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Mathematical Treasure: Sumario Compendioso

Author(s): 
Frank Swetz (Pennsylvania State University)

The Sumario Compendioso (1556) by Juan Diez Freyle is considered by many to be the first mathematics book published in Colonial Spain. (Was it really the first?) It is a treatise on arithmetic and algebra with numerous explanations and examples involving the calculations of percentage for monetary exchange and the valuation of gold and silver. The mathematics historian David Eugene Smith published a facsimile and translation of this work, along with a commentary on it, in 1921. His book has been reprinted as The Sumario Compendioso of Brother Juan Díez, the Earliest Mathematical Work of the New World, Camelot, Ormond Beach, Florida, 1996.

According to Bruce Stanley Burdick, author of Mathematical Works Printed in the Americas, 1554-1700 (Johns Hopkins Press, 2009), the title page shown below is from the copy of the Sumario Compendioso held by the University of Salamanca, Spain, and the note across the top reads, "De la Libreria del Colegio Mayor de Cuenca." (See page 37 of Mathematical Works for details.) Burdick noted recently that, as of August of 2013, the University of Salamanca's copy of the Sumario Compendioso remains the only complete copy known to exist. The three other known copies reside in the Huntington Library in San Marino, California; the British Library in London; and the Duke University Library in Durham, North Carolina.

Mathematical Works Printed in the Americas, 1554-1700, Bruce Stanley Burdick, 2009 - See more at: http://www.maa.org/publications/periodicals/convergence/mathematical-wor..., the title page shown below is from the copy of the Sumario Compendioso held by the University of Salamanca, Spain, and the notation across the top of the page reads, "De la Libreria del Colegio Mayor de Cuenca." Burdick also pointed out recently that, as of August of 2013, the University of Salamanca's copy was the only complete copy known to exist. (See p. 37, for details.)

Was the Sumario Compendioso the earliest mathematics book published in Colonial Spain? There is a clue in the title of Bruce Burdick's book, Mathematical Works Printed in the Americas, 1554-1700 (Johns Hopkins Press, 2009). Burdick has located two earlier items, a logic book and a book containing examples from geometry (including figures), both from 1554. He pointed out recently that, as of August of 2013, "The Sumario remains the earliest work on arithmetic and/or algebra from the Americas."

See the review of Burdick's Mathematical Works in Convergence; for another review, see MAA Reviews.

Frank Swetz (Pennsylvania State University), "Mathematical Treasure: Sumario Compendioso," Loci (August 2013)

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