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Professional and personal papers of Smith, including correspondence and manuscripts from his students, family, contemporary mathematicians and teaching colleagues about the history and teaching of mathematics, his many committees, administrative matters at Teachers College, and his travels and collecting. Also, the manuscripts of his writings and his notes.

Personal, business, and legal letters; manuscripts including prose, poetry, and diaries; and documents including deeds, receipts, invoices, and account books. The 18th century materials focus on the personal and business correspondence of Calvin, Jotham, and Martin Gay, sons of Ebenezer Gay who were engaged in shipping between New England and the Maritime Provinces. There are occasional letters of Jotham and Martin referring to the American Revolution. The Otis family correspondence of the 18th century, likewise, is of a purely routine and personal nature. There are only four letters of Col. James Otis, and only two of his son, James. Gay and Otis family interests intertwine during the 19th century with the marriage of Mary Allyne Otis to Ebenezer Gay, who are among the chief correspondents of this century, along with their children including Sidney Howard Gay and Winckworth Allan Gay. The Otis correspondence centers around business, real estate, and personal interests of Mary A. Otis Gay's brothers John, Joseph, and William Otis.

The main portion of the collection is made up of letters, documents, notes, manuscript and typescript articles and speeches, and scrapbooks and notebooks which are contained in 270 envelopes, folders, manuscript boxes, and bundles. Another 153 bundles, boxes, folders, and envelopes are devoted chiefly to clippings, tear sheets, pamphlets, and books and other printed matter. Proofs of the printing plates for one of Mr. Bancroft's works on Carl Schurz are preserved in eleven envelopes. Pictorial material includes two envelopes of photographs, one envelope of photostats, thirty-four photographs, and eighty-five framed photographs, many with manuscript letters by or relating to the subject of the photograph. The collection is rich in the papers and personal correspondence of Frederic Bancroft and includes notes and various other source materials for his books dealing largely with African Americans, the South, the Civil War, Seward, Calhoun, and the life and work of Carl Schurz. Also, a wealth of material by and about Edgar Bancroft (1857-1925), Frederic's brother and U.S. ambassador to Japan.

Autograph letters, official and private documents, and accounts, which were previously mounted in eleven volumes. Most of these relate to Columbia University or people associated with the University.