# Person: Al-Baghdadi, Abu Mansur ibn Tahir

Al-Baghdadi was an Islamic mathematician who wrote about different systems of arithmetic in a work of great importance in the history of mathematics.

### Mathematical Profile (Excerpt):

• His full name is Abu Mansur Abr al-Qahir ibn Tahir ibn Muhammad ibn Abdallah al-Tamini al-Shaffi al-Baghdadi.
• We can deduce from al-Baghdadi's last two names that he was descended from the Bani Tamim tribe, one of the Sharif tribes of ancient Arabia, and that he belonged to the Madhhab Shafi'i school of religious law.
• We have a few details of al-Baghdadi's life.
• When riots broke out in Nishapur, al-Baghdadi decided that he required a more peaceful place to continue his life as an academic so he moved to Asfirayin.
• This town was quieter and al-Baghdadi was able to teach and study in more peaceful surroundings.
• In Asfirayin, al-Baghdadi taught for many years in the mosque.
• This treatise, al-Takmila fi'l-Hisab, is a work in which al-Baghdadi considers different systems of arithmetic.
• In this work al-Baghdadi stresses the benefits of each of the systems but seems to favour the Indian numerals.
• This becomes clear from the references to the lost work by al-Baghdadi.
• Al-Baghdadi gives an interesting discussion of abundant numbers, deficient numbers, perfect numbers and equivalent numbers.
• Al-Baghdadi gives some elementary results and then states that 945 is the smallest odd abundant number, a result usually attributed to Bachet in the early 17th century.
• However, al-Baghdadi knew that certain claims made by Nicomachus were false.
• Next al-Baghdadi goes on to define equivalent numbers, and appears to be the first to study them.
• The results that al-Baghdadi gives on amicable numbers are only a slight variations on results given earlier by Thabit ibn Qurra.

View full biography at MacTutor

Ancient Arab, Origin Iraq, Special Numbers And Numerals

Thank you to the contributors under CC BY-SA 4.0!

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### References

#### Adapted from other CC BY-SA 4.0 Sources:

1. Oâ€™Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive