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In this publication, the author proposes to find an elementary proof of Fermat's Last Theorem from the point of view of an engineering approach. As a model, a construction of three concentrically nested n-cubes or spheres with a common centre and integer edges or radii, a, b, c, is studied, provided that each point/unit cube of a small sphere corresponds to another point/unit cube of this subset of layers between the middle and the large sphere enclosed spheres. An insoluble conflict between the symmetric form and the content of the construction is studied for the case when n is greater than two. The proposed proof forces us to make broader generalisations concerning the necessity of the asymmetry of the universe as a condition for the emergence of matter and the origin of life. The proof of Fermat's Last Theorem, known as the "mathematical pearl", has an important symbolic, historical and educational significance.