{"title":"希尔伯特的第十题","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":"{\"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}","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}
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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