The Biggest Number in the World: A Journey to the Edge of Mathematics

by David Darling, Agnijo Banerjee

The weird and wonderful quest for unfathomably large numbers

From cells in our bodies to measuring the universe, big numbers are everywhere

We all know that numbers go on forever, that you could spend your life counting and never reach the end of the line, so there can’t be such a thing as a ‘biggest number’. Or can there?

To find out, David Darling and Agnijo Banerjee embark on an epic quest, revealing the answers to questions like: are there more grains of sand on Earth or stars in the universe? Is there enough paper on Earth to write out the digits of a googolplex? And what is a googolplex?

Then things get serious.

Enter the strange realm between the finite and the infinite, and float through a universe where the rules we cling to no longer apply. Encounter the highest number computable and infinite kinds of infinity. At every turn, a cast of wild and wonderful characters threatens the status quo with their ideas, and each time the numbers get larger.

Genres: Science, Nonfiction, Mathematics, Physics

256 pages, Paperback

First published May 5, 2022

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

[Nilesh Jasani · Rating 5 out of 5]

For those interested in numbers, The Biggest Number is a unique and tremendously interesting book. It is not always understandable, but that's precisely what the dilettantes interested in the subject would be looking for. The professionals of the field - which are some of our race's best minds - have predictably taken the search of the largest finite and transfinite numbers to realms inaccessible without decades of training and more.

Almost every part of the book beyond the initial chapters boggles the mind. One gets transfixed in the maze created by the new nomenclatures, let alone by the enormity of what is put forward. In the end, there is not much of utility value for a common reader as could be expected of what one does for most hobbies. That does not reduce the joy of this ride in the tiniest, though.

[Davy Buntinx · Rating 4 out of 5]

Dat wiskunde echt is, maar ook een beetje niet, en dat het tegelijk een spelletje en serieus kan zijn, dat is toch schoon?

[Marko Beljac · Rating 5 out of 5]

My thoughts sum to m=b where m is mind and b is blown. A sheer delight - with insights not just from mathematics, but logic, physics, and philosophy. At the centre is not so much large numbers as the means of generating them - recursion. The opportunity was there to delve into the mind, for recursion is key to language, so thereby exploring the nexus between Popper’s three worlds. There was a bit with occasional references to ideas about understanding. Every page will get you thinking - with each page feeding upon thoughts in preceding in recursive fashion. I had many thoughts about many things upon reading this - most of which I don’t understand because hazy. Just two. Physicists abhor infinities - sticking to Aristotle here - so what does this abhorrence entail about what we mean by “physical” - like if we don’t really have a concept physical then how can we be so dogmatic about all things physical being finite? This is important because singularities in general relativity are widely said to mean the theory is incomplete - on grounds of an argued connection between infinite physical quantities and acausalities. Was G64 discovered or was it generated - like would a sentence with G64 words have been discovered or generated? I’d think on the sentence we’d say generated, and recursion is used to generate sentences. Anyway I’m kinda rambling - you know a book is good and broaches deep stuff when it gets you thinking and you don’t even know what you’re thinking grrrrrh.

[Jeneva Izorion · Rating 5 out of 5]

มนุษย์สนใจเลขที่เยอะมหาศาลมาตั้งนานแล้ว เช่น จำนวนดาวบนท้องฟ้า จำนวนเม็ดทรายบนโลก ไปจนถึงจำนวนเม็ดทรายที่ใช้ถมจักรวาล (อันสุดท้ายมีคนคิดจริง ๆ คนแรกที่คิดนี่ย้อนไปสมัยกรีกเลยทีเดียว)

เล่มนี้ค่อย ๆ พาไปดูตั้งแต่เลขใหญ่ ๆ ที่เคยมีคนพูดถึงในอดีต ตั้งแต่เลขที่ปรากฏในคัมภีร์พุทธมหายาน อัตราเงินเฟ้อที่สูงที่สุดในโลก googol ไปจนถึงจำนวนปีที่ประมาณไว้ (โดย poincare) ว่าเอกภพจะกลับมาอยู่ในสภาพเริ่มต้น

แน่นอนว่าที่เขียนมาในย่อหน้าที่ 2 ยังไม่ได้แตะอาณาจักรคณิตศาสตร์เลย เพราะอาณาจักรนี้จะพาเราไปยังเลขที่เกินกว่าจะจินตนาการในโลกความเป็นจริง แต่ยังเป็นจำนวนนับ! ไล่ตั้งแต่เลขที่เกี่ยวกับ prime number theorem, จำนวนวิธีเรียงสับเปลี่ยนไพ่, จำนวนปีที่จะเจอลิงตัวหนึ่ง กดแป้นพิมพ์มั่ว ๆ แล้วได้หนังสือเชคสเปียร์ยกเซต

ที่เขียนมาย่อหน้าที่ 3 ก็ยังเป็นเลขกะจ้อยร้อยเมื่อเราเริ่มพัฒนา operation ให้ไปไกลกว่าการยกกำลัง เช่น up arrow, chain arrow, หรือกระทั่งการใช้รูปหลายเหลี่ยม หลังจากนี้จะเริ่มเป็นพาร์ทหนักสำหรับคนไม่เคยเรียน Set, Recursion ละ เพราะมีทั้ง Ackermann, Fast-Growing Heirarchy และปัญหาเกี่ยวกับ Turing Machine ที่ให้เลขที่ใหญ่มาก ๆ

มี community ที่สนใจเรื่องเลขเบิ้ม ๆ พวกนี้จริงจังเลย เรียกว่านัก googologist ซึ่งกลุ่มพวกนี้ก็พยายามหาวิธีสร้างเลขใหญ่ ๆ "อย่างสร้างสรรค์" (ไม่ใช่แค่เอาเลขเดิม +1 เอามายกกำลังสอง บลา ๆ) ก็น่าทึ่งดีเหมือนกัน

โดยรวมแล้วชอบ ถ้าไม่เคยเรียน set,recursion น่าจะเหนื่อยนิดหน่อย นึกไม่ออกว่าจะมี สนพ ไหนมานั่งแปล 555

[Nestor · Rating 4 out of 5]

I love these Popular Science books about Mathematics that try to show amateur mathematicians the latest advancements. This one is about the biggest number. Finding the biggest number is not at the core of maths, but it may help find new limits, especially everything regarding finite-infinite boundaries. The book is very well written and has many equations, but we who love maths like it. I think chapters 10 and 11 are not very well explained, though no errors, the language is not clear.

Please keep publishing these kinds of books at the edge of math with the latest findings for the public and amateurs to enjoy.

Thanks, Prof. Sabugal, Prof. Liesegang, and Prof. Cohen Tarica for teaching me maths to you is that I love math.

[Mark Nelson · Rating 4 out of 5]

You’ve got to have a lot of math running through your veins to get anything out of this book, but given the title, I have to believe that there’s not going to be a problem there. No bait and switch.

Ultimately, the title is kind of misleading, probably intentionally, because this is really just a book about some really big numbers, how they came to be discovered or defined, and what they mean to us.

Of necessity a fair amount of hand waving has to take place for this to reach a general audience, and even then it’s going to be a bit of work for most readers.

Still, I found it fun.

[Arjun B · Rating 4 out of 5]

The book is a great read to understand our history with large numbers (both computable and uncomputable), however, some of the later concepts mentioned in the book are (understandably) hard to understand without external resources.

[Mark Schnitzius · Rating 4 out of 5]

The first physical book I've bought in I can't remember how long. And I enjoyed it quite a lot. I worried a bit that I knew enough about the subject that I would end up either bored or lost, but I ended up learning a fair bit, which is always what I hope for from maths popularisations.

[Emily Morrison · Rating 3 out of 5]

Beginning was definitely a five star but the further I went, the harder it was to continue. So three stars is the average rating I would give the whole book. Overall it had some very thought provoking concepts and I don’t regret reading it.

[Matt Whitby · Rating 1 out of 5]

Boring. Really, really dull. I would imagine it's too basic for professionals, and too complex for amateurs. The biggest number in the World? That'll be the sum total of the number of exclamation marks the authors chose to put in this book.

[Liam · Rating 4 out of 5]

This book melted my brain.

[Steve Showalter · Rating 1 out of 5]

Virtually unreadable. I hung in there through chapter eight….

I love math, but not this book…

[Yuganka Sharan · Rating 5 out of 5]

A lovely book on the biggest numbers in maths and how they came to be formulated.

[Cassie · Rating 3 out of 5]

The minute you refer to multiplication as repeated addition, you’ve offended me.

[Kirsten Hill]

Tried this one as a Kindle book in 2022-2023, but had a hard time getting into it. I now own the Audiobook and will try again later in that format.

[Malay · Rating 3 out of 5]

Most of the popular science books I've read are dry and devoid of humour. This isn't. The space of large numbers is dominated by passion and hobbies instead of academic pursuit so it has always had a base in humor. The authors build on that and keep the conversation light.

The problem is that the depth felt missing. There are large sections that felt like a workbook. The quest for the largest number obviously involves turing machines and set theory among other things. Based on their explanation of the familiar (to me), I don't think they've done a good job explaining the unfamiliar.

Overall the book is easy to read and follow but not a very strong introduction to the topic.