Leyton's books in MIT Press, Springer and Birkhauser have developed New Foundations to Geometry which are opposed to the Standard Foundations to Geometry. In the Standard Foundations, a geometric object is defined as an invariant, which, Leyton argues, destroys memory storage. In contrast, in Leyton's New Foundations, a geometric object is defined as a memory store, and he has created the corresponding mathematics, which has fundamental differences from standard mathematics. Leyton's mathematics has been applied by scientists in over 40 disciplines, which shows their interoperability. Furthermore, because, he argues that this mathematics gives the structure of memory stores, it is appropriate for the history-based parametrics program of ISO. Since, in the New Foundations, the geometry is generative, it is also called Generative Geometry. Two basic principles of this geometry are maximisation of transfer and maximisation of recoverability of the generative operations. Leyton's geometry invents the mathematics of transfer and recoverability.
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