Born in 1817 in Bollwiller, France, Baumann was a descendant of an Alsatian family who founded a leading European nursery. He studied at the Grand Ducal Gardens in Karlsruhe before coming to the U.S. in 1854, where he entered practice as a landscape gardener with Jacob Weidenmann in1856. He was involved in the creation of the Picturesque planned community Llewellyn Park in New Jersey, where he delineated plans for the Ramble and the grounds of the Arcade Cottage. Baumann was one of many unsuccessful contenders in the Central Park competition of 1857, but having made the acquaintance of Calvert Vaux, he designed and oversaw the layout of the grounds of Federico Barreda’s estate at Newport circa 1859, subsequently known as Beaulieu, for which Vaux was the architect. There Baumann created curving footpaths leading to the rear of the mansion, where he raised the ground significantly to form a terrace overlooking the sea. Baumann penned and copiously illustrated the third chapter of Peter Henderson’s Practical Floriculture: A Guide to the Successful Cultivation of Florists' Plants for the Amateur and Professional Florist, and two of his garden designs were featured posthumously in the American Agriculturalist. By the early 1860s he ran nurseries in Morrisania, New York, which he relocated in 1865 to Rahway, New Jersey, where he opened a larger nursery operated by his descendants into the mid-1970s. He is buried there in Hazelwood Cemetery.