Why mathematicians want to destroy infinity – and may succeed

Mathematicians who call themselves ultrafinitists think that extremely large numbers are holding back science, from logic to cosmology, and they have a radical plan to do something about it

How many atoms are there in the observable universe? Current estimates point to a number we would write as 1 followed by 80 zeroes, or 1080. If you peered inside each of these atoms and counted their subatomic particles, you could count a bit higher. But what happens beyond that? Take 1090 – even if you counted every atom and subatomic particle in the known universe, you wouldn’t reach this number. In some sense, 1090 has no relation to physical reality.

But it gets worse. If 1090 invites suspicion, then what about infinity? For some people, infinity is a stand-in for a process, such as counting, that could go on forever, but doesn’t necessarily do so. For others, it means an unknowably large number. In any case, relating it to human experience becomes difficult, even if we turn to the biggest thing we know of. While the standard picture of cosmology tells us that the universe is endlessly, boundlessly infinite, we also know that it does, in some sense, have an “edge” – a bubble within the cosmos that we call the observable universe, marked out by the light that has been travelling towards us since the big bang. Anything beyond this is, effectively, unknowable.

Does this matter? Since the 1960s, a small but relentless contingent of mathematicians, philosophers, computer scientists and physicists have argued that, yes, it does. Calling themselves ultrafinitists, they warn against being overly trusting of numbers like 1090 that elude our real-world experience. And don’t even get them started on infinity. “That is just an illusion,” says Doron Zeilberger at Rutgers University, New Jersey.

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