A subway ride in NYC costs $3. Gizmodo has been around for 24 years. The Sun is just one of several hundred billion stars in the Milky Way, which is just one of the trillions of galaxies in the universe. In science, a hypothesis is better tested if it undergoes many empirical studies. Equations that describe how the world works essentially place one number in relation to another.
Our reality is profoundly rich in numbers—a realization that has been discussed at length (no pun intended). Big Numbers: The Story of Ambitious Counting from 4 1/2 to Pisces 7By Richard Elwes. The book deals not only with incomprehensibly large numbers, but also with numbers that sound small but represent incomprehensibly large concepts. Overall, the story explores the history of humanity’s fascination with numbers, especially giants, and how that fascination drives our ongoing quest to understand the universe (again, no pun intended).
Richard Elwes is a mathematician at the University of Leeds in the UK and an active science communicator as a YouTube host. Numberphile. Gizmodo spoke to Elwes about the new book, as well as the unique humanity behind the way we understand and work with numbers. The conversation below has been edited for grammar and clarity.
Gayoung Lee, Gizmodo: This is the name of the books Big Numbers. What does this mean? What makes a number big?
Richard Elwes: Yes, this is a fairly important question in the book. I should have answered the question you asked me very early in the process. What is the big number? And you can give a contextual answer. If you’re trying to balance golf balls on top of each other, then 5 is a pretty big number. The result is that any number can be either too large or too small depending on the context.
What I understood was how people think about numbers, use numbers, and work with numbers. We do this through various Intelligent tools or systems we build. And I’m starting to think that by “big number” I mean a number that’s just getting started challenge some of these systems.
Gizmodo: Subtitle mentions 4½ and Pisces 7. How do these numbers fit into this approach?
Elves: The most basic tool we have for working with numbers is what cognitive scientists call subitizing—basically instant recognition. If I put three marbles on the table and say, “Gayoung, how many marbles are there?” You will immediately see that there are three people. No need to stop. You don’t have to count. You won’t get it wrong.
If I put nine marbles on the table, you will probably get it wrong. If you want to finish correctly, you need to use something more complicated: stop and count. According to William Stanley Jevons, who experimented first4½ was the limit. Why four and a half? When he was four years old, he always got it right. And he almost always got it right by the time he was five. He said, “Well, the limit is in the middle, which is four and a half.”
Gizmodo: So in this context, anything over 4½ is a “big number” to our brain.
Elves: Exactly. If you mean this internal, subitizing process for immediate number recognition, anything over 4½ is, in that sense, a large number.
Gizmodo: What about Fish 7?
Elves: So Fish 7 is the largest number that appears in the book. There is a Japanese googologist – someone who is interested in big numbers – “writes under the pseudonym”Fish.” And it’s “7” because that’s his seventh number. This is an attempt to write the largest number he can. It’s definitely one of the biggest numbers anyone has ever described. He did this armed with a strong language in modern mathematical logic.
Among these are many interesting systems developed by humans. Quite a bit of the book is between two extremes: about numbers big enough to break or at least challenge some human system.
Gizmodo: In the beginning, you say that the story is about numbers that are big from a human user perspective. This means that numbers are a construct, even though we believe they make up our objective reality. What do numbers reveal about the human mind?
Elves: It is an interesting question. As they say, numbers are just the language of science. I think many have said it. Interestingly, we are the only life form we know of that can precisely control numbers above the 4½ subitization limit, or whatever the limit is for some other species. But we don’t do it instinctively or innately. It is not something we are born with.
And indeed, there are many people whose culture has not developed a clear language for a large number of people. There are people who speak unwritten languages where the number system eventually runs out. This is actually quite surprising for people living in more technologically advanced societies. We would think that counting to the desired number is something that anyone can do, but this is not the case.
Gizmodo: Why do you think society tends toward a very fixed number system in general?
Elves: If we go back in history, really the main reason was the beginning of cities. Because with the cities we started getting money. If you want money, you have to have numbers. Also, there are more people in one place. You want to pay taxes. You want to make sure you get enough food for the community. No matter what, you will have to to count things.
Many early number systems will not work for the globalist, high-tech age we live in now. An easy example is Roman numerals. Imagine trying to run the modern world with Roman numerals – it just won’t work! Roman numerals also simply run out at some point. This was true of many older, traditional number systems.
The system we use now originated in India. There is no point in ending it. He doesn’t have a “biggest number”. What eventually happens is that it starts to get a little inconvenient. If you want to do science, you have to talk about billions, trillions, and beyond for the number of cells in the body or the number of stars in the galaxy. We need a slight modification, not an entirely new system: modern scientific notation. Instead of writing 12 zeros after 1, you write 10 with a small superscript, 12, which is 10¹², or 10 multiplied by itself 12 times.
And that makes a huge difference. On the one hand, this is a ridiculously large number. On the other hand, we can express it in a very short sequence of symbols, none of which are complex. How powerful is this system? How people view the universe and try to describe our home has become absolutely essential.
Gizmodo: If you add just one little hyphen, a minus sign, to the superscript, you are now describing impossibly small things.
Elves: Exactly! Isn’t that amazing? Throughout history, many people have not had access to this. Compared to them, our horizons are wider because we can easily just ask questions and discuss things on a really extreme scale – small. and huge
Gizmodo: The history of number systems really emphasizes how they came about out of necessity, because there was a practical need for these scales. But as I understand it, there are a lot of people chasing after people. Is there a complex reason behind this interest? Where is the necessity behind these initiatives?
Elves: At various points in history, there have been people who deviated from this system. The Classic Maya of Central America were certainly engraved in more monuments than any practical need. But they also had a really simplified, efficient number system that could easily go beyond what was needed. So it looks like, you know, they took it and ran.
Gizmodo: This attraction to inexplicably large numbers has been a long-standing thing for humans.
Elves: As soon as you mention any number – be it big or small, tiny or huge – you think about a certain scale. If you’re talking about hundreds of people, it creates an image in your mind. Then imagine thousands of people, millions of people, billions of people. Numbers to do you think about things on a certain scale.
Then you say an unimaginably large number like a quintillion. Your mind is running on this huge scale that you can’t really comprehend. There is something a little dazzling about it. People react with a feeling of vertigo. It’s a little scary. It causes some kind of emotional response, I think, because the mind tries to fight them, but it can’t. Because we don’t have intuition for things in these scales. And this perhaps causes some concern or some surprise.
Gizmodo: You mention asking your fellow mathematicians for the largest number they’ve ever met. Memorable answers?
Elves: There was one I never expected from the mathematics of music. So it turns out that the numbers are 353 and 284 they are very close to each other. It was discovered 2,000 years ago and is a way to create a 53-note scale. There are a number of huge numbers that only appear within pure mathematics. The branch of mathematics that produces the largest numbers is mathematical logic. That’s because it’s all about learning different computing systems or different languages in some sort of formal, mathematical, logical sense. The absolute largest numbers in the book are obtained using set theory, a technical branch of mathematical logic.
Gizmodo: As a mathematician yourself, how has exploring large numbers influenced the way you approach your work?
Elves: I emphasize in the book that this is a human story. The tools we develop to describe numbers, or to reach very large numbers to describe the universe at any scale, are all (man-made) tools. I think most mathematicians are what you might call Platonists, at least for practical purposes. That is, we simply think that these things exist, and we study them. I think, you know – for practical purposes, I don’t want to get philosophical about it – I work the same way.
It doesn’t directly affect the way I teach math or the way I do research, but it feels like a healthy thing to implement as background awareness. We are a product of history and we are humans using human technology.
Big Numbers: The Story of Ambitious Counting from 4 1/2 to Pisces 7 Posted on April 28, 2026 via Basic books and is now available online or in volume.
