Yang Hui

Yang Hui triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD.

Yang Hui (; ca. 1238–1298), courtesy name Qianguang , was a Chinese mathematician and writer of the Southern Song and Yuan dynasties. Originally, from Qiantang (modern-day Hangzhou, Zhejiang), Yang worked on magic squares, magic circles and the binomial theorem, and is best known for his contribution of presenting Yang Hui's triangle. This triangle was the same as Pascal's triangle, discovered by Yang's predecessor Jia Xian. Yang was also a contemporary of Qin Jiushao, another well-known Chinese mathematician.

Written work The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiángjiě Jiǔzhāng Suànfǎ of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's triangle" was invented by mathematician Jia Xian who expounded it around 1100 AD, about 500 years before Pascal. His book (now lost), known as Rújī Shìsuǒ or Piling-up Powers and Unlocking Coefficients, was known through his contemporary mathematician Liu Ruxie . Jia described the method used as 'li cheng shi suo' (the tabulation system for unlocking binomial coefficients).

Around 1275 AD, Yang finally had two published mathematical books, which were known as the Xùgǔ Zhāijī Suànfǎ and the Suànfǎ Tōngbiàn Běnmò (, summarily called Yáng Huī Suànfǎ ). In the former book, Yang wrote of arrangement of natural numbers around concentric and non-concentric circles, known as magic circles and vertical-horizontal diagrams of complex combinatorial arrangements known as magic squares, providing rules for their construction. In his writing, he harshly criticized the earlier works of Li Chunfeng and Liu Yi , the latter of whom were both content with using methods without working out their theoretical origins or principle. However, the first books of Euclid to be translated into Chinese was by the cooperative effort of the Italian Jesuit Matteo Ricci and the Ming official Xu Guangqi in the early 17th century.

Yang's writing represents the first in which quadratic equations with negative coefficients of 'x' appear, although he attributes this to the earlier Liu Yi. Yang was also well known for his ability to manipulate decimal fractions. When he wished to multiply the figures in a rectangular field with a breadth of 24 paces 3 4⁄10 ft. and length of 36 paces 2 8⁄10, Yang expressed them in decimal parts of the pace, as 24.68 X 36.56 = 902.3008.

The Yang-Hui Award The Yang-Hui Award is presented to mathematicians or scientists who have gained international recognition for their exceptional contributions throughout their careers. It was awarded to Salvatore Capozziello for his work with Noether symmetries; Mahouton Norbert Hounkonnou for his work in deformed quantum algebras; and to Delfim F. M. Torres for his mathematical modelling of COVID-19 in 2023 at the International Conference on Mathematical Analysis, Applications and Computational Simulation (ICMAACS 2023), Shanghai, China, November 22–26, 2023.