Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was an Arab (or Persian) geographer, astronomer, and mathematician who lived from about 160-230 AH1, at the height of Abbasid power in Baghdad.

He is well known because his works, translated into Latin in the 12th century (primarily by Leonardo of Pisa, better known as Fibonacci), became the principal conduit of mathematical knowledge to the West.

Of principal note is al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala2, a collection of techniques of symbol manipulation.  It is unclear how many of these techniques he invented himself, and how many he adopted from earlier (including Indian and Ancient Greek) mathematicians.

From his works arose Western use of

  • algebra  (a corruption of Al-jabr),
  • Indian numbers (called "arabic numbers" in the West) including a zero, from a work (Algoritmi de numero Indorum3) whose Arabic text is now lost.
  • Decimal positional notation (known then as algorism or augrim)
  • As al-jabr was a really about strategies for solving mathematical problems, his name, or rather a corruption of it, "algorithm", became associated with such strategies.
  • John Napier may have invented the word logarithm to be parallel with "algorithm".  He never explained where he got the word from; another mathematician, Henry Briggs, ascribes a Greek origin to the word.
He also published Kitab surat al-ard4, a gazetteer improving on Claudius Ptolemy's Geographia.

1about 780-850 AD
2The Compendious Book on Calculation by Completion and Balancing”
3"Al-Khwarizmi Concerning the Hindu Art of Reckoning”.
4"The Image of the Earth", or more simply, "Geography"