Al-Samawal was born to a Jewish family living in Baghdad, Iraq. His main occupation was practising medicine and like so many he travelled the region trying to gain rich clients. He seems to have been successful and wrote a book about medicine.
He was also notable for taking an interest in psychology writing, for instance about depression, and arguing against the prevailing wisdom of the time which believed in the validity of astrology.
Mathematically he is remembered for a book he wrote aged just nineteen called The Brilliant in Algebra. During his medical studies he had looked at Hindu methods of calculation and learnt as much on the subject as he could. The work is important as it introduces us to some of the writings of al-karaji which would otherwise have been lost.
He was also the first to give the new subject of algebra a precise description and to develop it using polynomials with negative powers and zero. The book is also interesting in being one of the first to apply a form of induction to mathematics.