Not a mathematician here at all so perhaps my question is phrased incorrectly.
Let’s say through thorough testing in reality, we can prove with certainty Pi is correct up until 5 decimal places,
3.14159
The computers that are calculating Pi to an endless degree, how do they validate new values that are calculated as correct and cannot be otherwise?
In: 434
> how do they validate new values that are calculated as correct and cannot be otherwise?
Like this:
* a mathematician proves that a certain algorithm will generate digits of pi. Their proof can be checked.
* someone codes the algorithm into a computer program. This program can be checked.
* someone runs the program. The program can be run multiple times on different computers to check the work.
Fun fact: in the 1800’s a mathematician called William Shanks spent two decades calculating 707 digits of pi using pen and paper, finishing in 1873. This got him the world record for the most digits ever calculated.
His record stood for over 70 years, until someone else tried to break it in 1946, and discovered William Shanks had made a mistake – only 527 of his digits were correct.
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