page_title: Number theory
section_title: Arithmetic in the Islamic golden age
hierarchical_section_title: Number theory / History / Origins / Arithmetic in the Islamic golden age
caption_attribution_description: English: Frontispiece of Johannes Hevelius, Selenographia (Gdansk, 1647). Depictions of Alhasen [sic], Ibn al-Haytham, on the left, holding a geometrical diagram and symbolizing knowledge through reason and Galileo Galilei on the right, holding a telescope and symbolizing knowledge through the senses.
context_page_description: Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of objects made out of integers or defined as generalizations of the integers.
  Integers can be considered either in themselves or as solutions to equations. Questions in number theory are often best understood through the study of analytical objects that encode properties of the integers, primes or other number-theoretic objects in some fashion. One may also study real numbers in relation to rational numbers, for example, as approximated by the latter.
  The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory". The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is preferred as an adjective to number-theoretic.
context_section_description: In the early ninth century, the caliph Al-Ma'mun ordered translations of many Greek mathematical works and at least one Sanskrit work (the Sindhind,
  which may  or may not be Brahmagupta's Brāhmasphuṭasiddhānta).
  Diophantus's main work, the Arithmetica, was translated into Arabic by Qusta ibn Luqa (820–912).
  Part of the treatise al-Fakhri (by al-Karajī, 953 – ca. 1029) builds on it to some extent. According to Rashed Roshdi, Al-Karajī's contemporary Ibn al-Haytham knew what would later be called Wilson's theorem.
caption: Al-Haytham seen by the West: frontispice of Selenographia, showing Alhasen  [sic] representing knowledge through reason, and Galileo representing knowledge through the senses.
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