One subway ride in NYC costs $3. Gizmodo has been around for 24 years. The Sun is just one of some several hundred billion stars in the Milky Way, which is also just one of some trillions of galaxies in the universe. In science, a hypothesis is better tested if it’s weathered a good number of empirical studies. The equations describing how the world works essentially place one number in relation to another.
Our reality is deeply steeped in numbers—a realization discussed at length (no pun intended) in Huge Numbers: A Story of Counting Ambitiously, from 4 1/2 to Fish 7, by Richard Elwes. The book discusses not only incomprehensibly large numbers but also numbers that sound small but represent incomprehensibly large concepts. Overall, the story recounts (again, no pun intended) the history of humanity’s fascination with numbers—particularly huge ones—and how this enchantment drives our ongoing quest to understand the universe.
Richard Elwes is a mathematician at the University of Leeds in the U.K., and an active science communicator, including as a presenter on the YouTube channel 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 following conversation has been edited for grammar and clarity.
Gayoung Lee, Gizmodo: The title of the books is Huge Numbers. What does that mean? What makes a number big?
Richard Elwes: Well, that’s a fairly important question in the book. Quite early in the process, I had to basically answer the question you’ve just asked me. What is a 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 very big number. The consequence is that any number can either be very big or very small, just depending on the context.
What I came down to was how human beings think about numbers, use numbers, and work with numbers. We do that through various Intellectual tools or systems that we’ve built. And I started to think, well, what I mean by a “big number” is a number that starts to challenge some of those systems.
Gizmodo: The subtitle mentions 4½ and Fish 7. How do these numbers fit this approach?
Elwes: 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 said, “Gayoung, how many marbles are there?” You’d see immediately there are three. You don’t have to stop. You don’t have to count. You’re not going to get it wrong.
If I put nine marbles on the table, you’d probably get it wrong. If you want to get it right, you have to use something more sophisticated: stop and count. According to William Stanley Jevons, who did the experiment first, 4½ was the limit. Why four and a half? Well, he always got it right when it was four. And he almost always got it right when it was five. So he said, “Okay, the limit’s somewhere in between, so four and a half.”
Gizmodo: So in this context, to our brains, something beyond 4½ is a “big number.”
Elwes: Exactly. If what you’re thinking about is this inbuilt, subitizing process for instantly recognizing numbers, then anything beyond 4½ is, in that sense, a big number.
Gizmodo: And Fish 7?
Elwes: So Fish 7 is the biggest number that appears in the book. There’s a Japanese googologist—someone who’s interested in big numbers—who writes under the pseudonym “Fish.” And it’s “7” because it’s his seventh number. It’s his attempt to just write down the biggest number he possibly could, really. It is certainly one of the biggest numbers anyone has ever described. He did that by arming himself with a powerful language in modern mathematical logic.
In between those are lots of interesting systems humans have developed. Quite a lot of the book lies in between the two extremes: about numbers big enough to break, or at least challenge, some human system.
Gizmodo: At the very beginning, you say that the story is about numbers that are big from the perspective of a human user. That implies numbers are a construct, even as we believe they constitute our objective reality. What do numbers reveal about the human consciousness?
Elwes: That’s an interesting question. As you say, numbers are just the language of science. I think many people have said that. It’s interesting that we are the only life form that we know of that can handle numbers precisely beyond that subitizing limit of 4½ or whatever the limit may be for some other species. But we don’t do that instinctively, or innately. That’s not something we are born with.
And indeed, there are plenty of people whose culture has not developed precise language for large numbers. There are people who spoke unwritten languages where the number system just runs out at some point. That’s actually quite striking for people who live in more technologically sophisticated societies. We would think of being able to count up to whatever number you like as just something everyone can do, but that’s not the case.
Gizmodo: Why do you think society, generally speaking, gravitated toward a very defined number system?
Elwes: Going back in history, a really pivotal cause was the beginning of cities. Because with cities, we started getting, well, money. If you want money, you’ve got to have numbers. And you also have bigger numbers of people in one place. You want to pay taxes. You want to make sure you’ve got enough food for the community. Whatever it is, you’re going to have to count things.
A lot of early number systems wouldn’t work for the globalist, high-tech age that we’re in now. An easy example is Roman numerals. Imagine trying to run the modern world on Roman numerals—it’s just not going to work! Roman numerals also just run out of numbers at some point. That was true for a lot of older, traditional numeral systems.
The system that we’re now using originated in India. There’s no point where it runs out. It doesn’t have a “biggest number.” What does eventually happen is that it starts to become a bit unwieldy. If you want to do science, you need to talk about numbers in the billions, trillions, and beyond for the number of cells in the body or the number of stars in the galaxy. We don’t need a completely new system, but a slight modification: modern scientific notation. Instead of writing 1 followed by 12 zeros, you write 10 with a little superscript, 12, which means 10¹², or 10 multiplied by itself 12 times.
And that makes a big difference. On the one hand, it’s a ridiculously big number. On the other hand, we can express it with a very short sequence of symbols, and none of them are complicated. That’s how powerful this system is. And it’s become absolutely essential to how humans look up to the universe and try and describe our home.
Gizmodo: And if you just add one little dash, a minus symbol, to the superscript, now you’re describing impossibly small things.
Elwes: Exactly! Isn’t that amazing? Many people throughout history haven’t had access to that. So relative to them, our horizons are much broader, because we can easily just ask questions and discuss things on these really, really extreme scales—tiny and huge.
Gizmodo: The history of number systems really highlights how they emerged due to necessity—as in, there’s a practical need for these scales. But as I understand it, there are folks who are chasing large numbers, well, just because. Is there a sophisticated reason behind this curiosity? Where’s the necessity behind these ventures?
Elwes: There have been people throughout different points in history that just went way beyond this system. The classical Maya who lived in Central America certainly engraved on monuments numbers far bigger than any practical need would ever require them to do. But they also had a really streamlined, effective numerical system that could easily extend beyond what they needed. So it looks like, you know, they took it and ran with it.
Gizmodo: This fascination with incomprehensibly large numbers was a long-running thing for humans.
Elwes: As soon as you mention any number—whether it’s big or small or tiny or enormous—you’re thinking about a certain scale. If you’re talking about hundreds of people, that gives you an image in your mind. Then imagine thousands of people, millions of people, billions of people. Numbers make you think about things on a certain scale.
Then you say some unimaginably enormous number, like a quintillion. Your mind is being taken to this enormous scale that you can’t really comprehend. There’s something a bit dazzling about it. People react with a sense of vertigo. It’s a bit scary. It causes some sort of emotional response, I think, because the mind tries to tackle them, and it can’t. Because we just don’t have intuition for things on those scales. And that causes maybe some discomfort or some wonder.
Gizmodo: You mention asking your mathematician colleagues of the largest number they encountered. Any memorable responses?
Elwes: There was one which I wasn’t expecting at all, which comes out of the mathematics of music. So it turns out that the numbers 353 and 284 are very close together. It was discovered 2,000 years ago and is a way of generating a 53-note scale. Just within pure mathematics, there are a number of enormous numbers that arise. The branch of mathematics that generates the largest numbers is mathematical logic. The reason for that is that it’s all about studying different computational systems or different languages in a sort of formal, mathematical, logical sense. The absolute biggest numbers in the book come out of using set theory, which is a technical branch of mathematical logic.
Gizmodo: As a mathmatician yourself, how has investigating huge numbers influenced the way you approach your work?
Elwes: I emphasize in the book that it’s a human story. The tools we develop to describe numbers—or to access very big numbers in describing the universe on whatever scale—are all [human-made] tools. I think most mathematicians are, at least for practical purposes, what you might call Platonists. That is to say, we just think this stuff exists, and we’re out there studying it. I think, you know—for practical purposes, I don’t want to philosophically commit to it—I work in that in the same way.
It doesn’t directly affect the way I teach or research math, but the realization feels like a healthy thing to have as background awareness. We are the products of history, and we are humans using human technology.
Huge Numbers: A Story of Counting Ambitiously, from 4 1/2 to Fish 7 was published on April 28, 2026 via Basic Books and is now available online or in hardcover.
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