15th century

• 1400 - 1500 - [related] Third wave of devastation of Muslim resources, lives, properties, institutions, and infrastructure. End of Muslim rule in Spain after the completion of the Reconquista in 1492. More than one million volumes of Muslim works on science, arts, philosophy and culture were burnt in the public square of Vivarrambla in Granada. Colonization began in Africa, Asia, and the Americas.

• 1400s [mathematics] Ibn al-Banna and al-Qalasadi used symbols for mathematics in the 15th century "and, although we do not know exactly when their use began, we know that symbols were used at least a century before this."

• 1400 - 1406 [astronomy, mathematics, physics] Jamshīd al-Kāshī is invited to the Samarqand observatory by Ulugh Beg to pursue his study of mathematics, astronomy and physics.

• 1400 - 1429 [astronomy, mathematics] Jamshīd al-Kāshī is the first to use the decimal point notation in arithmetic and Arabic numerals. His works include The Key of arithmetics, Discoveries in mathematics, The Decimal point, and The benefits of the zero. The contents of the Benefits of the Zero are an introduction followed by five essays: "On whole number arithmetic", "On fractional arithmetic", "On astrology", "On areas", and "On finding the unknowns [unknown variables]". He also wrote the Thesis on the sine and the chord; The garden of gardens or Promenade of the gardens describing an instrument he devised and used at the Samarqand observatory to compile an ephemeris and for computing solar and lunar eclipses; the ephemeresis Zayj Al-Khaqani which also includes mathematical tables and corrections of the ephemeresis by al-Tusi; Thesis on finding the first degree sine; and more.

• 1400 - 1429 [astronomical instruments] Al-Kashi invents the Plate of Conjunctions, an analog computer instrument used to determine the time of day at which planetary conjunctions will occur, and for performing linear interpolation. He also invents a mechanical planetary computer which he calls the Plate of Zones, which could graphically solve a number of planetary problems, including the prediction of the true positions in longitude of the Sun and Moon, and the planets in terms of elliptical orbits; the latitudes of the Sun, Moon, and planets; and the ecliptic of the Sun. The instrument also incorporated an alhidade and ruler.

• 1400 - 1474 [astronomy, astrophysics, mathematics, physics] Ali al-Qushji (d. 1474) rejected Aristotelian physics and completely separated natural philosophy from Islamic astronomy, allowing astronomy to become a purely empirical and mathematical science. This allowed him to explore alternatives to the Aristotelian notion of a stationery Earth, as he explored the idea of a moving Earth instead. He found empirical evidence for the Earth's rotation through his observation on comets and concluded, on the basis of empiricism rather than speculative philosophy, that the moving Earth theory is just as likely to be true as the stationary Earth theory. Ali al-Qushji also improved on Nasir al-Din al-Tusi's planetary model and presented an alternative planetary model for Mercury.

• 1403 - 1433 [navigation] The Chinese Muslim general Zheng He travels across the Indian Ocean in newly-constructed troopships and treasure ships.

• 1406 - 1409 [astronomy] Jamshīd al-Kāshī computed and observed the solar eclipses of 809 AH, 810 AH and 811 AH.

• 1411 [mathematics] Al-Kashi writes Compendium of the Science of Astronomy.

• 1424 [mathematics] Al-Kashi writes Treatise on the Circumference giving a remarkably accurate approximation to pi in both sexagesimal and decimal forms, computing pi to 8 sexagesimal places and 16 decimal places.

• 1427 [mathematics] Al-Kashi completes The Key to Arithmetic containing work of great depth on decimal fractions. It applies arithmetical and algebraic methods to the solution of various problems, including several geometric ones and is one of the best textbooks in the whole of medieval literature.

• 1437 [mathematics] Ulugh Beg publishes his star catalogue, the Zij-i-Sultani. It contains trigonometric tables correct to eight decimal places based on Ulugh Beg's calculation of the sine of one degree which he calculated correctly to 16 decimal places.

• 1453 [military technology] The first supergun was the Great Turkish Bombard, used by the troops of Mehmed II to capture Constantinople. It had a 762 mm bore, and fired 680 kg (1500 lb) stones.

• 1470 - 1550 - [ceramics, pottery] Tabriz becomes a center for innovative Islamic pottery and ceramics.