Private communication has been a concern throughout history. People have developed many clever ways to send secret messages to their partners in business, politics, war, and adultery. In the age of computer communication, we assume that anyone may examine the bits flying around the internet, and we use mathematical techniques to scramble the bits in our message so that it is intelligible only at the endpoints of the transmission.
{"title":"RSA encryption","authors":"K. Bryan","doi":"10.1090/mbk/121/65","DOIUrl":"https://doi.org/10.1090/mbk/121/65","url":null,"abstract":"Private communication has been a concern throughout history. People have developed many clever ways to send secret messages to their partners in business, politics, war, and adultery. In the age of computer communication, we assume that anyone may examine the bits flying around the internet, and we use mathematical techniques to scramble the bits in our message so that it is intelligible only at the endpoints of the transmission.","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131304663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"National Museum of Mathematics","authors":"","doi":"10.1090/mbk/121/100","DOIUrl":"https://doi.org/10.1090/mbk/121/100","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"157 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114358194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Elementary proof of the prime number\u0000 theorem","authors":"","doi":"10.1090/mbk/121/36","DOIUrl":"https://doi.org/10.1090/mbk/121/36","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"149 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128344152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Zeros of 𝜁(𝑠)","authors":"","doi":"10.1090/mbk/121/30","DOIUrl":"https://doi.org/10.1090/mbk/121/30","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117086271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Transcendence of 𝑒 centennial","authors":"","doi":"10.1090/mbk/121/61","DOIUrl":"https://doi.org/10.1090/mbk/121/61","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127481043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Khinchin’s constant","authors":"","doi":"10.1090/mbk/121/22","DOIUrl":"https://doi.org/10.1090/mbk/121/22","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134441064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Carmichael numbers","authors":"","doi":"10.1090/mbk/121/98","DOIUrl":"https://doi.org/10.1090/mbk/121/98","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126974378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rubik’s Cube","authors":"","doi":"10.1090/mbk/121/62","DOIUrl":"https://doi.org/10.1090/mbk/121/62","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133538773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A child learns of the nonnegative numbers at an early age. Polynomials, on the other hand, demand a little more sophistication and are reserved in a U.S. child’s education for middle school. Those fortunate enough to take an undergraduate abstract algebra class realize that the chasm between the integers and polynomials is not so vast. One learns there are similarities: both integers and polynomials form rings; and that there are analogies: the integers have prime factors as their basic building blocks, whereas polynomials (over C) have linear factors. Given this, it is not that surprising that we have the following definitions:
{"title":"The Mason–Stothers theorem","authors":"Manuel Eberl","doi":"10.1090/mbk/121/69","DOIUrl":"https://doi.org/10.1090/mbk/121/69","url":null,"abstract":"A child learns of the nonnegative numbers at an early age. Polynomials, on the other hand, demand a little more sophistication and are reserved in a U.S. child’s education for middle school. Those fortunate enough to take an undergraduate abstract algebra class realize that the chasm between the integers and polynomials is not so vast. One learns there are similarities: both integers and polynomials form rings; and that there are analogies: the integers have prime factors as their basic building blocks, whereas polynomials (over C) have linear factors. Given this, it is not that surprising that we have the following definitions:","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"30 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131609338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Primes, the zeta function, randomness, and\u0000 physics","authors":"","doi":"10.1090/mbk/121/75","DOIUrl":"https://doi.org/10.1090/mbk/121/75","url":null,"abstract":"","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127773965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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