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[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics". [8] However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results. [8] [9]
v. t. e. Ilm al-kalam [a] or ilm al-lahut, [b] often shortened to kalam, is the scholastic, speculative, or rational study of Islamic theology (aqida). [2] It can also be defined as the science that studies the fundamental doctrines of Islamic faith (usul al-din), proving their validity, or refuting doubts regarding them. [3] Kalām was born ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
The word mathematics comes from Ancient Greek máthēma (μάθημα), meaning "that which is learnt", [7] "what one gets to know", hence also "study" and "science". The word came to have the narrower and more technical meaning of "mathematical study" even in Classical times.
Muhammad ibn Musa al-Khwarizmi [note 1] (Persian: محمد بن موسى خوارزمی; c. 780 – c. 850), or simply al-Khwarizmi, was a Khwarazm-born polymath who produced vastly influential Arabic-language works in mathematics, astronomy, and geography.
t. e. Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
—Omar Khayyam In effect, Khayyam's work is an effort to unify algebra and geometry. : 241 This particular geometric solution of cubic equations was further investigated by M. Hachtroudi and extended to solving fourth-degree equations. Although similar methods had appeared sporadically since Menaechmus, and further developed by the 10th-century mathematician Abu al-Jud, : 29 : 110 Khayyam's ...
The Tusi couple, a mathematical device invented by the Persian polymath Nasir al-Din Tusi to model the not perfectly circular motions of the planets. Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Abbasid Caliphate of Baghdad, the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids and the Buyids in ...