Why humans are obsessed with numbers too big to understand

At a glance:

• Mathematician Richard Elwes examines humanity's fascination with incomprehensibly large numbers in his new book Huge Numbers: A Story of Counting Ambitiously, from 4½ to Fish 7, published April 28, 2026 by Basic Books.
• The book's range spans from the cognitive limit of subitizing — roughly 4½ objects — to Fish 7, one of the largest numbers anyone has ever formally described, created by a Japanese googologist known only by the pseudonym "Fish."
• Through the lens of number systems past and present, Elwes argues that the way humans invent tools to handle numbers reveals as much about consciousness and culture as it does about mathematics itself.

What the book is about and where it came from

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. His latest book, Huge Numbers: A Story of Counting Ambitiously, from 4½ to Fish 7, was published on April 28, 2026 via Basic Books and is now available online or in hardcover. In it, Elwes traces humanity's long-running enchantment with huge numbers — not just as abstract curiosities, but as windows into how we build intellectual frameworks to make sense of reality.

The book is structured around two anchor points. At one end is 4½, a deceptively small number that represents the upper boundary of subitizing — the innate human ability to instantly recognize a quantity without counting. At the other is Fish 7, a number so staggeringly large that it pushes the limits of formal mathematical language. In between lies a sweeping history of the systems humans have built to grapple with quantities that exceed our natural intuitions.

How our brains handle numbers — and where they break down

The most basic tool humans have for working with numbers is subitizing, which Elwes describes as "basically instant recognition." Put three marbles on a table and most people will immediately know there are three — no counting required. But push that to nine marbles and the system fails; you have to stop, slow down, and count deliberately. According to William Stanley Jevons, who first experimented with this phenomenon, the subitizing limit works out to approximately 4½. Jevons arrived at the half-integer because he always got four right and almost always got five right, concluding that the true threshold lies somewhere in between.

Elwes argues that anything beyond that 4½ threshold is, from the brain's built-in perspective, a "big number." This reframing matters because it shifts the question from a purely mathematical one to a cognitive one: a number's bigness is not intrinsic — it depends entirely on the mental tool you are using to process it. Once you move past subitizing, you need counting. Once counting becomes unwieldy, you need notation systems. Each leap represents a human-made scaffold that extends what is otherwise a very limited biological faculty.

The rise and fall of number systems

Numbers did not emerge in a vacuum. Elwes points to the rise of cities as a pivotal historical driver: with urbanization came money, taxes, trade, and the need to track large quantities of people and resources. Early number systems — Roman numerals being a well-known example — were adequate for their eras but woefully unfit for modern demands. Roman numerals not only make arithmetic cumbersome but also run out of convenient symbols at higher values, making them impractical for the scale of computation required today.

The positional numeral system the world uses now originated in India and has no built-in ceiling — there is no "biggest number." But even this system becomes unwieldy at extreme scales. Writing out 1 followed by twelve zeros is manageable; writing out 1 followed by a googol of zeros is not. This is where scientific notation enters: instead of laboriously writing out zeros, you express the number as a base multiplied by a power of ten (for example, 10¹²). With just a few symbols, you can compactly represent numbers that would otherwise be physically impossible to write down, a breakthrough Elwes calls essential to how humans describe and explore the universe.

Why humans chase numbers beyond any practical need

Not all large-number pursuits are born of necessity. The classical Maya, who lived in Central America, engraved numbers on monuments far larger than any practical application would ever demand. Elwes notes that the Maya had a streamlined, effective numeral system that could readily extend beyond practical use — and they simply chose to push it further. This suggests that the drive to produce ever-larger numbers is not purely utilitarian; it is also expressive, even playful.

Elwes describes a particular emotional quality to encountering enormous numbers: a sense of vertigo. When you move from hundreds to thousands to millions to billions, each step conjures a different mental image. But at some point — around a quintillion, or beyond — the mind loses its grip. Numbers that large provoke what Elwes calls a mix of discomfort and wonder, because the human brain simply lacks intuition for those scales. That emotional response, he argues, is part of what keeps people coming back to the pursuit of bigger and bigger numbers.

What numbers reveal about human consciousness

Numbers are often called the language of science, but Elwes pushes the observation further: the way humans relate to numbers says something fundamental about consciousness itself. Humans appear to be the only known life form capable of handling numbers with precision beyond the subitizing threshold. Yet this ability is not innate — it is cultural, learned, and built through shared systems of language and notation.

Strikingly, there are communities throughout history whose languages lacked precise words for large numbers, where the counting system simply stopped at a certain point. For people raised in technologically advanced societies, the idea that counting has a ceiling feels almost alien. Elwes uses this contrast to underscore that our numerical horizons are not fixed — they are products of the tools and cultures we build. Relative to earlier civilizations, our own horizons are vastly broader, simply because we have access to notations and concepts like negative exponents that let us comfortably discuss both impossibly large and impossibly small quantities.

The mathematician's own reflection

Asked how his deep dive into huge numbers has shaped his own mathematical practice, Elwes is candid: it has not changed how he teaches or conducts research. But he emphasizes that the book is fundamentally a human story. The tools mathematicians use to describe numbers — from scientific notation to set theory, the branch of mathematical logic that produces the absolute biggest numbers in the book — are all human inventions. He describes himself, for practical purposes, as a Platonist: someone who believes mathematical objects exist independently and that we are studying them rather than inventing them. But he acknowledges that this is a philosophical stance he chooses not to commit to rigidly.

What the investigation did give him, he says, is a "healthy thing to have as background awareness" — a recognition that mathematics, for all its power, is a product of human history and human cognition, not a feature of the universe that simply waits to be discovered.