The Expressionist utopia of an Architect imitating the rigorous and -at the same time- extremely bizarre formative principles of Nature, linked with the engineering "must" of a coherent and correct structure are apparent antithesis if only played as the manifestation of an irrational and uncontrolled freedom. We explore the ancient idea of Harmony and Beauty and the historical confidence in the logarithmic spiral as the symbol of perfection in an unbuilt project for a 565 m (1,854 ft) high skyscraper that was supposed to be built on the tip of Manhattan, NYC. The role of geometry is no more exploited as an instrument for controlling architectural form, but for its liberation: the project for a helicoidal skyscraper consisted of a succession of warped wings developed on the layout of the logarithmic spiral. The helicoidal shape, works better than the others in splitting up the force of the wind in resistance, has a positive influence on the stability of the building and is the result of a strong design theory wondering about the power of invention, the power of geometry, the power of relationships among numbers, and finally the beauty of (deriving from) mathematics (in Architecture).