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Our study [7] of the genesis and evolution of geometric ideas and techniques related to movable singularities of ordinary differential equations (ODEs) has led us to the work of Mihailo Petrović on algebraic differential equations and his geometric ideas captured in his polygonal method from the last years of the nineteenth century. These ideas and results of Petrović have been left completely unnoticed by experts. It appeared that a similar concept was also developed independently by Henry Fine in a somewhat different direction. These results generalize the famous Newton–Puiseux polygonal method and apply to algebraic ODEs rather than algebraic equations. Mihailo Petrović (1868–1943) was an extraordinary person and the leading Serbian mathematician of his time. His results are, despite their significance, practically unknown to mathematicians working in the field, in the past and nowadays. The situation is less severe with Fine’s results. Thus, we emphasized in [7] the development of the ideas of Petrović and Fine from the point of view of contemporary mathematics. In its essence, this is a story about two outstanding individuals, Henry Fine and Mihailo Petrović (see Figure 1). Along with doing science, both made transformational efforts in elevating of the mathematical research in their native countries to a remarkable new level. At the same time both left the deepest traces in the development of their own academic institutions at the moments of their transformation from being local colleges to renowned universities: Fine to American mathematics and Princeton University and Petrović to Serbian mathematics and the University of Belgrade. The list of striking similarities between the two scientists is not even

About the cover: The Fine–Petrović Polygons and the Newton–Puiseux Method for Algebraic Ordinary Differential Equations