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zkmontoday at 6:32 AM1 replyview on HN

We are entering into a probabilistic era where things are not strictly black and white. Things are not binary. There is no absolute fake.

A mathematical proof is an assertion that a given statement belongs to the world defined by a set of axioms and existing proofs. This world need not have strict boundaries. Proofs can have probabilities. Maybe Reimann's hypothesis has a probability of 0.999 of belonging to that mathematical box. New proofs that would have their own probability which is a product of probabilities of the proofs they depend on. We should attach a probability and move on. Just like how we assert that some number is probably prime.


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teiferertoday at 6:54 AM

Definitely not.

"Probability" does not mean "maybe yes, maybe not, let me assign some gut feeling value measuring how much I believe something to be the case." The mathematical field of probability theory has very precise notions of what a probability is, based in a measurable probability space. None of that applies to what you are suggesting.

The Riemann Hypothesis is a conjecture that's either true or not. More precisely, either it's provable within common axioms like ZFC or its negation is. (A third alternative is that it's unprovable within ZFC but that's not commonly regarded as a realistic outcome.)

This is black and white, no probability attached. We just don't know the color at this point.

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