In the fall of 1862 most of his militia unit (the 4th National Guard made up mostly of policeman) were mustered in as the 173rd New York Volunteer Infantry. The regiment served most of its first two years in Louisiana, taking part in the siege of Port Hudson and in General Banks's Red River campaign. When Early raided Washington, the 173rd NYVI was transported from Louisiana to the Shenandoah Valley. It served briefly in Georgia before being mustered out. Mathias rose from Lieutenant to brevet Major. After the war he continued to serve in ceremonial militia posts in Brooklyn.
Mathias entered politics following the war and represented Brooklyn's 16th Ward in the Commons Council, Board of Supervisors, and as an Alderman. In the last case he got into some trouble. In 1879 he was censured by the Republican Party for having voted for some Democratic nominees. I think that was about the end of his political career. He spent the rest of days engaged in real estate and insurance sales. He died at the age of 63 years, 2 months, and 25 days in 1896.
I wish I knew more about Mathias. For example, where in Germany was he from? what were the names of his parents? did he have brothers or sisters? As with most genealogical research, it is slow going, but I hope to get some answers soon.