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This is probably a dumb question, but do we actually know that pi has an infinite number of decimal digits or are we assuming that it does because we haven’t de
by hnlmorg 5mo ago
This is probably a dumb question, but do we actually know that pi has an infinite number of decimal digits or are we assuming that it does because we haven’t developed a sufficiently powerful computer to calculate the last digit of pi?
I’m guessing this is something that could be formally proven?
- deleted 5mo ago[deleted]
- pixel_popping 5mo agoWell, that should get GPT-5.5 extended thinking going for a few weeks.
- hasteg 5mo agoHere is a one page proof that pi is irrational - https://heuklyd.github.io/papers/pdf/Niven-1947.pdf https://heuklyd.github.io/papers/pdf/Niven-1947.pdf
- stackghost 5mo agoIt's amazing how inscrutable calculus can be when you return to reading it after not doing so for a period of time, much like lisp or forth. I don't think I've actually done an integral or taken a derivative in years. I can see the elegance of that proof but I'll be damned if I can actually follow the mathematics from one step to the next.
- liglam 5mo ago[dead]
- partsch 5mo agoThanks for the PDF. I feel like I understand even less now than I did before.
- hnlmorg 5mo agoThanks for sharing. That’s a nice read. I’m glad I asked :)
- simonreiff 5mo agoFor a superb explanation of Niven's proof (which leaves more questions than answers when you first read it), I like Michael Penn's video: https://youtu.be/dFKbVTHK4tU?is=d2DbV5HDP0IpP9tA https://youtu.be/dFKbVTHK4tU?is=d2DbV5HDP0IpP9tA ....notwithstanding the length of the proof, this is quite a hard problem.
- mike_hock 5mo agoWe definitely know that Pi is irrational, we just don't know if it's normal (i.e. if the PiFS joke even works).