The creation of the Gömböc provided a constructive proof of Vladimir Igorevich Arnold’s 1995 conjecture that there exists a convex homogeneous object with fewer than four equilibrium points. This property is also known as mono-monostatic. Many mathematicians believed that such an object could not be created, and in fact, they had proved it for two-dimensional polygons. Arnold, however, believed that the problem could be solved in three dimensions, as suggested by Gabor Domokos.
Domokos and Várkonyi realized that these hypothetical objects could not have certain properties: they could not be too thin or too flat, as these properties would inherently lead to two or more stable equilibrium points. Therefore, the Gömböc had to have spherical properties: its thickness and narrowness had to be minimal. If the shape of the Gömböc were even slightly altered, it would cease to be a Gömböc. Therefore, it was unlikely that a Gömböc-shaped stone would be found.
Defining the properties of the Gömböc simplified the search, and researchers were able to describe an object that satisfied the required conditions and had only two equilibrium points. However, this form was indistinguishable from a sphere to the naked eye, with a difference of only 0.01 mm in the case of a 1 m diameter Gömböc. It was also impossible to produce industrially. The researchers continued their search, abandoning some of their other restrictions (previously, they had wanted to find a Gömböc without sharp corners). Once again, their efforts were successful, and the second Gömböc was found to be feasible, now available under the name “Gömböc.”