Borromean rings = Walknot = Odin's triangle
Choose axioms in one area and apply across the board. Best area? Set theory.
Mathematicians' anathema: "Truth is a more powerful concept than proof."

[Thomas Schulte · Rating 4 out of 5]

A quarter century ago, writers such as Martin Gardner and Clifford A. Pickover so excited my interest in the mathematical -- especially the speculatively mathematical -- that their works fueled me though undergraduate and graduate studies. I am pleased to see these two authors continue in the tradition of telegraphing excitement to lay readers and embracing deviations from the norm: “A teenage genius and his teacher take readers on a wild ride to the extremes of mathematics.” ...

[Look for my entire review at MAA Reviews]

[Sourya Dey · Rating 5 out of 5]

I find these science and math related books generally fun to read (or listen to, as I normally do for these kind of books), but they normally fall short of 5 stars. This one is better than the others. For one, it's crisp, by which I mean that it covers really big and important topics in not too many words, which reduces wastage of words. Secondly, the examples given serve to increase the fascination one feels for the concepts. Overall, if you want to get started reading books of this genre or just want to read one, I'd quite recommend this one.

[Nadina · Rating 3 out of 5]

So theoretically this book is interesting if you are interested in math, but it is also a lot to take in and I am just not in the mental state to do so, not does it interest me that much that I want to continue. That being said I am giving it three stars because it is decently written and it doesn't seem to complicated to understand what is being said. It is divided into chapters nicely, and I think it would really interest those who are really into learning about math without being mathematicians.

[Mancman · Rating 3 out of 5]

I’m giving this three stars, because I should never have read this, I made a poor choice in selecting this book. I found it dry, incomprehensible in places and frankly a chore to read. In reality I’d mark this much lower.
But that’s on me, for not researching the book properly, I picked it up on a whim, one which I regret.
I would warn any potential reader that this isn’t a quaint, flippant foray into the world of mathematics. You need an interest that n the subject, and, I think, more than a passing knowledge of the subject matter.

[Cassian Lynne · Rating 4 out of 5]

Written in (predominantly) lay-terminology, Darling and Banerjee do a great job in this book laying out the wild ways that math intersects all our lives and the truly weird things math reveals and proves. Two chapters went a smiiiidge over my head but not so far that it become unenjoyable. I especially loved the chapter about music and math, and thought that the discussions about infinity and large numbers were very intriguing.

[Michael crage · Rating 3 out of 5]

In this book the co-authors talked about some none ever day things involving mathematics. Some of the things involved chance and probabilities. A lot involved talking about very large numbers some countable and some not and the various classes of infinities, actually too much of the book was involved in that in my opinion. I did get a math major, but it was not required t understand what the authors were saying.

[Ann Straight · Rating 4 out of 5]

Definitely can be interesting at or above the high school math level. Includes a number of math related ideas including historic proof and development but also newer concepts such as multi-dimensions, extremely large numbers, topology, chaos, probability, logic, computers and even music. Some ideas were harder to follow when they are new to me.

Using language to understand math is counter-intuitive to me. C'est La Vie.

[Andrea · Rating 3 out of 5]

Somewhat dry, somewhat interesting, and it doesn't really work just as an audio book (although I really like the reader's voice). Sometimes you need to see what's happening in print. Ideally, to listen and have the print book in front of you might be good. But if you're not a fan of math, this probably isn't the book for you.

[Normandy · Rating 1 out of 5]

I made it through this book with quite a few pages just lightly skimmed. There were a few interesting moments but overall it was a sleeper and I don't mean that in a good way. If you would like to read some really interesting books on math try:
1. Infinite Powers: D. Strogatz
2. The Golden Ratio: M. Livio
3. Zero: C. Seife
4. e: E.Maor
5.Fermat's Enigma: S.Singh

[Nath Ong · Rating 3 out of 5]

Great starter book on weird phenomena in math. I appreciated how didactic every topic was made, where an intuitive understanding of the topic over mathematical rigor was the focus for the most part.

My only qualm would be to be more liberal with the use of graphics (some were used), since a lot of intuition is visual and huge chunks of paragraphs can only go so much.

Math is weird.

[Rod Innis · Rating 3 out of 5]

Some parts of this book were quite easy to understand; other parts were difficult to understand and some parts were, in my opinion, nonunderstandable. I enjoyed the parts that I could understand, making the book worth reading.

[Michelle Groninger · Rating 4 out of 5]

Even though it’s been a few decades since I’ve used most of the math vocabulary in the book, I found that I could (mostly) understand what was presented. If you like Math, this was an interesting read.

[Levi Stelljes · Rating 4 out of 5]

Didn’t love some of the editorializing about subjectivity in this book, but did pick up on some really interesting bits for my math classes, like fractal coastlines, the Ham Sandwich Theorem, and Gauss’s Triangular Numbers Conjecture.

[Jordan Jones · Rating 3 out of 5]

a bit over your head in places, would’ve liked to see more how do you approach math to everyday things. This book bordered on the very abstract which wasn’t bad but not exactly what i was looking for - still made me excited to learn more math

[Aizc · Rating 3 out of 5]

С одной стороны неплохая книга про разные проблемы математики и ее применения.
С другой тут очень мало про использование математики в обыденной жизни, что может привести в недоумение читателя, взявшего эту книгу из-за названия.

[Ruth · Rating 3 out of 5]

I know I studied mathematics in college and grad school, and have heard of most of the topics covered. But sorry, just not enough info to really get into it. More of a gee whiz.