Raised in Osnabrück, Wiesbaden and Berlin, where he studied four terms of philosophy, history of art and languages, Wieman wanted to actually become an airplane technical designer and flier.

His fellow stage actors included his future wife, Erika Meingast, Marlene Dietrich, Dora Gerson and Max Schreck (the vampire in Nosferatu).

At the height of his film career, during the decade of the 1930s, Wieman acted in such productions as Man Without a Name, L'Atlantide, The Countess of Monte Cristo, Fräulein Hoffmanns Erzählungen, The Rider on the White Horse, Victoria, Patriots, and Togger.

In 1936 Wieman produced the Frankenburger Würfelspiel of the Nazi playwright Eberhard Wolfgang Möller in association with the 1936 Summer Olympics and the inauguration of the Dietrich-Eckart-Bühne, and also played the Black Knight.

After the failed 20 July plot to assassinate Adolf Hitler happened in 1944, Mathias and his wife Erika helped the family of Count Fritz-Dietlof von der Schulenburg.

To his fairly well known work belongs No Greater Love, As Long as You're Near Me, The Last Summer, Ripening Youth, The Girl and the Legend, and opposite Ingrid Bergman in Roberto Rossellini's Fear.