What would happen if a supercomputer calculated pi out and discovered that it does end finitely?

To make things clearer, let’s remove the marketing hype and the bits which may be unclear. Here’s an alternative question:

What would happen if my iPhone calculator calculated 6 and discovered that it equals -17,384.23?

You know what would happen: the world wouldn’t end and mathematics wouldn’t be upended. You’d hurry to the Apple store and demand a refund.

Same thing.

You may be confused by the term “Supercomputer”. Supercomputers aren’t magical beings capable of reversing time or proving that Yes is No. They are just ordinary computers with plenty of processors and memory.

(The same is true if you replace “supercomputer” with “quantum computer”, “quantum supercomputer” or “multiquantumsupercomputer”. Quantum computers, in their various versions, cannot compute anything that cannot be computed by an ordinary computer given sufficient time, and they are not magical either.)

You may be confused by what we know about \pi. There’s no uncertainty about whether or not its decimal expansion ends.

Are you familiar with the decimal expansion of \frac{1}{7}? It goes 0.142857 142857 142857 \ldots, repeating. Do you expect there’s a chance we will patiently calculate more and more digits in this simple sequence and all of a sudden, boom, we’ll have reached the end?

No, this ain’t happening. There’s a very, very, very simple rule which specifies the sequence of digits in the decimal expansion of \frac{1}{7}, and that rule leaves no room for even the most magical of beings to suddenly “discover” that it ends.

The digits in the decimal expansion of \pi are in the exact same situation. They’re a bit less obvious, but that is all.

To clarify a few points: \pi is an irrational number, known to be so since before the US Declaration of Independence. Irrational numbers have non-terminating, non-repeating decimal expansions – this is something you can prove by yourself as soon as you learn what a decimal expansion is.

My point in comparing the decimal expansion of \frac{1}{7} and the decimal expansion of \pi was to clarify how unambiguous is the statement that the decimal expansion of \pi does not terminate. It’s not a hope, not an empirical observation, not something that can be overturned by more computational effort: it’s a fact, as solid and clear as the non-terminating nature of the decimal expansion of \frac{1}{7}.

The world is full of deep mysteries. This just isn’t one of them.