• Nuh Aydin
  • Lakhdar Hammoudi


On March 2, 1427 [6, p. 32] and [15], Ghiyāth al-Dı̄n Jamshı̄d bin Mas’ūd bin Maḥmood al-Tabı̄b al-Kāshı̄ (or al-Kāshānı̄) completed a monumental book in Arabic on arithmetic called Miftāḥ al-Ḥisāb. The most commonly used translation of this title, the one which we prefer as well, is “Key to Arithmetic.” Other possible translations include “Calculator’s Key” and “Key to Calculation.” Henceforth we will be referring to it as Miftāḥ and its author as al-Kāshı̄. This encyclopedic work includes three general subjects: arithmetic, geometry, and algebra. It comprises five treatises on arithmetic of integers, arithmetic of fractions, arithmetic of sexagesimal numbers, geometry and measurement, and algebra. Al-Kāshı̄ dedicated the Miftāḥ to Ulugh Beg who was the ruler of Samarkand at the time and was a prominent scientist himself. In Berggren’s assessment Miftāḥ was “the crowning achievement of Islamic arithmetic, and truly a gift fit for a king” [12, p. 22]. Saidan agrees by stating “Miftāḥ represents the peak of Islamic arithmetic” [31, p. 29].


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nuh Aydin
    • 1
  • Lakhdar Hammoudi
    • 2
  1. 1.Department of MathematicsKenyon CollegeGambierUSA
  2. 2.Department of MathematicsOhio University – ChillicotheChillicotheUSA

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