Roest, Idske (2025) To Solve is Not to Solve: Hilbert's Tenth Problem over Z and Rings of Integers. Bachelor's Thesis, Mathematics.
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Abstract
When David Hilbert posed his famous 23 questions, he shaped the mathematical research of the 20th century and beyond. This thesis focuses on Hilbert's Tenth Problem, a decision problem that asks whether there exists a general algorithm to solve any given Diophantine equation over the integers. In 1970, this problem was proven to be undecidable: there is no such algorithm. We present a detailed and accessible account of this proof. We then explore generalizations of this problem over other rings, particularly rings of integers. This version was proven undecidable only extremely recently, in December 2024. We investigate this new proof and see how it differs from the original approach over the integers.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Ozman, E. and Verbrugge, L.C. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 01 Jul 2025 08:05 |
| Last Modified: | 01 Jul 2025 08:05 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/35643 |
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