In the early s, he developed continuous fractal space-filling curves in multiple dimensions, building on earlier work by Guiseppe Peano.
Prof. David Hilbert, townwonnopinats.tkR.S. | Nature
As early as , he proposed a whole new formal set of geometrical axioms, known as Hilbert's axioms, to substitute the traditional axioms of Euclid. But perhaps his greatest legacy is his work on equations, often referred to as his finiteness theorem. He showed that although there were an infinite number of possible equations, it was nevertheless possible to split them up into a finite number of types of equations which could then be used, almost like a set of building blocks, to produce all the other equations. Interestingly, though, Hilbert could not actually construct this finite set of equations, just prove that it must exist sometimes referred to as an existence proof, rather than constructive proof.
At the time, some critics passed this off as mere theology or smoke-and-mirrors, but it effectively marked the beginnings of a whole new style of abstract mathematics.
This use of an existence proof rather than constructive proof was also implicit in his development, during the first decade of the 20th Century, of the mathematical concept of what came to be known as Hilbert space. Around , Hilbert dedicated himself to the study of differential and integral equations. His work had direct consequences for important parts of modern functional analysis. In order to carry out these studies, Hilbert introduced the concept of an infinite dimensional Euclidean space, later called Hilbert space.
His work in this part of analysis provided the basis for important contributions to the mathematics of physics in the next two decades, though from an unanticipated direction.
Later on, Stefan Banach amplified the concept, defining Banach spaces. Hilbert spaces are an important class of objects in the area of functional analysis, particularly of the spectral theory of self-adjoint linear operators, that grew up around it during the 20th century. At yovisto academic search engine you can listen to Prof. References and further Reading:.
David Hilbert’s 23 Fundamental Problems
Your email address will not be published. David Hilbert 23 January — 14 February Related Posts. Leave a Reply Cancel reply Your email address will not be published. A Nature Research Journal. David Hilbert, of Gottingen, died recently. He was born on January 23, , and was a mathematician of tremendous power who ranged over a wide field and had an unusual influence on present-day mathematics.
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An indication of the breadth of Hilbert's influence is the number of mathematical topics which are associated with his name. For example, we have Hilbert space, Hilbert inequality, Hilbert transform, Hilbert invariant integral, Hilbert irreducibility theorem, Hilbert base theorem, Hilbert axiom, Hilbert sub-groups, Hilbert class field.
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