B.Tech Thesis

David Hilbert(1862-1943) was one of the most outstanding mathematicians of his generation. His twenty-three problems (and the recently discovered twenty-fourth problem reported in American Mathematical Monthly) have perplexed even the greatest geniuses and a solution to even one of them has given the concerned much deserving publicity. Amongst the numerous mathematical creations of David Hilbert is the idea of Hilbert Space. Hilbert’s work in integral equations in about 1909 led directly to 20th-century research in functional analysis (the branch of mathematics in which functions are studied collectively). This work also established the basis for his work on infinite-dimensional space, later called Hilbert space, a concept that is useful in mathematical analysis and quantum mechanics. Hilbert’s was motivated by the analogy of n-dimensional Euclidean Spaces, which he extended to be infinite dimensional spaces. Hilbert and Schmidt together gave the foundation of complex L2 spaces and the notion of inner product and norm, orthogonality, closed sets, and linear subspaces. It was von Neumann who later developed the theory of linear operators in Hilbert Spaces. This work is dedicated to all such mathematicians behind the development of Hilbert spaces.

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