# Mathematics with a metamathematical flavour.

- Added on
2020-10-16

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Among the most fascinating results of mathematics are unprovability theorems, that is, rigorous proofs that certain statements cannot be deduced from certain axioms. A very famous example is Paul Cohen's demonstration that the continuum hypothesis cannot be deduced from the ZFC axioms . For this, Cohen invented a technique known as forcing, which is far too advanced for a page like this. (Indeed, I am incapable of presenting it anyway - if you are curious you could try visiting this site for some notes on forcing. They seem all right, but I don't know enough to be able to judge with any confidence.) Instead, I shall present here a few examples of low-level unprovability theorems, by which I mean purely mathematical results that, in one way or another, tell us that proofs of certain theorems must necessarily have certain properties. Such conclusions I shall loosely refer to as metamathematics.

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- MathematicsWithAMetamathematicalFlavour
- type
- article
- date_added
- 2020-10-16

### BibTeX entry

@article{MathematicsWithAMetamathematicalFlavour, key = {MathematicsWithAMetamathematicalFlavour}, type = {article}, title = {Mathematics with a metamathematical flavour. }, author = {Timothy Gowers}, abstract = {Among the most fascinating results of mathematics are unprovability theorems, that is, rigorous proofs that certain statements cannot be deduced from certain axioms. A very famous example is Paul Cohen's demonstration that the continuum hypothesis cannot be deduced from the ZFC axioms . For this, Cohen invented a technique known as forcing, which is far too advanced for a page like this. (Indeed, I am incapable of presenting it anyway - if you are curious you could try visiting this site for some notes on forcing. They seem all right, but I don't know enough to be able to judge with any confidence.) Instead, I shall present here a few examples of low-level unprovability theorems, by which I mean purely mathematical results that, in one way or another, tell us that proofs of certain theorems must necessarily have certain properties. Such conclusions I shall loosely refer to as metamathematics. }, comment = {}, date_added = {2020-10-16}, date_published = {}, urls = {https://www.dpmms.cam.ac.uk/{\~{}}wtg10/metamathematics.html}, collections = {about-proof,the-act-of-doing-maths}, url = {https://www.dpmms.cam.ac.uk/{\~{}}wtg10/metamathematics.html}, year = {}, urldate = {2020-10-16} }