Herman G. Breyer (or Breijer) was a teacher in Amsterdam when he obtained a doctorate in mathematics and physics at the University of Amsterdam in 1893. That same year he published what was probably his thesis, De grondvormen der krommen van de derde klasse... (Amsterdam, 1893, 72p). In July that year he was appointed lecturer in physical science at the State Gymnasium (a high school established in 1892) in Pretoria. During the same year the State Museum of the South African Republic (later the Transvaal Museum) was founded in Pretoria and Breyer became a member of its board of trustees. He also served as honorary director of the museum from 1893 to 1897, before Dr. J.W.B. Gunning* was appointed as the first full time director. Breyer also served as secretary of the republic's Council of Examiners. In January 1897 he was appointed as the only lecturer and acting director of the newly established State Mining School, but the institution foundered at the outbreak of the Anglo-Boer War in October 1899. After the war, in August 1902, Breyer began lecturing in mathematics and physical science at the newly founded Normal College in Pretoria. In 1905 he became professor of mathematics at the Transvaal Technical Institute in Johannesburg and remained during its development into the Transvaal University College (1906) and the South African School of Mines and Technology (1910). In 1913 he became director of the Transvaal Museum, which that same year moved into its new building in Paul Kruger Street, Pretoria, where it is still housed as the Ditsong National Museum of Natural History. He served as a member of council of the University of the Cape of Good Hope from 1909 to 1916. In 1921 he resigned his post for health reasons.
Breyer was a naturalist and collected extensively in the Transvaal and on museum expeditions. One of these expeditions went to Mozambique from 27 May to 3 July 1914 and Breyer read a paper, "An account of the Transvaal Museum expedition to the Maputa River", to the Transvaal Biological Society in November that year. His account of the expedition was written up for the Annals of the Transvaal Museum (1915, Vol. 5(2), pp. 111-115), while a collection of butterflies that he had made during the expedition was described in the same issue by C.J. Swierstra*. He went on other short expeditions to Komatipoort in June 1916 (Annals, 1917, Vol. 5(4), pp. 279-282), and to Gazaland, along the lower Limpopo River, in August the same year (Annals, 1917, Vol. 5(4), pp. 283-290). In addition to his contributions to the museum's collections of lepidoptera and coleoptera he also collected plants. Several plant species were named in his honour, including Warburgia breyeri and Cleome breyeri. He is also commemorated in the names of two lizards, Tetradactylus breyeri and Cordylus warreni breyeri.
Breyer joined the South African Philosophical Society in 1898, but was a member for a few years only. He became a member of the South African Association for the Advancement of Science in 1915 and joined the South African Biological Society as a foundation member, serving as its first president during 1917-1918. He was survived by his wife, Emilie Louis Cornelia, born Hartkamp.