August 26 – Battle of Manzikert: The Byzantine army (35,000 man) under Emperor Romanos IV meets the Seljuk Turk forces of Sultan Alp Arslan near the town of Manzikert. Although the armies are initially evenly matched, as the Byzantines advance the Seljuk Turks withdraw before them, launching hit-and-run attacks on the Byzantine flanks. While attempt to withdraw the Byzantine army falls apart, either through treachery or confusion - the battle ends in a decisive defeat for the Byzantine Empire. Romanos is captured (later released by Alp Arslan within a week) and much of the elite Varangian Guard is destroyed.
October 7 – Alfonso VI becomes king of León and Castile, following the assassination of Sancho II. He is bestowed with the title of "Emperor of Spain", and is forced by Rodrigo Diaz de Vivar (El Cid), the standard-bearer of Sancho, to take an oath denying any involvement in his brother's death.
Shen Kuo, Chinese polymathic scientist and statesman, is appointed as the head official for the Bureau of Astronomy - where he begins his work with the colleague Wei Pu on accurately plotting the orbital paths of the stars, planets, and moon three times a night, for a continuum of five years.
Fall – Shen Kuo is sent to supervise Wang Anshi's program of surveying the building of silt deposits in the Bian Canal, outside the capital city of Kaifeng. Using an original technique, Shen successfully dredges the canal and demonstrates the formidable value of the silt gathered as a fertilizer.
Wang Anshi, Chinese chief chancellor of the Song Dynasty, creates a new bureau of the central government (called the Directorate of Weapons), which supervises the manufacture of military armaments and ensures quality control.
Summer – Shen Kuo, Chinese polymath scientist and statesman, solves a border dispute with the Liao Dynasty by dredging up old diplomatic records. He refutes Emperor Dao Zong's bluffs point for point during a meeting at Mt. Yongan (near modern-day Pingquan), reestablishing the rightful borders of the Song Dynasty.
Omar Khayyam, Persian mathematician and astronomer, computes the length of the year to be exactly 365 days and 8 leap years that includes 366 days. The most accurate calculation of his time. Khayyam, in his Treatise on Demonstrations of Problems in Algebra, produces a complete classification of cubic equations and their geometric solutions (approximate date).
^Minguez Fernández, José María (2009). Alfonso VI/Gregorio VII. Soberanía imperial frente a soberanía papal, pp. 30-33. ISSN 1575-801X.
^ "Fires, Great", in The Insurance Cyclopeadia: Being an Historical Treasury of Events and Circumstances Connected with the Origin and Progress of Insurance, p. 25. Cornelius Walford, ed. (C. and E. Layton, 1876).
^Claude Cahen (1968). Pre-Ottoman Turkey: a general survey of the material and spiritual culture and history c. 1070-1330. Trans. J. Jones-Williams, pp. 73-74 (New York: Taplinger).