University of Illinois at Urbana-Champaign
Rare Book Room Exhibit

Waring did not give up his day job as a physician until 1770; in fact, he practiced medicine at several locations including Addenbrooke hospital, which may be familiar to some visitors to Cambridge, England. He discovered Cauchy's ratio test. It is stated in Waring's Meditationes Algebraicae that every integer is a sum of not more than 9 cubes, a sum of not more than 19 biquadrates and so forth. Hilbert proved the general assertion in 1909.

NOTE: This book is famous because it asked a problem that wasn't solved for more than 199 years. Hilbert's 1909 paper refers to pages 349-350 (3d ed.) Cambridge 1782 of Waring's work. The Rate Book and Special Collections Library has both the 1782 edition (on exhibit) and an earlier edition.

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