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The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers not because it is abstract, but because it is a representation of actual things.
In N. Rose, Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Italian armillary sphere
An armillary sphere is a mechanical model of the universe. The metal bands within the spheres represented the circular orbits of the planets revolving around a central Earth or the sun, depending on the particular scientific theory depicted; pre or post Copernican. When devised, they were among the most complex mechanical devices of their time. Renaissance personages frequently had themselves portrayed in paintings standing next to an armillary sphere indicating their association with wisdom and knowledge. The sphere shown is dated 1550 and is probably of Italian origin. The wide, foremost, band contains the divisions of the zodiac. Its wooden stand was constructed at a later date. This sphere was probably ornamental, decorating the house of a rich merchant or aristocrat, attesting to the fact that he was aware of the importance of science.