In the 1900 US Census in Chicago, Max seems to be living as a boarder in the home of John C. Rice, working as a hardware salesman. In the same home are a Henry & Lizzie Matthews, aged 70 and 52 respectively, both born in Germany, both having immigrated in 1879 (the same year as Max). Henry is a retired grocer.
Max was naturalized in the Cook County Superior Court in 1892, indicating he was a minor of 9 years of age when he arrived in the US.
From the Cook County Death Index at familysearch.org:
Name: Henry W. Matthews Titles and Terms: Event Date: 14 Oct 1900 Event Place: Chicago, Cook, Illinois Gender: Male Race (Original): White Race: White Age (Formatted): 68y Birth Year (Estimated): 1832 Birth Date: Birthplace: Germany Marital Status: Spouse's Name: Spouse's Titles and Terms: Father's Name: Father's Titles and Terms: Father's Birthplace: Mother's Name: Mother's Titles and Terms: Mother's Birthplace: Occupation: Address: Residence Place: Cemetery: Oak Ridge Burial Place: Burial Date: 17 Oct 1900