The Brauer-Hasse-Noether Theorem in Historical Perspective

The legacy of Helmut Hasse, consisting of letters, manuscripts and other - pers, is kept at theHandschriftenabteilung of the University Library at Gottin- ¨ gen.Hassehadanextensivecorrespondence;helikedtoexchangemathematical ideas, results and methods freely with his colleagues. There are more than 8000 documents preserved. Although not all of them are of equal mathematical - terest, searching through this treasure can help us to assess the development of Number Theory through the 1920's and 1930's. Unfortunately, most of the correspondence is preserved on one side only, i.e., the letterssenttoHasse are availablewhereasmanyoftheletterswhichhadbeensentfromhim,oftenha- written, seem to be lost. So we have to interpolate, as far as possible, from the repliestoHasseandfromothercontexts,inorderto?ndoutwhathehadwritten 1 in his outgoing letters. The present article is largely based on the letters and other documents which I have found concerning the Brauer-Hasse-NoetherTheorem in the theory of algebras; this covers the years around 1931. Besides the do- ments from the Hasse and the Brauer legacy in Gottingen, ¨ I shall also use some letters from Emmy Noether to Richard Brauer which are preserved at the Bryn Mawr College Library (Pennsylvania, USA).