Levi was born to Georg Levi and Emma Blum in Mulhouse in Alsace-Lorraine, then part of the German Empire. He received his Ph.D. in 1911 under Heinrich Martin Weber at the University of Strasbourg. He served his mandatory military service in the German Army in 1906–1907, and was called up again serving in the artillery during World War I, 1914–18. Awarded the Iron Cross, he was discharged as a lieutenant. In 1917, he married Barbara Fitting, with whom he eventually had three children (Paul Levi (Framer), Charlotte, Suzanne). He taught at the University of Leipzig between 1920 and 1935, when the Nazi government fired him because of his Jewish ancestry. In 1935 he accepted an offer as head of the Mathematics Department at the University of Calcutta. His mother and a sister remained in Germany