[viscountchocula]

Sure. There is definitely a googolth digit of pi. Computing what the digit is, however, is not necessary to prove that such a digit exists.

[raincole]

It's a quite bad analogy because the googolth digit of pi is completely constructive. (You don't need to calculate it, but it is constructive)

P = NP proof could be not constructive.

[xhkkffbf]

Note: finding arbitrary digits of pi doesn't require finding the preceding digits. It's kind of freaky.

https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%9...

[paulddraper]

Proving the Nth digit of pi exists is not (necessarily) constructive.

Though to make it an actual proof and not a truism you might say "when writing pi in the shortest decimal representation, there is a millionth digit".

Proving pi is irrational would suffice, without actually calculating the first million digits.

[wddkcs]

My intuition was that if a proof for P = NP exists, it would be incomparable to the kind of Pi example you provide- Pi is defined as an irrational ratio, so the existence of whether x digit of Pi exists. It would instead be like saying, 'the x digit of P is 7, and here is a proof that is not a straight calculation'. The idea of a proof which can demonstrate knowledge of X digit of Pi, without verification, doesn't click for me.