Jacob Ammen, born January 7, 1806, in Botetourt County, Virginia. He graduated from West Point, the United States Military Academy, with honors in 1831. He served a short career in the military following his graduation, acting as assistant professor of mathematics and assistant instructor in infantry tactics at West Point until being stationed at Charleston Harbor from 1832 to 1833 during the Nullification crisis. After a stint at Fort Trumbull from 1833 to 1834, he returned to West Point to serve again as assistant professor of mathematics as well as natural philosophy. He resigned from his commission in 1837.

After Ammen's early military career, he served as professor of mathematics at Bacon College in Georgetown, Kentucky until 1839, and briefly at Jefferson College, Mississippi. He left Jefferson College after only a year due to issues with the banks that prevented Ammen and other faculty from being paid for their work. Ammen then taught at Indiana University, serving as chair of Mathematics, from 1840-1843. His departure from Indiana was not the most amicable, as he resigned his position following a pay cut from $1,200 to $1,000 per year. In a retrospective diary entry on July 16, 1844, Ammen also expressed his dissatisfaction with the perceived insularity of Bloomington. Although the financial circumstances surrounding his departure from Indiana University bear resemblance to his prior departure from Jefferson College, he nevertheless returned to the Mississippi college for another professorship (though not without persuasion from his peers). He taught at Jefferson College until 1848, after which he taught at Georgetown College in Kentucky. His relationship with Indiana University may not have been completely tarnished, however, as he indicates in a diary entry that he travelled to and taught in Bloomington once again in September 1854.

In 1855 Ammen left academia altogether, working as a civil engineer in Ripley, Ohio, during which time he met his wife, Martha Ann Shaw. He maintained this position until 1861, when the Civil War broke out. He returned to military service, organizing a volunteer company for the Twelfth Ohio. Ammen eventually attained to the rank of Brigadier General in the Union army and fought in multiple battles, including Cheat Mountain, Greenbrier River, and Shiloh. He resigned from his post in 1865, near the end of the Civil War.

After the war, he lived a comparatively quiet life, working as the Surveyor and Engineer of Hamilton County, Ohio, as well as other offices of public distinction. He lost his vision in the last years of his life, and he died in 1894 in Lockland, Ohio, where he lived with his son.