BY EVERETT PITCHER

THE SINGLE MOST SIGNIFICANT contribution of Marston Morse to mathematics and his undoubted claim to enduring fame lie in the area of critical point theory, also known because of the force and scope of his contribution as Morse theory. His work in this field was initiated in the paper (1925) and was expanded and elaborated in several subsequent papers, particularly (1928). He further developed and organized the material in his Colloquium Lectures, presented before the American Mathematical Society in 1931 and published by the society in 1934 as vol. 18 in its series Colloquium Publications (1934,3). It was paper (1928) that was specifically cited when he was awarded the Bôcher Prize of the American Mathematical Society in 1933. He returned to aspects and developments of the theory in papers and books throughout his life.

Morse theory is concerned with a real valued function on a topological space and relates two apparently quite different kinds of quantities. One is the algebraic topology of the underlying space. This is exhibited in its homology groups, or in its most elementary form by its Betti numbers. The other is the set of critical points of the function, separated into connected sets that are classified analytically and algebraically or by local homological properties. In the most