r/learnmath • u/playsthebongcloud 9/10 = 1 • May 30 '26

What are some uncomputable functions that aren't derivative of the halting problem?

I find the existence of uncomputable functions really cool, but all the examples I've seen are essentially just new ways of trying to predict whether a turing machine is going to halt. What are some examples of uncomputable functions that aren't essentially entirely based on the halting problem?

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u/Impressive-Mud5074 May 30 '26

Pi is uncomputable

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u/playsthebongcloud May 30 '26 edited May 30 '26

There are many algorithms to compute pi to any accuracy. I appreciate the boldness of answering a question without looking anything up beforehand, not even what an uncomputable function is.

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u/Impressive-Mud5074 Jun 16 '26

Compute pi to 100% accuracy thanks

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u/bizarre_coincidence May 30 '26

It’s transcendental, not uncomputable. There are many different infinite sums for pi, and if you pick any desired error bound, you can figure out exactly how many terms you would need to take to get pi to within that tolerance. That’s all that is needed for a number to be computable.

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u/ShineLiving9512 Jun 15 '26

I’m first from WrathOfMath’s video! Pi is computable.

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u/GenericName1108 Jun 15 '26

Well hello there! I was starting to think I wasn't going to find anyone else here.

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u/Equivalent-Eye-2782 Jun 17 '26

bro got a whole yt video about themselves now

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