{"title":"Hilbert’s tenth problem","authors":"Andrew J. Misner","doi":"10.1090/mbk/121/58","DOIUrl":null,"url":null,"abstract":"In the following paper, I will give a brief introduction to the theory of Diophantine sets as well as the theory of computability. I will then present the Matiyasevich-Robinson-Davis-Putnam (MRDP) theorem, which is immediately comprehensible given just a cursory understanding of the mathematical basics, and give some details of its proof. Finally, I will present some further work in the area of Diophantine computability and various applications or corollaries of the celebrated MRDP theorem.","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"100 Years of Math Milestones","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mbk/121/58","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In the following paper, I will give a brief introduction to the theory of Diophantine sets as well as the theory of computability. I will then present the Matiyasevich-Robinson-Davis-Putnam (MRDP) theorem, which is immediately comprehensible given just a cursory understanding of the mathematical basics, and give some details of its proof. Finally, I will present some further work in the area of Diophantine computability and various applications or corollaries of the celebrated MRDP theorem.
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