Person: Al-Mahani, Abu Abd Allah Muhammad ibn Isa

Al-Mahani was an Islamic mathematician who tried to solve some of Archimedes' problems on cutting up spheres.

We do know a little about al-Mahani's work in astronomy from Ibn Yunus's astronomical handbook al-Zij al-Hakimi al-kabir.
In this work Ibn Yunus quotes from writings by al-Mahani, which have since been lost, which describe observations which al-Mahani made between the years 853 and 866.
At least we have accurate dating of al-Mahani's life from this source.
It gives a full account of the Arabic literature which was available in the 10th century and in particular mentions al-Mahani, not for his work in astronomy, but rather for his work in geometry and arithmetic.
However the work which al-Mahani did in mathematics may well have been motivated by various problems of an astronomical nature.
We know that some of al-Mahani's work in algebra was motivated by trying to solve problems due to Archimedes.
It was Omar Khayyam, giving an important historical description of algebra, who puts al-Mahani's work into context.
It would be too easy to say that since al-Mahani has proposed a method of solution which he could not carry through then his work was of little value.
However, this, as Omar Khayyam is well aware, is not so at all and the fact that al-Mahani conceived the idea of reducing problems such as duplicating the cube to problems in algebra was an important step forward.
A number of works by al-Mahani have survived, in particular commentaries which he wrote on parts of Euclid's Elements.

Born about 820, Mahan, Kerman, Persia (now Iran). Died 880, Baghdad, Iraq.

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Ancient Arab, Astronomy, Origin Iran

Epochs: 1

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O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive