Ilia Vekua (Georgian: ილია ვეკუა, Russian: Илья́ Не́сторович Ве́куа; 23 April 1907 in the village of Sheshelety, Kutaisi Governorate, Russian Empire (modern day Ochamchira District, Abkhazia, Republic of Georgia – 2 December 1977 in Tbilisi, USSR) was a distinguished Georgian mathematician, specializing in partial differential equations, singular integral equations, generalized analytic functions and the mathematical theory of elastic shells.
Ilia Vekua was born in 1907 in the Georgian village Sheshelety. After finishing school in Zugdidi, he entered Physics and Mathematics Department at Tbilisi State University. Vekua graduated in 1930  and was made a professor there in 1940. He was also deputy-director of the Steklov Institute of Mathematics (1954–1959), the first rector of Novosibirsk State University (1959–1964), and vice-president (1964–1965) and president (1972–1977) of the Georgian Academy of Sciences. In 1969 he became the Hero of Socialist Labour. Vekua was awarded the Stalin Prize (1950), Lenin Prize (1963), USSR State Prize (1984), three Orders of Lenin and the Order of the Badge of Honor. The Sukhumi Institute of Physics and Technology, formerly near Sukhumi (Abkhazia), now in Tbilisi/Georgia, which was involved in the nuclear weapons program of the Soviet Union, is also named after him.