Hismostimportantworkisacompletesurveyofnumbertheorygivingboththeresultsandanevaluationofthemethodsofproof.Zahlentheorie.VersucheinerGesamtdarstellungdieserWissenschaftinihrenHauptteilenwhichheworkedonafterresigninghischairinMünster,waspublishedinfivevolumesbetween1892and1923.

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His most important work is a complete survey of number theory giving both the results and an evaluation of the methods of proof. Zahlentheorie. Versuch einer Gesamtdarstellung dieser Wissenschaft in ihren Hauptteilen which he worked on after resigning his chair in Münster, was published in five volumes between 1892 and 1923.