The following is based on biographical information kindly supplied by Professor Meinhard Peters, Münster from the Universitätsarchiv Münster and the Hauptstaatsarchiv Hannover.
Arthur Wieferich was born on 27th April 1884 in Münster, the son of a businessman. He studied from 1903-1909 in Münster and thereafter became a secondary school teacher in Konitz, Elbing, Zoppot, Neustadt, Jülich, Stade (near Hamburg) and finally Meppen.
From 1945 to 1949 he earned a living as a private tutor.
Athur Wieferich married in 1916 and had no children. He died on the 15th September 1954 in Meppen.
He was a member of the DMV (Deutsche Mathematiker Vereinigung) from 1909 to about 1929.
His five mathematical publications stem from 1908, when he was a student in Münster. Max Dehn taught a number theory course in 1907 and may have had an influence on Wieferich.
Concerning paper 1, Edmund Landau remarked in the same volume:
I salute the paper of Mr. Wieferich as one of the gratifying recent advances in elementary number theory. The author has solved an old problem conjectured in 1782 and attempted by many number theorists.A gap in the proof was filled by A.J. Kempner in Math. Ann. 72 (1912) 387-399.
Regarding paper 4, Paulo Ribenboim in his book 13 Lectures on Fermat's Last Theorem (p. 139) remarks:
Then in 1909 came Wieferich. He discovered a criterion for the first case of an entirely different nature. His first proof was an enigma. Few people were able to understand how Wieferich succeeded, like a magician, in unravelling from very complicated formuale, so simple and beautiful a criterion ...Back to some biographies of past contributors to number theory