Sheffield Scientific School was founded in 1847 as a school of Yale College in New Haven, Connecticut, for instruction in science and engineering. Originally named the Yale Scientific School, it was renamed in 1861 in honor of Joseph E. Sheffield, a railroad executive. The school was incorporated in 1871. The Sheffield Scientific School helped establish a model of American higher education which incorporated both the sciences and the liberal arts. Following World War I, its curriculum gradually became completely integrated with Yale College. "The Sheff" ceased to function as a separate entity in 1956.

After technological developments in the early nineteenth century, such as the electric telegraph, an interest was fostered in teaching applied science at universities. Harvard established the Lawrence Scientific School in 1846 and Dartmouth began the Chandler Scientific School in 1852. The stage was set at Yale for the transition in education beginning in 1846, when professorships of agricultural chemistry (John Pitkin Norton) and practical chemistry (Benjamin Silliman Jr.) were established. In 1847, the School of Applied Chemistry became part of a newly created Department of Philosophy and the Arts (later, the Yale Graduate School). Classes and labs were hosted in the Second President's House on Yale's Old Campus until funding and a suitable facility could be found.

Norton died in 1852 and was followed by John Addison Porter. The professorship for applied chemistry was followed in 1852 by one for civil engineering, (William Augustus Norton) establishing a school of engineering. These programs made up the Yale Scientific School.^{[citation needed]}

In 1853 and 1854, science and engineering courses were listed in the Yale College course catalog as offered by the Yale Scientific School. Porter elicited help from his father-in-law, Joseph Earl Sheffield (1793-1882), and in 1858, Sheffield donated over US$100,000 to purchase the old Medical Department building for the scientific school. This gift included two newly-renovated wings within the building. The old Yale Medical School building on the northeast corner of Grove and Prospect Streets was renovated and renamed (South) Sheffield Hall. (It was demolished in 1931 and was on the current site of Sterling Tower, Sheffield Hall and Strathcona Hall (SSS).) Sheffield's building reinforced the division of Hillhouse Avenue into an upper, residential section, and a lower section devoted to education. In 1861, the school became the Sheffield Scientific School.^{[citation needed]}

Sheffield was one of Yale's greatest benefactors and continued to support the school throughout his life, giving a total of about US$500,000. Yale also received US$591,000 from his will as well as his house, the Sheffield mansion, designed and originally owned by Ithiel Town (demolished in 1957). The school also benefited from the Morrill Act starting in 1863 and an agricultural course was begun. Land grant status, however, was transferred to the Storrs Agricultural School in 1893 after arguments by the state grange that the school was not a proper "farm school".

The Sheffield School innovated with an undergraduate course offering science and mathematics as well as economics, English, geography, history, modern languages, philology and political science. Sheffield also pioneered graduate education in the United States, granting the first Ph.D. in the United States in 1861 as well as the first engineering Ph.D. to Josiah Willard Gibbs in 1863, and the first geology Ph.D. to William North Rice in 1867.^{[citation needed]}

Unlike Yale College students at the time, Sheffield students had "no dorms, no required chapel, no disciplinary marks and no proctors". The Academical Department of Yale (Ac) and Sheffield (Sheff) became rivals. Loomis Havemeyer, alumnus and registrar at Sheffield, stated: "During the second half of the nineteenth century Yale College and Sheffield Scientific School, separated by only a few streets, were two separate countries on the same planet." The Ac students studied liberal arts and would look down on the practical Sheff students.^{[citation needed]}

Sheffield had its own student secret societies, including the Colony Club, 1848 (now Berzelius), the Cloister, 1863 (now Book and Snake), St. Anthony Hall, 1867 (now a 3-year society, also called Delta Psi), St. Elmo, 1889 (also a senior society), as well as Franklin Hall, 1865 (Theta Xi), York Hall, 1877 (Chi Phi), Sachem Hall, 1893 (Phi Sigma Kappa), and Vernon Hall, 1908 (now Myth and Sword). The Yale Scientific magazine was founded at Sheffield in 1894, the first student magazine devoted to the sciences.^{[citation needed]}