# Is it possible that the Reimann hypothesis is an actual example of a Godel unprovable proposition? **URL:** \ **Category:** Great Debates\ **Created:** [June 3, 2023, 7:17pm UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966 "2023-06-03T19:17:27Z")\ **Posts on this page:** 8\ **Page:** 3
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [June 16, 2023, 2:09am UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/41 "2023-06-16T02:09:22Z")
It is unprovable (and undecidable!), but that does not make it “true” any more than it makes it false. Indeed, there have been compelling arguments why it should be false as well as compelling arguments why it should be true. It can depend on what other axioms you might want or need to take as true, e.g. Martin’s maximum. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [June 16, 2023, 3:08am UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/42 "2023-06-16T03:08:41Z")
> [@DPRK](#): > > It is unprovable (and undecidable!) Which “it” are you refering to? ---
**Author:** ![74westy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/74westy/32/3950_2.png) [@74westy](https://boards.straightdope.com/u/74westy)\ **Post date:** [June 16, 2023, 3:54pm UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/43 "2023-06-16T15:54:07Z")
Sorry for replying to a question for @DPRK but “it” could be any proposition that is “true” but provably undecidable in some system. We could always create a new system by including its negation as an axiom. The resulting system would be as consistent as the original and the proposition would be false by definition. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [June 16, 2023, 5:37pm UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/44 "2023-06-16T17:37:28Z")
> [@Thudlow\_Boink](#): > > > [@DPRK](#): > > > > It is unprovable (and undecidable!) > > Which “it” are you refering to? The Continuum Hypothesis > [@74westy](#): > > We could always create a new system by including its negation as an axiom. The resulting system would be as consistent as the original and the proposition would be false by definition. That is true. In set theory the truth of the continuum hypothesis may be determined by other axioms. For example (unless I confused something) you cannot have _both_ the “proper forcing axiom” and the continuum hypothesis. On the other hand, “every set is constructible” implies the continuum hypothesis. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [June 16, 2023, 5:52pm UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/45 "2023-06-16T17:52:11Z")
> [@DPRK](#): > > > [@Thudlow\_Boink](#): > > > > Which “it” are you refering to? > > The Continuum Hypothesis Right; thanks. ---
**Author:** ![xtenkfarpl](https://avatars.discourse-cdn.com/v4/letter/x/c2a13f/32.png) [@xtenkfarpl](https://boards.straightdope.com/u/xtenkfarpl)\ **Post date:** [June 16, 2023, 6:12pm UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/46 "2023-06-16T18:12:35Z")
I certainly agree: for doing long symbol manipulation tasks, computers are almost certainly less likely to make a mistake than a human. But again, as you say, that’s probably not the interesting part. The creative step is framing the problem in a way that it can be ‘crunched’ by brute force exhaustion. ---
**Author:** ![xtenkfarpl](https://avatars.discourse-cdn.com/v4/letter/x/c2a13f/32.png) [@xtenkfarpl](https://boards.straightdope.com/u/xtenkfarpl)\ **Post date:** [June 16, 2023, 6:18pm UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/47 "2023-06-16T18:18:54Z")
GPT is well known for generating complete bullshit. Have you looked into independent verification of any of these? ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [June 16, 2023, 7:43pm UTC](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966/48 "2023-06-16T19:43:18Z")
> [@xtenkfarpl](#): > > GPT is well known for generating complete bullshit. > Have you looked into independent verification of any of these? According to Wikipedia they are all examples of true but unprovable theorems. > **[Goodstein's theorem](https://en.wikipedia.org/wiki/Goodstein%27s_theorem)** > > In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0. Laurence Kirby and Jeff Paris showed that it is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic). This was the third example of a true statement that is unprovable in Peano arithmetic, after the examples provided by Gödel's incompleteness theorem a Ki... > **[Paris–Harrington theorem](https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem)** > > In mathematical logic, the Paris–Harrington theorem states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in Peano arithmetic, is not provable in this system. The combinatorial principle is however provable in slightly stronger systems. > This result has been described by some (such as the editor of the Handbook of Mathematical Logic in the references below) as the first "natural" example of a true statement about the in... [Previous page](https://boards.straightdope.com/t/is-it-possible-that-the-reimann-hypothesis-is-an-actual-example-of-a-godel-unprovable-proposition/984966.md?page=2)