Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all … - David Hilbert

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Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

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About David Hilbert

David Hilbert (January 23, 1862 – February 14, 1943) was a German logician, mathematician, and mathematical physicist. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry, as well as the theory of Hilbert spaces, one of the foundations of functional analysis. Hilbert and his students also supplied much of the mathematics needed for quantum mechanics and general relativity.

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Alternative Names: Hilbert
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Additional quotes by David Hilbert

[O]ur purpose is to give a presentation of geometry... in its visual, intuitive aspects. With the aid of visual imagination we can illuminate the manifold facts and problems... beyond this, it is possible... to depict the geometric outline of the methods of investigation and proof, without... entering into the details... In this manner, geometry being as many-faceted as it is and being related to the most diverse branches of mathematics, we may even obtain a summarizing survey of mathematics as a whole, and a valid idea of the variety of problems and the wealth of ideas it contains. Thus a presentation of geometry in large brushstrokes... and based on the approach through visual intuition, should contribute to a more just appreciation of mathematics by a wider range of people than just the specialists.

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