English mathematician whose contributions to analysis placed him at the forefront of his profession.

Titchmarsh graduated from the University of Oxford (Oxford, University of) in 1922 and undertook research under the supervision of Godfrey Hardy (Hardy, Godfrey Harold), who became the main influence on his mathematical career. In 1923 Titchmarsh was appointed lecturer at university college, London, and in 1929 he was elected professor of pure mathematics at the University of Liverpool. Two years later he returned to Oxford as the Savilian Professor of Geometry. He devoted his early research to the theory of Fourier integrals and series (analysis) and added new findings to the study of Fourier transforms and the theory of conjugate functions, all of which formed a major part of his Introduction to the Theory of Fourier Integrals (1937). He next turned his attention to the theory of integral functions (integral equation), especially the Riemann zeta function; he published his results in The Zeta-Function of Riemann (1930) and more fully elaborated this work in The Theory of the Riemann Zeta-Function (1951). From his studies of complex variable theory, he wrote The Theory of Functions (1932), which became a leading textbook on real and complex function theory and was translated into numerous languages.

After 1939 Titchmarsh concentrated his research on the theory of function expansion in eigenfunctions (see eigenvalue) of differential equations (differential equation), an area of vital importance to quantum field theory, and published many of his results in Eigenfunction Expansions Associated with Second-Order Differential Equations (Part 1, 1946; Part 2, 1958). His contributions helped resolve the differences between the general theory of quantum mechanics and the methods used to solve particular problems in quantum theory. He also wrote a popular Mathematics for the General Reader (1948).

Titchmarsh was elected a fellow of the Royal Society (1931) and was president of the London Mathematical Society (1945–47).