I’m not sure if I worded this correctly but I’ll try to elaborate more. I know that there are formulas that can calculate pi to the Nth digit. But my question is how can we be certain that the formulas accurately calculate the Nth digit of pi when we have nothing to compare it to since pi is an irrational number that keeps on going?
For example if I discovered a new formula than can calculate pi to 1 higher digit than what we currently know and the value I got was 4. How do I confirm that it is indeed 4 and not any other number? I have nothing else to compare it to?
I hope this makes sense
In: Mathematics
Certain truth is the subject matter of mathematics, not the reward you get for doing it. Mathematicians know the nth digit through having a good explanation that it is so. Same as any other knowledge. There’s no absolute revelation or perfect source of truth to compare it to. It’s all conjectural, but the best ideas have survived criticism so much that there’s no good reason to suspect that it’s wrong.
But that’s as far as it’s known. “The smallest distance between two points is a straight line” was also self-evidently true to most people in the past, yet was proven false later on.
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